Sample records for cell-centered finite difference

  1. High-order conservative finite difference GLM-MHD schemes for cell-centered MHD (United States)

    Mignone, Andrea; Tzeferacos, Petros; Bodo, Gianluigi


    We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different reconstruction techniques based on recently improved versions of the weighted essentially non-oscillatory (WENO) schemes, monotonicity preserving (MP) schemes as well as slope-limited polynomial reconstruction. The proposed numerical methods are highly accurate in smooth regions of the flow, avoid loss of accuracy in proximity of smooth extrema and provide sharp non-oscillatory transitions at discontinuities. We suggest a numerical formulation based on a cell-centered approach where all of the primary flow variables are discretized at the zone center. The divergence-free condition is enforced by augmenting the MHD equations with a generalized Lagrange multiplier yielding a mixed hyperbolic/parabolic correction, as in Dedner et al. [J. Comput. Phys. 175 (2002) 645-673]. The resulting family of schemes is robust, cost-effective and straightforward to implement. Compared to previous existing approaches, it completely avoids the CPU intensive workload associated with an elliptic divergence cleaning step and the additional complexities required by staggered mesh algorithms. Extensive numerical testing demonstrate the robustness and reliability of the proposed framework for computations involving both smooth and discontinuous features.

  2. Implementations of the optimal multigrid algorithm for the cell-centered finite difference on equilateral triangular grids

    Energy Technology Data Exchange (ETDEWEB)

    Ewing, R.E.; Saevareid, O.; Shen, J. [Texas A& M Univ., College Station, TX (United States)


    A multigrid algorithm for the cell-centered finite difference on equilateral triangular grids for solving second-order elliptic problems is proposed. This finite difference is a four-point star stencil in a two-dimensional domain and a five-point star stencil in a three dimensional domain. According to the authors analysis, the advantages of this finite difference are that it is an O(h{sup 2})-order accurate numerical scheme for both the solution and derivatives on equilateral triangular grids, the structure of the scheme is perhaps the simplest, and its corresponding multigrid algorithm is easily constructed with an optimal convergence rate. They are interested in relaxation of the equilateral triangular grid condition to certain general triangular grids and the application of this multigrid algorithm as a numerically reasonable preconditioner for the lowest-order Raviart-Thomas mixed triangular finite element method. Numerical test results are presented to demonstrate their analytical results and to investigate the applications of this multigrid algorithm on general triangular grids.

  3. A mass-conservative adaptive FAS multigrid solver for cell-centered finite difference methods on block-structured, locally-cartesian grids (United States)

    Feng, Wenqiang; Guo, Zhenlin; Lowengrub, John S.; Wise, Steven M.


    We present a mass-conservative full approximation storage (FAS) multigrid solver for cell-centered finite difference methods on block-structured, locally cartesian grids. The algorithm is essentially a standard adaptive FAS (AFAS) scheme, but with a simple modification that comes in the form of a mass-conservative correction to the coarse-level force. This correction is facilitated by the creation of a zombie variable, analogous to a ghost variable, but defined on the coarse grid and lying under the fine grid refinement patch. We show that a number of different types of fine-level ghost cell interpolation strategies could be used in our framework, including low-order linear interpolation. In our approach, the smoother, prolongation, and restriction operations need never be aware of the mass conservation conditions at the coarse-fine interface. To maintain global mass conservation, we need only modify the usual FAS algorithm by correcting the coarse-level force function at points adjacent to the coarse-fine interface. We demonstrate through simulations that the solver converges geometrically, at a rate that is h-independent, and we show the generality of the solver, applying it to several nonlinear, time-dependent, and multi-dimensional problems. In several tests, we show that second-order asymptotic (h → 0) convergence is observed for the discretizations, provided that (1) at least linear interpolation of the ghost variables is employed, and (2) the mass conservation corrections are applied to the coarse-level force term.

  4. Mimetic Theory for Cell-Centered Lagrangian Finite Volume Formulation on General Unstructured Grids

    Energy Technology Data Exchange (ETDEWEB)

    Sambasivan, Shiv Kumar [Los Alamos National Laboratory; Shashkov, Mikhail J. [Los Alamos National Laboratory; Burton, Donald E. [Los Alamos National Laboratory; Christon, Mark A. [Los Alamos National Laboratory


    A finite volume cell-centered Lagrangian scheme for solving large deformation problems is constructed based on the hypo-elastic model and using the mimetic theory. Rigorous analysis in the context of gas and solid dynamics, and arbitrary polygonal meshes, is presented to demonstrate the ability of cell-centered schemes in mimicking the continuum properties and principles at the discrete level. A new mimetic formulation based gradient evaluation technique and physics-based, frame independent and symmetry preserving slope limiters are proposed. Furthermore, a physically consistent dissipation model is employed which is both robust and inexpensive to implement. The cell-centered scheme along with these additional new features are applied to solve solids undergoing elasto-plastic deformation.

  5. Cell-centered high-order hyperbolic finite volume method for diffusion equation on unstructured grids (United States)

    Lee, Euntaek; Ahn, Hyung Taek; Luo, Hong


    We apply a hyperbolic cell-centered finite volume method to solve a steady diffusion equation on unstructured meshes. This method, originally proposed by Nishikawa using a node-centered finite volume method, reformulates the elliptic nature of viscous fluxes into a set of augmented equations that makes the entire system hyperbolic. We introduce an efficient and accurate solution strategy for the cell-centered finite volume method. To obtain high-order accuracy for both solution and gradient variables, we use a successive order solution reconstruction: constant, linear, and quadratic (k-exact) reconstruction with an efficient reconstruction stencil, a so-called wrapping stencil. By the virtue of the cell-centered scheme, the source term evaluation was greatly simplified regardless of the solution order. For uniform schemes, we obtain the same order of accuracy, i.e., first, second, and third orders, for both the solution and its gradient variables. For hybrid schemes, recycling the gradient variable information for solution variable reconstruction makes one order of additional accuracy, i.e., second, third, and fourth orders, possible for the solution variable with less computational work than needed for uniform schemes. In general, the hyperbolic method can be an effective solution technique for diffusion problems, but instability is also observed for the discontinuous diffusion coefficient cases, which brings necessity for further investigation about the monotonicity preserving hyperbolic diffusion method.

  6. A multi-dimensional finite volume cell-centered direct ALE solver for hydrodynamics (United States)

    Clair, G.; Ghidaglia, J.-M.; Perlat, J.-P.


    In this paper we describe a second order multi-dimensional scheme, belonging to the class of direct Arbitrary Lagrangian-Eulerian (ALE) methods, for the solution of non-linear hyperbolic systems of conservation law. The scheme is constructed upon a cell-centered explicit Lagrangian solver completed with an edge-based upwinded formulation of the numerical fluxes, computed from the MUSCL-Hancock method, to obtain a full ALE formulation. Numerical fluxes depend on nodal grid velocities which are either set or computed to avoid most of the mesh problems typically encountered in purely Lagrangian simulations. In order to assess the robustness of the scheme, most results proposed in this paper have been obtained by computing the grid velocities as a fraction of the Lagrangian nodal velocities, the ratio being set before running the test case. The last part of the paper describes preliminary results about the triple point test case run in the ALE framework by computing the grid velocities with the fully adaptive Large Eddy Limitation (L.E.L.) method proposed in [1]. Such a method automatically computes the grid velocities at each node defining the mesh from the local characteristics of the flow. We eventually discuss the advantages and the drawback of the coupling.

  7. Finite element and finite difference methods in electromagnetic scattering

    CERN Document Server

    Morgan, MA


    This second volume in the Progress in Electromagnetic Research series examines recent advances in computational electromagnetics, with emphasis on scattering, as brought about by new formulations and algorithms which use finite element or finite difference techniques. Containing contributions by some of the world's leading experts, the papers thoroughly review and analyze this rapidly evolving area of computational electromagnetics. Covering topics ranging from the new finite-element based formulation for representing time-harmonic vector fields in 3-D inhomogeneous media using two coupled sca

  8. A finite difference, multipoint flux numerical approach to flow in porous media: Numerical examples

    KAUST Repository

    Osman, Hossam Omar


    It is clear that none of the current available numerical schemes which may be adopted to solve transport phenomena in porous media fulfill all the required robustness conditions. That is while the finite difference methods are the simplest of all, they face several difficulties in complex geometries and anisotropic media. On the other hand, while finite element methods are well suited to complex geometries and can deal with anisotropic media, they are more involved in coding and usually require more execution time. Therefore, in this work we try to combine some features of the finite element technique, namely its ability to work with anisotropic media with the finite difference approach. We reduce the multipoint flux, mixed finite element technique through some quadrature rules to an equivalent cell-centered finite difference approximation. We show examples on using this technique to single-phase flow in anisotropic porous media.

  9. A parallel adaptive finite difference algorithm for petroleum reservoir simulation

    Energy Technology Data Exchange (ETDEWEB)

    Hoang, Hai Minh


    Adaptive finite differential for problems arising in simulation of flow in porous medium applications are considered. Such methods have been proven useful for overcoming limitations of computational resources and improving the resolution of the numerical solutions to a wide range of problems. By local refinement of the computational mesh where it is needed to improve the accuracy of solutions, yields better solution resolution representing more efficient use of computational resources than is possible with traditional fixed-grid approaches. In this thesis, we propose a parallel adaptive cell-centered finite difference (PAFD) method for black-oil reservoir simulation models. This is an extension of the adaptive mesh refinement (AMR) methodology first developed by Berger and Oliger (1984) for the hyperbolic problem. Our algorithm is fully adaptive in time and space through the use of subcycling, in which finer grids are advanced at smaller time steps than the coarser ones. When coarse and fine grids reach the same advanced time level, they are synchronized to ensure that the global solution is conservative and satisfy the divergence constraint across all levels of refinement. The material in this thesis is subdivided in to three overall parts. First we explain the methodology and intricacies of AFD scheme. Then we extend a finite differential cell-centered approximation discretization to a multilevel hierarchy of refined grids, and finally we are employing the algorithm on parallel computer. The results in this work show that the approach presented is robust, and stable, thus demonstrating the increased solution accuracy due to local refinement and reduced computing resource consumption. (Author)

  10. Electron-phonon coupling from finite differences. (United States)

    Monserrat, Bartomeu


    The interaction between electrons and phonons underlies multiple phenomena in physics, chemistry, and materials science. Examples include superconductivity, electronic transport, and the temperature dependence of optical spectra. A first-principles description of electron-phonon coupling enables the study of the above phenomena with accuracy and material specificity, which can be used to understand experiments and to predict novel effects and functionality. In this topical review, we describe the first-principles calculation of electron-phonon coupling from finite differences. The finite differences approach provides several advantages compared to alternative methods, in particular (i) any underlying electronic structure method can be used, and (ii) terms beyond the lowest order in the electron-phonon interaction can be readily incorporated. But these advantages are associated with a large computational cost that has until recently prevented the widespread adoption of this method. We describe some recent advances, including nondiagonal supercells and thermal lines, that resolve these difficulties, and make the calculation of electron-phonon coupling from finite differences a powerful tool. We review multiple applications of the calculation of electron-phonon coupling from finite differences, including the temperature dependence of optical spectra, superconductivity, charge transport, and the role of defects in semiconductors. These examples illustrate the advantages of finite differences, with cases where semilocal density functional theory is not appropriate for the calculation of electron-phonon coupling and many-body methods such as the $GW$ approximation are required, as well as examples in which higher-order terms in the electron-phonon interaction are essential for an accurate description of the relevant phenomena. We expect that the finite difference approach will play a central role in future studies of the electron-phonon interaction. . © 2018 IOP

  11. Electron–phonon coupling from finite differences (United States)

    Monserrat, Bartomeu


    The interaction between electrons and phonons underlies multiple phenomena in physics, chemistry, and materials science. Examples include superconductivity, electronic transport, and the temperature dependence of optical spectra. A first-principles description of electron–phonon coupling enables the study of the above phenomena with accuracy and material specificity, which can be used to understand experiments and to predict novel effects and functionality. In this topical review, we describe the first-principles calculation of electron–phonon coupling from finite differences. The finite differences approach provides several advantages compared to alternative methods, in particular (i) any underlying electronic structure method can be used, and (ii) terms beyond the lowest order in the electron–phonon interaction can be readily incorporated. But these advantages are associated with a large computational cost that has until recently prevented the widespread adoption of this method. We describe some recent advances, including nondiagonal supercells and thermal lines, that resolve these difficulties, and make the calculation of electron–phonon coupling from finite differences a powerful tool. We review multiple applications of the calculation of electron–phonon coupling from finite differences, including the temperature dependence of optical spectra, superconductivity, charge transport, and the role of defects in semiconductors. These examples illustrate the advantages of finite differences, with cases where semilocal density functional theory is not appropriate for the calculation of electron–phonon coupling and many-body methods such as the GW approximation are required, as well as examples in which higher-order terms in the electron–phonon interaction are essential for an accurate description of the relevant phenomena. We expect that the finite difference approach will play a central role in future studies of the electron–phonon interaction.

  12. Hybrid finite difference/finite element immersed boundary method. (United States)

    E Griffith, Boyce; Luo, Xiaoyu


    The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach. © 2017 The Authors International  Journal  for  Numerical  Methods  in  Biomedical  Engineering Published by John Wiley & Sons Ltd.

  13. Nonstandard finite difference schemes for differential equations

    Directory of Open Access Journals (Sweden)

    Mohammad Mehdizadeh Khalsaraei


    Full Text Available In this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (NSFDs. Numerical examples confirming then efficiency of schemes, for some differential equations are provided. In order to illustrate the accuracy of the new NSFDs, the numerical results are compared with standard methods.

  14. Finite difference order doubling in two dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Killingbeck, John P [Mathematics Centre, University of Hull, Hull HU6 7RX (United Kingdom); Jolicard, Georges [Universite de Franche-Comte, Institut Utinam (UMR CNRS 6213), Observatoire de Besancon, 41 bis Avenue de l' Observatoire, BP1615, 25010 Besancon cedex (France)


    An order doubling process previously used to obtain eighth-order eigenvalues from the fourth-order Numerov method is applied to the perturbed oscillator in two dimensions. A simple method of obtaining high order finite difference operators is reported and an odd parity boundary condition is found to be effective in facilitating the smooth operation of the order doubling process.

  15. Integral and finite difference inequalities and applications

    CERN Document Server

    Pachpatte, B G


    The monograph is written with a view to provide basic tools for researchers working in Mathematical Analysis and Applications, concentrating on differential, integral and finite difference equations. It contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools and will be a valuable source for a long time to come. It is self-contained and thus should be useful for those who are interested in learning or applying the inequalities with explicit estimates in their studies.- Contains a variety of inequalities discovered which find numero

  16. Abstract Level Parallelization of Finite Difference Methods

    Directory of Open Access Journals (Sweden)

    Edwin Vollebregt


    Full Text Available A formalism is proposed for describing finite difference calculations in an abstract way. The formalism consists of index sets and stencils, for characterizing the structure of sets of data items and interactions between data items (“neighbouring relations”. The formalism provides a means for lifting programming to a more abstract level. This simplifies the tasks of performance analysis and verification of correctness, and opens the way for automaticcode generation. The notation is particularly useful in parallelization, for the systematic construction of parallel programs in a process/channel programming paradigm (e.g., message passing. This is important because message passing, unfortunately, still is the only approach that leads to acceptable performance for many more unstructured or irregular problems on parallel computers that have non-uniform memory access times. It will be shown that the use of index sets and stencils greatly simplifies the determination of which data must be exchanged between different computing processes.

  17. Determination of finite-difference weights using scaled binomial windows

    KAUST Repository

    Chu, Chunlei


    The finite-difference method evaluates a derivative through a weighted summation of function values from neighboring grid nodes. Conventional finite-difference weights can be calculated either from Taylor series expansions or by Lagrange interpolation polynomials. The finite-difference method can be interpreted as a truncated convolutional counterpart of the pseudospectral method in the space domain. For this reason, we also can derive finite-difference operators by truncating the convolution series of the pseudospectral method. Various truncation windows can be employed for this purpose and they result in finite-difference operators with different dispersion properties. We found that there exists two families of scaled binomial windows that can be used to derive conventional finite-difference operators analytically. With a minor change, these scaled binomial windows can also be used to derive optimized finite-difference operators with enhanced dispersion properties. © 2012 Society of Exploration Geophysicists.

  18. High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains (United States)

    Fisher, Travis C.; Carpenter, Mark H.


    Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.

  19. Finite Mathematics and Discrete Mathematics: Is There a Difference? (United States)

    Johnson, Marvin L.

    Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…

  20. RSW Cell Centered Grids (United States)

    National Aeronautics and Space Administration — New cell centered grids are generated to complement the node-centered ones uploaded. Six tarballs containing the coarse, medium, and fine mixed-element and pure tet....

  1. A Comparison of Continuous Mass-lumped Finite Elements and Finite Differences for 3D

    NARCIS (Netherlands)

    Zhebel, E.; Minisini, S.; Kononov, A.; Mulder, W.A.


    The finite-difference method is widely used for time-domain modelling of the wave equation because of its ease of implementation of high-order spatial discretization schemes, parallelization and computational efficiency. However, finite elements on tetrahedral meshes are more accurate in complex

  2. Fourth order compact finite difference method for solving singularly ...

    African Journals Online (AJOL)

    A numerical method based on finite difference scheme with uniform mesh is presented for solving singularly perturbed two-point boundary value problems of 1D reaction-diffusion equations. First, the derivatives of the given differential equation is replaced by the finite difference approximations and then, solved by using ...

  3. Fourth Order Compact Finite Difference Method for Solving ...

    African Journals Online (AJOL)


    A numerical method based on finite difference scheme with uniform mesh is presented for solving singularly perturbed two-point boundary value problems of 1D reaction-diffusion equations. First, the derivatives of the given differential equation is replaced by the finite difference approximations and then, solved by using ...

  4. Comparison of different precondtioners for nonsymmtric finite volume element methods

    Energy Technology Data Exchange (ETDEWEB)

    Mishev, I.D.


    We consider a few different preconditioners for the linear systems arising from the discretization of 3-D convection-diffusion problems with the finite volume element method. Their theoretical and computational convergence rates are compared and discussed.

  5. Implicit finite-difference simulations of seismic wave propagation

    KAUST Repository

    Chu, Chunlei


    We propose a new finite-difference modeling method, implicit both in space and in time, for the scalar wave equation. We use a three-level implicit splitting time integration method for the temporal derivative and implicit finite-difference operators of arbitrary order for the spatial derivatives. Both the implicit splitting time integration method and the implicit spatial finite-difference operators require solving systems of linear equations. We show that it is possible to merge these two sets of linear systems, one from implicit temporal discretizations and the other from implicit spatial discretizations, to reduce the amount of computations to develop a highly efficient and accurate seismic modeling algorithm. We give the complete derivations of the implicit splitting time integration method and the implicit spatial finite-difference operators, and present the resulting discretized formulas for the scalar wave equation. We conduct a thorough numerical analysis on grid dispersions of this new implicit modeling method. We show that implicit spatial finite-difference operators greatly improve the accuracy of the implicit splitting time integration simulation results with only a slight increase in computational time, compared with explicit spatial finite-difference operators. We further verify this conclusion by both 2D and 3D numerical examples. © 2012 Society of Exploration Geophysicists.

  6. Practical aspects of prestack depth migration with finite differences

    Energy Technology Data Exchange (ETDEWEB)

    Ober, C.C.; Oldfield, R.A.; Womble, D.E.; Romero, L.A. [Sandia National Labs., Albuquerque, NM (United States); Burch, C.C. [Conoco Inc. (United States)


    Finite-difference, prestack, depth migrations offers significant improvements over Kirchhoff methods in imaging near or under salt structures. The authors have implemented a finite-difference prestack depth migration algorithm for use on massively parallel computers which is discussed. The image quality of the finite-difference scheme has been investigated and suggested improvements are discussed. In this presentation, the authors discuss an implicit finite difference migration code, called Salvo, that has been developed through an ACTI (Advanced Computational Technology Initiative) joint project. This code is designed to be efficient on a variety of massively parallel computers. It takes advantage of both frequency and spatial parallelism as well as the use of nodes dedicated to data input/output (I/O). Besides giving an overview of the finite-difference algorithm and some of the parallelism techniques used, migration results using both Kirchhoff and finite-difference migration will be presented and compared. The authors start out with a very simple Cartoon model where one can intuitively see the multiple travel paths and some of the potential problems that will be encountered with Kirchhoff migration. More complex synthetic models as well as results from actual seismic data from the Gulf of Mexico will be shown.

  7. Solving difference equations in finite terms

    NARCIS (Netherlands)

    Hendriks, Peter; Singer, MF

    We define the notion of a Liouvillian sequence and show that the solution space of a difference equation with rational function coefficients has a basis of Liouvillian sequences iff the Galois group of the equation is solvable. Using this we give a procedure to determine the Liouvillian solutions of

  8. An implicit finite-difference operator for the Helmholtz equation

    KAUST Repository

    Chu, Chunlei


    We have developed an implicit finite-difference operator for the Laplacian and applied it to solving the Helmholtz equation for computing the seismic responses in the frequency domain. This implicit operator can greatly improve the accuracy of the simulation results without adding significant extra computational cost, compared with the corresponding conventional explicit finite-difference scheme. We achieved this by taking advantage of the inherently implicit nature of the Helmholtz equation and merging together the two linear systems: one from the implicit finite-difference discretization of the Laplacian and the other from the discretization of the Helmholtz equation itself. The end result of this simple yet important merging manipulation is a single linear system, similar to the one resulting from the conventional explicit finite-difference discretizations, without involving any differentiation matrix inversions. We analyzed grid dispersions of the discrete Helmholtz equation to show the accuracy of this implicit finite-difference operator and used two numerical examples to demonstrate its efficiency. Our method can be extended to solve other frequency domain wave simulation problems straightforwardly. © 2012 Society of Exploration Geophysicists.

  9. A finite difference Taylor series method applied to thermal problems (United States)

    Collins, R. L.


    A new technique has been developed for solving finite difference equations that approximate parabolic (transient) and elliptic (steady) partial differential equations for heat transfer problems. The approach utilizes a Taylor series method and a variable-weighted implicit finite difference approximation. The weighting function for each difference equation is determined from the power-law suggested by S. Patankar and B. Baliga. An automatic-time-step selection process has been incorporated to enhance the transient solution scheme. Both the transient and steady-state equation sets are solved iteratively. The Aitken extrapolation process is used to accelerate convergence to steady state. Although this solution process was developed for the SINDA thermal analyzer, application to other finite difference thermal analysis codes should be fairly straightforward. The potential of this new scheme is demonstrated by solving three transient and two steady-state heat transfer problems that involve conduction and radiation.

  10. Finite-difference schemes for anisotropic diffusion

    Energy Technology Data Exchange (ETDEWEB)

    Es, Bram van, E-mail: [Centrum Wiskunde and Informatica, P.O. Box 94079, 1090GB Amsterdam (Netherlands); FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, Association EURATOM-FOM (Netherlands); Koren, Barry [Eindhoven University of Technology (Netherlands); Blank, Hugo J. de [FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, Association EURATOM-FOM (Netherlands)


    In fusion plasmas diffusion tensors are extremely anisotropic due to the high temperature and large magnetic field strength. This causes diffusion, heat conduction, and viscous momentum loss, to effectively be aligned with the magnetic field lines. This alignment leads to different values for the respective diffusive coefficients in the magnetic field direction and in the perpendicular direction, to the extent that heat diffusion coefficients can be up to 10{sup 12} times larger in the parallel direction than in the perpendicular direction. This anisotropy puts stringent requirements on the numerical methods used to approximate the MHD-equations since any misalignment of the grid may cause the perpendicular diffusion to be polluted by the numerical error in approximating the parallel diffusion. Currently the common approach is to apply magnetic field-aligned coordinates, an approach that automatically takes care of the directionality of the diffusive coefficients. This approach runs into problems at x-points and at points where there is magnetic re-connection, since this causes local non-alignment. It is therefore useful to consider numerical schemes that are tolerant to the misalignment of the grid with the magnetic field lines, both to improve existing methods and to help open the possibility of applying regular non-aligned grids. To investigate this, in this paper several discretization schemes are developed and applied to the anisotropic heat diffusion equation on a non-aligned grid.

  11. Nonstandard Finite Difference Method Applied to a Linear Pharmacokinetics Model

    Directory of Open Access Journals (Sweden)

    Oluwaseun Egbelowo


    Full Text Available We extend the nonstandard finite difference method of solution to the study of pharmacokinetic–pharmacodynamic models. Pharmacokinetic (PK models are commonly used to predict drug concentrations that drive controlled intravenous (I.V. transfers (or infusion and oral transfers while pharmacokinetic and pharmacodynamic (PD interaction models are used to provide predictions of drug concentrations affecting the response of these clinical drugs. We structure a nonstandard finite difference (NSFD scheme for the relevant system of equations which models this pharamcokinetic process. We compare the results obtained to standard methods. The scheme is dynamically consistent and reliable in replicating complex dynamic properties of the relevant continuous models for varying step sizes. This study provides assistance in understanding the long-term behavior of the drug in the system, and validation of the efficiency of the nonstandard finite difference scheme as the method of choice.

  12. Nonstandard Finite Difference Method Applied to a Linear Pharmacokinetics Model. (United States)

    Egbelowo, Oluwaseun; Harley, Charis; Jacobs, Byron


    We extend the nonstandard finite difference method of solution to the study of pharmacokinetic-pharmacodynamic models. Pharmacokinetic (PK) models are commonly used to predict drug concentrations that drive controlled intravenous (I.V.) transfers (or infusion and oral transfers) while pharmacokinetic and pharmacodynamic (PD) interaction models are used to provide predictions of drug concentrations affecting the response of these clinical drugs. We structure a nonstandard finite difference (NSFD) scheme for the relevant system of equations which models this pharamcokinetic process. We compare the results obtained to standard methods. The scheme is dynamically consistent and reliable in replicating complex dynamic properties of the relevant continuous models for varying step sizes. This study provides assistance in understanding the long-term behavior of the drug in the system, and validation of the efficiency of the nonstandard finite difference scheme as the method of choice.

  13. Finite difference computing with PDEs a modern software approach

    CERN Document Server

    Langtangen, Hans Petter


    This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.

  14. Finite-Difference Algorithms For Computing Sound Waves (United States)

    Davis, Sanford


    Governing equations considered as matrix system. Method variant of method described in "Scheme for Finite-Difference Computations of Waves" (ARC-12970). Present method begins with matrix-vector formulation of fundamental equations, involving first-order partial derivatives of primitive variables with respect to space and time. Particular matrix formulation places time and spatial coordinates on equal footing, so governing equations considered as matrix system and treated as unit. Spatial and temporal discretizations not treated separately as in other finite-difference methods, instead treated together by linking spatial-grid interval and time step via common scale factor related to speed of sound.

  15. Least squares principle unifying finite element, finite difference and nodal methods for diffusion theory

    Energy Technology Data Exchange (ETDEWEB)

    Ackroyd, R.T.


    A least squares principle is described which uses a penalty function treatment of boundary and interface conditions. Appropriate choices of the trial functions and vectors employed in a dual representation of an approximate solution established complementary principles for the diffusion equation. A geometrical interpretation of the principles provides weighted residual methods for diffusion theory, thus establishing a unification of least squares, variational and weighted residual methods. The complementary principles are used with either a trial function for the flux or a trial vector for the current to establish for regular meshes a connection between finite element, finite difference and nodal methods, which can be exact if the mesh pitches are chosen appropriately. Whereas the coefficients in the usual nodal equations have to be determined iteratively, those derived via the complementary principles are given explicitly in terms of the data. For the further development of the connection between finite element, finite difference and nodal methods, some hybrid variational methods are described which employ both a trial function and a trial vector.

  16. Comparing finite elements and finite differences for developing diffusive models of glioma growth. (United States)

    Roniotis, Alexandros; Marias, Kostas; Sakkalis, Vangelis; Stamatakos, Georgios; Zervakis, Michalis


    Glioma is the most aggressive type of brain tumor. Several mathematical models have been developed during the last two decades, towards simulating the mechanisms that govern the development of glioma. The most common models use the diffusion-reaction equation (DRE) for simulating the spatiotemporal variation of tumor cell concentration. The proposed diffusive models have mainly used finite differences (FDs) or finite elements (FEs) for the approximation of the solution of the partial differential DRE. This paper presents experimental results on the comparison of the FEs and FDs, especially focused on the glioma model case. It is studied how the different meshes of brain can affect computational consistency, simulation time and efficiency of the model. The experiments have been studied on a test case, for which there is a known algebraic expression of the solution. Thus, it is possible to calculate the error that the different models yield.

  17. Some quantitative evaluations on finite difference local and global results

    Directory of Open Access Journals (Sweden)

    Costamagna Eugenio


    Full Text Available Refined Schwarz-Christoffel (SC conformal transformations allow us to perform reliable quantitative evaluation of the accuracy of local computation of electric and magnetic fields with limited effort, which can be useful to complement well known comparisons of global results. In this paper some examples are presented for mesh point potentials obtained by means of finite difference (FD methods, but it is possible that similar considerations will be useful in the case of finite element methods (FEM or meshless computations too.

  18. Finite element analysis of thermal stress distribution in different ...

    African Journals Online (AJOL)

    Purpose: Cervical lesions are restored with class V preparation. The aim of this study was to use a three-dimensional finite element method to carry out a thermal analysis of the temperature and stress distributions of three different restorative materials used for class V cavities of maxillary molar teeth. Materials and Methods: ...

  19. Chebyshev Finite Difference Method for Fractional Boundary Value Problems

    Directory of Open Access Journals (Sweden)



    Full Text Available This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivatives are described in the Caputo sense. Numerical results show that this method is of high accuracy and is more convenient and efficient for solving boundary value problems involving fractional ordinary differential equations. AMS Subject Classification: 34A08 Keywords and Phrases: Chebyshev polynomials, Gauss-Lobatto points, fractional differential equation, finite difference 1. Introduction The idea of a derivative which interpolates between the familiar integer order derivatives was introduced many years ago and has gained increasing importance only in recent years due to the development of mathematical models of a certain situations in engineering, materials science, control theory, polymer modelling etc. For example see [20, 22, 25, 26]. Most fractional order differential equations describing real life situations, in general do not have exact analytical solutions. Several numerical and approximate analytical methods for ordinary differential equation Received: December 2014; Accepted: March 2015 57 Journal of Mathematical Extension Vol. 9, No. 3, (2015, 57-71 ISSN: 1735-8299 URL: Chebyshev Finite Difference Method for Fractional Boundary Value Problems H. Azizi Taft Branch, Islamic Azad University Abstract. This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivative

  20. Alternating Direction Implicit Finite Difference Time Domain Acoustic ...

    African Journals Online (AJOL)

    A time domain numerical technique is presented for the modelling of acoustic wave phenomena. The technique is an adaptation of the alternating direction implicit finite difference time domain method. The stability condition for the algorithm is given. Simple illustrations of propagation in an infinite homogeneous medium are ...

  1. Optimisation of Plate Thickness Using Finite Difference Method ...

    African Journals Online (AJOL)

    A finite difference numerical method of solving biharmonic equation is presented. The biharmonic equation and plate theory are used to solve a classical engineering problem involving the optimisation of plate thickness to minimise deformations and stresses in the plate. Matlab routines were developed to solve the ...

  2. Finite difference simulation of biological chromium (VI) reduction in ...

    African Journals Online (AJOL)


    May 8, 2013 ... test columns. For the first time, the performance of a simulated barrier was evaluated internally in porous media using a finite difference approach. Parameters in the model were optimised at .... sis, only a black-box approach may be employed allowing pre- diction only in a narrow range of operating ...

  3. Time-dependent optimal heater control using finite difference method

    Energy Technology Data Exchange (ETDEWEB)

    Li, Zhen Zhe; Heo, Kwang Su; Choi, Jun Hoo; Seol, Seoung Yun [Chonnam National Univ., Gwangju (Korea, Republic of)


    Thermoforming is one of the most versatile and economical process to produce polymer products. The drawback of thermoforming is difficult to control thickness of final products. Temperature distribution affects the thickness distribution of final products, but temperature difference between surface and center of sheet is difficult to decrease because of low thermal conductivity of ABS material. In order to decrease temperature difference between surface and center, heating profile must be expressed as exponential function form. In this study, Finite Difference Method was used to find out the coefficients of optimal heating profiles. Through investigation, the optimal results using Finite Difference Method show that temperature difference between surface and center of sheet can be remarkably minimized with satisfying temperature of forming window.

  4. Time dependent wave envelope finite difference analysis of sound propagation (United States)

    Baumeister, K. J.


    A transient finite difference wave envelope formulation is presented for sound propagation, without steady flow. Before the finite difference equations are formulated, the governing wave equation is first transformed to a form whose solution tends not to oscillate along the propagation direction. This transformation reduces the required number of grid points by an order of magnitude. Physically, the transformed pressure represents the amplitude of the conventional sound wave. The derivation for the wave envelope transient wave equation and appropriate boundary conditions are presented as well as the difference equations and stability requirements. To illustrate the method, example solutions are presented for sound propagation in a straight hard wall duct and in a two dimensional straight soft wall duct. The numerical results are in good agreement with exact analytical results.

  5. The Laguerre finite difference one-way equation solver (United States)

    Terekhov, Andrew V.


    This paper presents a new finite difference algorithm for solving the 2D one-way wave equation with a preliminary approximation of a pseudo-differential operator by a system of partial differential equations. As opposed to the existing approaches, the integral Laguerre transform instead of Fourier transform is used. After carrying out the approximation of spatial variables it is possible to obtain systems of linear algebraic equations with better computing properties and to reduce computer costs for their solution. High accuracy of calculations is attained at the expense of employing finite difference approximations of higher accuracy order that are based on the dispersion-relationship-preserving method and the Richardson extrapolation in the downward continuation direction. The numerical experiments have verified that as compared to the spectral difference method based on Fourier transform, the new algorithm allows one to calculate wave fields with a higher degree of accuracy and a lower level of numerical noise and artifacts including those for non-smooth velocity models. In the context of solving the geophysical problem the post-stack migration for velocity models of the types Syncline and Sigsbee2A has been carried out. It is shown that the images obtained contain lesser noise and are considerably better focused as compared to those obtained by the known Fourier Finite Difference and Phase-Shift Plus Interpolation methods. There is an opinion that purely finite difference approaches do not allow carrying out the seismic migration procedure with sufficient accuracy, however the results obtained disprove this statement. For the supercomputer implementation it is proposed to use the parallel dichotomy algorithm when solving systems of linear algebraic equations with block-tridiagonal matrices.

  6. Algorithmic vs. finite difference Jacobians for infrared atmospheric radiative transfer (United States)

    Schreier, Franz; Gimeno García, Sebastián; Vasquez, Mayte; Xu, Jian


    Jacobians, i.e. partial derivatives of the radiance and transmission spectrum with respect to the atmospheric state parameters to be retrieved from remote sensing observations, are important for the iterative solution of the nonlinear inverse problem. Finite difference Jacobians are easy to implement, but computationally expensive and possibly of dubious quality; on the other hand, analytical Jacobians are accurate and efficient, but the implementation can be quite demanding. GARLIC, our "Generic Atmospheric Radiation Line-by-line Infrared Code", utilizes algorithmic differentiation (AD) techniques to implement derivatives w.r.t. atmospheric temperature and molecular concentrations. In this paper, we describe our approach for differentiation of the high resolution infrared and microwave spectra and provide an in-depth assessment of finite difference approximations using "exact" AD Jacobians as a reference. The results indicate that the "standard" two-point finite differences with 1 K and 1% perturbation for temperature and volume mixing ratio, respectively, can exhibit substantial errors, and central differences are significantly better. However, these deviations do not transfer into the truncated singular value decomposition solution of a least squares problem. Nevertheless, AD Jacobians are clearly recommended because of the superior speed and accuracy.

  7. The mimetic finite difference method for elliptic problems

    CERN Document Server

    Veiga, Lourenço Beirão; Manzini, Gianmarco


    This book describes the theoretical and computational aspects of the mimetic finite difference method for a wide class of multidimensional elliptic problems, which includes diffusion, advection-diffusion, Stokes, elasticity, magnetostatics and plate bending problems. The modern mimetic discretization technology developed in part by the Authors allows one to solve these equations on unstructured polygonal, polyhedral and generalized polyhedral meshes. The book provides a practical guide for those scientists and engineers that are interested in the computational properties of the mimetic finite difference method such as the accuracy, stability, robustness, and efficiency. Many examples are provided to help the reader to understand and implement this method. This monograph also provides the essential background material and describes basic mathematical tools required to develop further the mimetic discretization technology and to extend it to various applications.

  8. Integral equations with difference kernels on finite intervals

    CERN Document Server

    Sakhnovich, Lev A


    This book focuses on solving integral equations with difference kernels on finite intervals. The corresponding problem on the semiaxis was previously solved by N. Wiener–E. Hopf and by M.G. Krein. The problem on finite intervals, though significantly more difficult, may be solved using our method of operator identities. This method is also actively employed in inverse spectral problems, operator factorization and nonlinear integral equations. Applications of the obtained results to optimal synthesis, light scattering, diffraction, and hydrodynamics problems are discussed in this book, which also describes how the theory of operators with difference kernels is applied to stable processes and used to solve the famous M. Kac problems on stable processes. In this second edition these results are extensively generalized and include the case of all Levy processes. We present the convolution expression for the well-known Ito formula of the generator operator, a convolution expression that has proven to be fruitful...

  9. Optimized Finite-Difference Coefficients for Hydroacoustic Modeling (United States)

    Preston, L. A.


    Responsible utilization of marine renewable energy sources through the use of current energy converter (CEC) and wave energy converter (WEC) devices requires an understanding of the noise generation and propagation from these systems in the marine environment. Acoustic noise produced by rotating turbines, for example, could adversely affect marine animals and human-related marine activities if not properly understood and mitigated. We are utilizing a 3-D finite-difference acoustic simulation code developed at Sandia that can accurately propagate noise in the complex bathymetry in the near-shore to open ocean environment. As part of our efforts to improve computation efficiency in the large, high-resolution domains required in this project, we investigate the effects of using optimized finite-difference coefficients on the accuracy of the simulations. We compare accuracy and runtime of various finite-difference coefficients optimized via criteria such as maximum numerical phase speed error, maximum numerical group speed error, and L-1 and L-2 norms of weighted numerical group and phase speed errors over a given spectral bandwidth. We find that those coefficients optimized for L-1 and L-2 norms are superior in accuracy to those based on maximal error and can produce runtimes of 10% of the baseline case, which uses Taylor Series finite-difference coefficients at the Courant time step limit. We will present comparisons of the results for the various cases evaluated as well as recommendations for utilization of the cases studied. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

  10. A finite difference method for free boundary problems

    KAUST Repository

    Fornberg, Bengt


    Fornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax-based optimization procedure to rapidly solve a wide range of elliptic-type free boundary value problems. © 2009 Elsevier B.V. All rights reserved.

  11. Finite

    National Research Council Canada - National Science Library

    W.R. Azzam


    .... This technique is investigated numerically using finite element analysis. A four story reinforced concrete building that rests on a raft foundation is idealized as a two-dimensional model with and without skirts...

  12. Comparison of finite difference and finite element methods for simulating two-dimensional scattering of elastic waves

    NARCIS (Netherlands)

    Frehner, Marcel; Schmalholz, Stefan M.; Saenger, Erik H.; Steeb, Holger Karl


    Two-dimensional scattering of elastic waves in a medium containing a circular heterogeneity is investigated with an analytical solution and numerical wave propagation simulations. Different combinations of finite difference methods (FDM) and finite element methods (FEM) are used to numerically solve

  13. Thermal buckling comparative analysis using Different FE (Finite Element) tools

    Energy Technology Data Exchange (ETDEWEB)

    Banasiak, Waldemar; Labouriau, Pedro [INTECSEA do Brasil, Rio de Janeiro, RJ (Brazil); Burnett, Christopher [INTECSEA UK, Surrey (United Kingdom); Falepin, Hendrik [Fugro Engineers SA/NV, Brussels (Belgium)


    High operational temperature and pressure in offshore pipelines may lead to unexpected lateral movements, sometimes call lateral buckling, which can have serious consequences for the integrity of the pipeline. The phenomenon of lateral buckling in offshore pipelines needs to be analysed in the design phase using FEM. The analysis should take into account many parameters, including operational temperature and pressure, fluid characteristic, seabed profile, soil parameters, coatings of the pipe, free spans etc. The buckling initiation force is sensitive to small changes of any initial geometric out-of-straightness, thus the modeling of the as-laid state of the pipeline is an important part of the design process. Recently some dedicated finite elements programs have been created making modeling of the offshore environment more convenient that has been the case with the use of general purpose finite element software. The present paper aims to compare thermal buckling analysis of sub sea pipeline performed using different finite elements tools, i.e. general purpose programs (ANSYS, ABAQUS) and dedicated software (SAGE Profile 3D) for a single pipeline resting on an the seabed. The analyses considered the pipeline resting on a flat seabed with a small levels of out-of straightness initiating the lateral buckling. The results show the quite good agreement of results of buckling in elastic range and in the conclusions next comparative analyses with sensitivity cases are recommended. (author)

  14. Performance and scalability of finite-difference and finite-element wave-propagation modeling on Intel's Xeon Phi

    NARCIS (Netherlands)

    Zhebel, E.; Minisini, S.; Kononov, A.; Mulder, W.A.


    With the rapid developments in parallel compute architectures, algorithms for seismic modeling and imaging need to be reconsidered in terms of parallelization. The aim of this paper is to compare scalability of seismic modeling algorithms: finite differences, continuous mass-lumped finite elements

  15. Seismic imaging using finite-differences and parallel computers

    Energy Technology Data Exchange (ETDEWEB)

    Ober, C.C. [Sandia National Labs., Albuquerque, NM (United States)


    A key to reducing the risks and costs of associated with oil and gas exploration is the fast, accurate imaging of complex geologies, such as salt domes in the Gulf of Mexico and overthrust regions in US onshore regions. Prestack depth migration generally yields the most accurate images, and one approach to this is to solve the scalar wave equation using finite differences. As part of an ongoing ACTI project funded by the US Department of Energy, a finite difference, 3-D prestack, depth migration code has been developed. The goal of this work is to demonstrate that massively parallel computers can be used efficiently for seismic imaging, and that sufficient computing power exists (or soon will exist) to make finite difference, prestack, depth migration practical for oil and gas exploration. Several problems had to be addressed to get an efficient code for the Intel Paragon. These include efficient I/O, efficient parallel tridiagonal solves, and high single-node performance. Furthermore, to provide portable code the author has been restricted to the use of high-level programming languages (C and Fortran) and interprocessor communications using MPI. He has been using the SUNMOS operating system, which has affected many of his programming decisions. He will present images created from two verification datasets (the Marmousi Model and the SEG/EAEG 3D Salt Model). Also, he will show recent images from real datasets, and point out locations of improved imaging. Finally, he will discuss areas of current research which will hopefully improve the image quality and reduce computational costs.

  16. Mimetic Finite Differences for Flow in Fractures from Microseismic Data

    KAUST Repository

    Al-Hinai, Omar


    We present a method for porous media flow in the presence of complex fracture networks. The approach uses the Mimetic Finite Difference method (MFD) and takes advantage of MFD\\'s ability to solve over a general set of polyhedral cells. This flexibility is used to mesh fracture intersections in two and three-dimensional settings without creating small cells at the intersection point. We also demonstrate how to use general polyhedra for embedding fracture boundaries in the reservoir domain. The target application is representing fracture networks inferred from microseismic analysis.

  17. A convergent finite difference scheme for the variational heat equation (United States)

    Coclite, Giuseppe Maria; Ridder, Johanna; Risebro, Nils Henrik


    The variational heat equation is a nonlinear, parabolic equation not in divergence form that arises as a model for the dynamics of the director field in a nematic liquid crystal. We present a finite difference scheme for a transformed, possibly degenerate version of this equation and prove that a subsequence of the numerical solutions converges to a weak solution. This result is supplemented by numerical examples that show that weak solutions are not unique and give some intuition about how to obtain a viscosity type solution.

  18. Modeling pulse driven antenna systems with finite differences (United States)

    Barth, Marvin; Pennock, Steve; Ziolkowski, Richard; McLeod, Robert


    The capability was developed of modeling the performance of general, pulse driven, antenna systems. The approach is to use TSAR, a three dimensional finite difference time domain (FDTD) code, to model the antenna structure and the surrounding near field environment. A far field project algorithm was used to obtain its far field response. Specifically, this algorithm utilizes the tangential electric and magnetic fields at a specified surface of the TSAR FDTD computational volume and calculates the resulting fields far from the equivalent magnetic and electric sources. This approach is illustrated by considering the TEB antenna system. The system is modeled with the code and the results are compared with anechoic chamber data.

  19. Finite-Difference Frequency-Domain Method in Nanophotonics

    DEFF Research Database (Denmark)

    Ivinskaya, Aliaksandra

    Optics and photonics are exciting, rapidly developing fields building their success largely on use of more and more elaborate artificially made, nanostructured materials. To further advance our understanding of light-matter interactions in these complicated artificial media, numerical modeling...... is obtained through free space squeezing technique, and nonuniform orthogonal grids are built to greatly improve the accuracy of simulations of highly heterogeneous nanostructures. Examples of the use of the finite-difference frequency-domain method in this thesis range from simulating localized modes...

  20. Viscoelastic Finite Difference Modeling Using Graphics Processing Units (United States)

    Fabien-Ouellet, G.; Gloaguen, E.; Giroux, B.


    Full waveform seismic modeling requires a huge amount of computing power that still challenges today's technology. This limits the applicability of powerful processing approaches in seismic exploration like full-waveform inversion. This paper explores the use of Graphics Processing Units (GPU) to compute a time based finite-difference solution to the viscoelastic wave equation. The aim is to investigate whether the adoption of the GPU technology is susceptible to reduce significantly the computing time of simulations. The code presented herein is based on the freely accessible software of Bohlen (2002) in 2D provided under a General Public License (GNU) licence. This implementation is based on a second order centred differences scheme to approximate time differences and staggered grid schemes with centred difference of order 2, 4, 6, 8, and 12 for spatial derivatives. The code is fully parallel and is written using the Message Passing Interface (MPI), and it thus supports simulations of vast seismic models on a cluster of CPUs. To port the code from Bohlen (2002) on GPUs, the OpenCl framework was chosen for its ability to work on both CPUs and GPUs and its adoption by most of GPU manufacturers. In our implementation, OpenCL works in conjunction with MPI, which allows computations on a cluster of GPU for large-scale model simulations. We tested our code for model sizes between 1002 and 60002 elements. Comparison shows a decrease in computation time of more than two orders of magnitude between the GPU implementation run on a AMD Radeon HD 7950 and the CPU implementation run on a 2.26 GHz Intel Xeon Quad-Core. The speed-up varies depending on the order of the finite difference approximation and generally increases for higher orders. Increasing speed-ups are also obtained for increasing model size, which can be explained by kernel overheads and delays introduced by memory transfers to and from the GPU through the PCI-E bus. Those tests indicate that the GPU memory size

  1. Parallel finite-difference time-domain method

    CERN Document Server

    Yu, Wenhua


    The finite-difference time-domain (FTDT) method has revolutionized antenna design and electromagnetics engineering. This book raises the FDTD method to the next level by empowering it with the vast capabilities of parallel computing. It shows engineers how to exploit the natural parallel properties of FDTD to improve the existing FDTD method and to efficiently solve more complex and large problem sets. Professionals learn how to apply open source software to develop parallel software and hardware to run FDTD in parallel for their projects. The book features hands-on examples that illustrate the power of parallel FDTD and presents practical strategies for carrying out parallel FDTD. This detailed resource provides instructions on downloading, installing, and setting up the required open source software on either Windows or Linux systems, and includes a handy tutorial on parallel programming.

  2. Finite difference methods for coupled flow interaction transport models

    Directory of Open Access Journals (Sweden)

    Shelly McGee


    Full Text Available Understanding chemical transport in blood flow involves coupling the chemical transport process with flow equations describing the blood and plasma in the membrane wall. In this work, we consider a coupled two-dimensional model with transient Navier-Stokes equation to model the blood flow in the vessel and Darcy's flow to model the plasma flow through the vessel wall. The advection-diffusion equation is coupled with the velocities from the flows in the vessel and wall, respectively to model the transport of the chemical. The coupled chemical transport equations are discretized by the finite difference method and the resulting system is solved using the additive Schwarz method. Development of the model and related analytical and numerical results are presented in this work.

  3. Visualization of elastic wavefields computed with a finite difference code

    Energy Technology Data Exchange (ETDEWEB)

    Larsen, S. [Lawrence Livermore National Lab., CA (United States); Harris, D.


    The authors have developed a finite difference elastic propagation model to simulate seismic wave propagation through geophysically complex regions. To facilitate debugging and to assist seismologists in interpreting the seismograms generated by the code, they have developed an X Windows interface that permits viewing of successive temporal snapshots of the (2D) wavefield as they are calculated. The authors present a brief video displaying the generation of seismic waves by an explosive source on a continent, which propagate to the edge of the continent then convert to two types of acoustic waves. This sample calculation was part of an effort to study the potential of offshore hydroacoustic systems to monitor seismic events occurring onshore.

  4. Finite-difference modeling of commercial aircraft using TSAR

    Energy Technology Data Exchange (ETDEWEB)

    Pennock, S.T.; Poggio, A.J.


    Future aircraft may have systems controlled by fiber optic cables, to reduce susceptibility to electromagnetic interference. However, the digital systems associated with the fiber optic network could still experience upset due to powerful radio stations, radars, and other electromagnetic sources, with potentially serious consequences. We are modeling the electromagnetic behavior of commercial transport aircraft in support of the NASA Fly-by-Light/Power-by-Wire program, using the TSAR finite-difference time-domain code initially developed for the military. By comparing results obtained from TSAR with data taken on a Boeing 757 at the Air Force Phillips Lab., we hope to show that FDTD codes can serve as an important tool in the design and certification of U.S. commercial aircraft, helping American companies to produce safe, reliable air transportation.

  5. Flexible Automatic Discretization for Finite Differences: Eliminating the Human Factor (United States)

    Pranger, Casper


    In the geophysical numerical modelling community, finite differences are (in part due to their small footprint) a popular spatial discretization method for PDEs in the regular-shaped continuum that is the earth. However, they rapidly become prone to programming mistakes when physics increase in complexity. To eliminate opportunities for human error, we have designed an automatic discretization algorithm using Wolfram Mathematica, in which the user supplies symbolic PDEs, the number of spatial dimensions, and a choice of symbolic boundary conditions, and the script transforms this information into matrix- and right-hand-side rules ready for use in a C++ code that will accept them. The symbolic PDEs are further used to automatically develop and perform manufactured solution benchmarks, ensuring at all stages physical fidelity while providing pragmatic targets for numerical accuracy. We find that this procedure greatly accelerates code development and provides a great deal of flexibility in ones choice of physics.

  6. Thermo-mechanically coupled deformation with the finite difference method (United States)

    Duretz, Thibault; Raess, Ludovic; Podladchikov, Yury; Schmalholz, Stefan


    Numerous geological observations are the result of thermo-mechanical processes. In particular, tectonic processes such as ductile shear localization can be induced by the intrinsic coupling that exists between deformation, energy and rheology. In order to study these processes, we have designed two-dimensional implicit and explicit finite difference models. These models take into account a temperature-dependent power-law rheology as well as diffusion, advection, and conversion of mechanical work into heat. For implicit models, different non-linear solving strategies were implemented (implicit/explicit thermo-mechanical coupling, Picard/Newton linearisations). We model thermo-mechanically activated shear localization in lower crustal conditions using these different numerical methods. We show that all methods capture the thermo-mechanical instability and exhibit similar temporal evolution. We perform quantitative comparisons with specifically designed tests (conservation of energy, analytical solution, scaling law). For implicit approaches, we discuss the treatment of thermo-mechanical coupling (implicit/explicit) and the impact of the imposed accuracy (tolerance) of the non-linear solvers. We compare the accuracy of the explicit method with the one of the implicit methods. Numerical algorithms based on explicit methods to study thermo-mechanical shear localisation are attractive because they are easy to program and very comprehensible.

  7. The limitations of staggered grid finite differences in plasticity problems (United States)

    Pranger, Casper; Herrendörfer, Robert; Le Pourhiet, Laetitia


    Most crustal-scale applications operate at grid sizes much larger than those at which plasticity occurs in nature. As a consequence, plastic shear bands often localize to the scale of one grid cell, and numerical ploys — like introducing an artificial length scale — are needed to counter this. If for whatever reasons (good or bad) this is not done, we find that problems may arise due to the fact that in the staggered grid finite difference discretization, unknowns like components of the stress tensor and velocity vector are located in physically different positions. This incurs frequent interpolation, reducing the accuracy of the discretization. For purely stress-dependent plasticity problems the adverse effects might be contained because the magnitude of the stress discontinuity across a plastic shear band is limited. However, we find that when rate-dependence of friction is added in the mix, things become ugly really fast and the already hard-to-solve and highly nonlinear problem of plasticity incurs an extra penalty.

  8. Finite difference time domain analysis of chirped dielectric gratings (United States)

    Hochmuth, Diane H.; Johnson, Eric G.


    The finite difference time domain (FDTD) method for solving Maxwell's time-dependent curl equations is accurate, computationally efficient, and straight-forward to implement. Since both time and space derivatives are employed, the propagation of an electromagnetic wave can be treated as an initial-value problem. Second-order central-difference approximations are applied to the space and time derivatives of the electric and magnetic fields providing a discretization of the fields in a volume of space, for a period of time. The solution to this system of equations is stepped through time, thus, simulating the propagation of the incident wave. If the simulation is continued until a steady-state is reached, an appropriate far-field transformation can be applied to the time-domain scattered fields to obtain reflected and transmitted powers. From this information diffraction efficiencies can also be determined. In analyzing the chirped structure, a mesh is applied only to the area immediately around the grating. The size of the mesh is then proportional to the electric size of the grating. Doing this, however, imposes an artificial boundary around the area of interest. An absorbing boundary condition must be applied along the artificial boundary so that the outgoing waves are absorbed as if the boundary were absent. Many such boundary conditions have been developed that give near-perfect absorption. In this analysis, the Mur absorbing boundary conditions are employed. Several grating structures were analyzed using the FDTD method.

  9. A finite difference model for free surface gravity drainage

    Energy Technology Data Exchange (ETDEWEB)

    Couri, F.R.; Ramey, H.J. Jr.


    The unconfined gravity flow of liquid with a free surface into a well is a classical well test problem which has not been well understood by either hydrologists or petroleum engineers. Paradigms have led many authors to treat an incompressible flow as compressible flow to justify the delayed yield behavior of a time-drawdown test. A finite-difference model has been developed to simulate the free surface gravity flow of an unconfined single phase, infinitely large reservoir into a well. The model was verified with experimental results in sandbox models in the literature and with classical methods applied to observation wells in the Groundwater literature. The simulator response was also compared with analytical Theis (1935) and Ramey et al. (1989) approaches for wellbore pressure at late producing times. The seepage face in the sandface and the delayed yield behavior were reproduced by the model considering a small liquid compressibility and incompressible porous medium. The potential buildup (recovery) simulated by the model evidenced a different- phenomenon from the drawdown, contrary to statements found in the Groundwater literature. Graphs of buildup potential vs time, buildup seepage face length vs time, and free surface head and sand bottom head radial profiles evidenced that the liquid refills the desaturating cone as a flat moving surface. The late time pseudo radial behavior was only approached after exaggerated long times.

  10. Finite-difference numerical simulations of underground explosion cavity decoupling (United States)

    Aldridge, D. F.; Preston, L. A.; Jensen, R. P.


    Earth models containing a significant portion of ideal fluid (e.g., air and/or water) are of increasing interest in seismic wave propagation simulations. Examples include a marine model with a thick water layer, and a land model with air overlying a rugged topographic surface. The atmospheric infrasound community is currently interested in coupled seismic-acoustic propagation of low-frequency signals over long ranges (~tens to ~hundreds of kilometers). Also, accurate and efficient numerical treatment of models containing underground air-filled voids (caves, caverns, tunnels, subterranean man-made facilities) is essential. In support of the Source Physics Experiment (SPE) conducted at the Nevada National Security Site (NNSS), we are developing a numerical algorithm for simulating coupled seismic and acoustic wave propagation in mixed solid/fluid media. Solution methodology involves explicit, time-domain, finite-differencing of the elastodynamic velocity-stress partial differential system on a three-dimensional staggered spatial grid. Conditional logic is used to avoid shear stress updating within the fluid zones; this approach leads to computational efficiency gains for models containing a significant proportion of ideal fluid. Numerical stability and accuracy are maintained at air/rock interfaces (where the contrast in mass density is on the order of 1 to 2000) via a finite-difference operator "order switching" formalism. The fourth-order spatial FD operator used throughout the bulk of the earth model is reduced to second-order in the immediate vicinity of a high-contrast interface. Current modeling efforts are oriented toward quantifying the amount of atmospheric infrasound energy generated by various underground seismic sources (explosions and earthquakes). Source depth and orientation, and surface topography play obvious roles. The cavity decoupling problem, where an explosion is detonated within an air-filled void, is of special interest. A point explosion

  11. A hybrid finite-difference and analytic element groundwater model (United States)

    Haitjema, Henk M.; Feinstein, Daniel T.; Hunt, Randall J.; Gusyev, Maksym


    Regional finite-difference models tend to have large cell sizes, often on the order of 1–2 km on a side. Although the regional flow patterns in deeper formations may be adequately represented by such a model, the intricate surface water and groundwater interactions in the shallower layers are not. Several stream reaches and nearby wells may occur in a single cell, precluding any meaningful modeling of the surface water and groundwater interactions between the individual features. We propose to replace the upper MODFLOW layer or layers, in which the surface water and groundwater interactions occur, by an analytic element model (GFLOW) that does not employ a model grid; instead, it represents wells and surface waters directly by the use of point-sinks and line-sinks. For many practical cases it suffices to provide GFLOW with the vertical leakage rates calculated in the original coarse MODFLOW model in order to obtain a good representation of surface water and groundwater interactions. However, when the combined transmissivities in the deeper (MODFLOW) layers dominate, the accuracy of the GFLOW solution diminishes. For those cases, an iterative coupling procedure, whereby the leakages between the GFLOW and MODFLOW model are updated, appreciably improves the overall solution, albeit at considerable computational cost. The coupled GFLOW–MODFLOW model is applicable to relatively large areas, in many cases to the entire model domain, thus forming an attractive alternative to local grid refinement or inset models.

  12. On the difference between permutation poynomials over finite fields

    DEFF Research Database (Denmark)

    Anbar Meidl, Nurdagül; Odzak, Almasa; Patel, Vandita


    ˘glu and Winterhof in terms of the Carlitz rank of f. Cohen, Mullen and Shiue generalized the Chowla-Zassenhaus-Cohen Theorem significantly in 1995, by considering differences of permutation polynomials. More precisely, they showed that if f and f + g are both permutation polynomials of degree d ≥ 2 over Fp, with p......The well-known Chowla and Zassenhaus conjecture, proven by Cohen in 1990, states that if p > (d 2 − 3d + 4)2 , then there is no complete mapping polynomial f in Fp[x] of degree d ≥ 2. For arbitrary finite fields Fq, a similar non-existence result is obtained recently by I¸sık, Topuzo...... > (d 2−3d+4)2 , then the degree k of g satisfies k ≥ 3d/5, unless g is constant. In this article, assuming f and f + g are permutation polynomials in Fq[x], we give lower bounds for k in terms of the Carlitz rank of f and q. Our results generalize the above mentioned result of I¸sık et al. We also show...

  13. Evaluation of finite difference and FFT-based solutions of the transport of intensity equation. (United States)

    Zhang, Hongbo; Zhou, Wen-Jing; Liu, Ying; Leber, Donald; Banerjee, Partha; Basunia, Mahmudunnabi; Poon, Ting-Chung


    A finite difference method is proposed for solving the transport of intensity equation. Simulation results show that although slower than fast Fourier transform (FFT)-based methods, finite difference methods are able to reconstruct the phase with better accuracy due to relaxed assumptions for solving the transport of intensity equation relative to FFT methods. Finite difference methods are also more flexible than FFT methods in dealing with different boundary conditions.

  14. Staggered-Grid Finite Difference Method with Variable-Order Accuracy for Porous Media

    Directory of Open Access Journals (Sweden)

    Jinghuai Gao


    Full Text Available The numerical modeling of wave field in porous media generally requires more computation time than that of acoustic or elastic media. Usually used finite difference methods adopt finite difference operators with fixed-order accuracy to calculate space derivatives for a heterogeneous medium. A finite difference scheme with variable-order accuracy for acoustic wave equation has been proposed to reduce the computation time. In this paper, we develop this scheme for wave equations in porous media based on dispersion relation with high-order staggered-grid finite difference (SFD method. High-order finite difference operators are adopted for low-velocity regions, and low-order finite difference operators are adopted for high-velocity regions. Dispersion analysis and modeling results demonstrate that the proposed SFD method can decrease computational costs without reducing accuracy.

  15. Application of a Strong Tracking Finite-Difference Extended Kalman Filter to Eye Tracking


    Zhang, Zutao; Zhang, Jiashu


    This paper proposes a new eye tracking method using strong finite-difference Kalman filter. Firstly, strong tracking factor is introduced to modify priori covariance matrix to improve the accuracy of the eye tracking algorithm. Secondly, the finite-difference method is proposed to replace partial derivatives of nonlinear functions to eye tracking. From above deduction, the new strong finite-difference Kalman filter becomes very simple because of replacing partial derivatives calculation using...

  16. A total variation diminishing finite difference algorithm for sonic boom propagation models (United States)

    Sparrow, Victor W.


    It is difficult to accurately model the rise phases of sonic boom waveforms with traditional finite difference algorithms because of finite difference phase dispersion. This paper introduces the concept of a total variation diminishing (TVD) finite difference method as a tool for accurately modeling the rise phases of sonic booms. A standard second order finite difference algorithm and its TVD modified counterpart are both applied to the one-way propagation of a square pulse. The TVD method clearly outperforms the non-TVD method, showing great potential as a new computational tool in the analysis of sonic boom propagation.

  17. High order accurate finite difference schemes based on symmetry preservation (United States)

    Ozbenli, Ersin; Vedula, Prakash


    In this paper, we present a mathematical approach that is based on modified equations and the method of equivariant moving frames for construction of high order accurate invariant finite difference schemes that preserve Lie symmetry groups of underlying partial differential equations (PDEs). In the proposed approach, invariant (or symmetry preserving) numerical schemes with a desired (or fixed) order of accuracy are constructed from some non-invariant (base) numerical schemes. Modified forms of PDEs are used to improve the order of accuracy of existing schemes and these modified forms are obtained through addition of defect correction terms to the original forms of PDEs. These defect correction terms of modified PDEs that are noted from truncation error analysis are either completely removed from schemes or their representation is significantly simplified by considering convenient moving frames. This feature of the proposed method can especially be useful to avoid cumbersome numerical representations when high order schemes are developed from low order ones via the method of modified equations. The proposed method is demonstrated via construction of invariant numerical schemes with fixed (and higher) order of accuracy for some common linear and nonlinear problems (including the linear advection-diffusion equation in 1D and 2D, inviscid Burgers' equation, and viscous Burgers' equation) and the performance of these invariant numerical schemes is further evaluated. Our results indicate that such invariant numerical schemes obtained from existing base numerical schemes have the potential to significantly improve the quality of results not only in terms of desired higher order accuracy but also in the context of preservation of appropriate symmetry properties of underlying PDEs.

  18. A simple finite-difference scheme for handling topography with the second-order wave equation

    NARCIS (Netherlands)

    Mulder, W.A.


    The presence of topography poses a challenge for seismic modeling with finite-difference codes. The representation of topography by means of an air layer or vacuum often leads to a substantial loss of numerical accuracy. A suitable modification of the finite-difference weights near the free

  19. Combining finite element and finite difference methods for isotropic elastic wave simulations in an energy-conserving manner

    KAUST Repository

    Gao, Longfei


    We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain to account for the topography, and combined with the more efficient finite difference method that is applied to the deep region of the simulation domain. We demonstrate that these two discretization methods, albeit starting from different formulations of the elastic wave equation, can be joined together smoothly via weakly imposed interface conditions. Discrete energy analysis is employed to derive the proper interface treatment, leading to an overall discretization that is energy-conserving. Numerical examples are presented to demonstrate the efficacy of the proposed interface treatment.

  20. Error Estimation Methods for the Finite-Difference Solution for Poisson’s Equation


    Omar, Haji Omar


    The finite-difference method is universally used for the approximation of differential equations. In this thesis two different approaches are reviewed for the error estimation of the approximation of the Dirichlet problem for elliptic equations, specifically Poisson’s and Laplace’s equations using various finite-difference schemes. The first approach is based on the difference analogue of the maximum principle. Applying Gerschgorin’s majorant method to the analysis , also the order of a...

  1. Similarity and generalized finite-difference solutions of parabolic partial differential equations. (United States)

    Clausing, A. M.


    Techniques are presented for obtaining generalized finite-difference solutions to partial differential equations of the parabolic type. It is shown that the advantages of similarity in the solution of similar problems are generally not lost if the solution to the original partial differential equations is effected in the physical plane by finite-difference methods. The analysis results in a considerable saving in computational effort in the solution of both similar and nonsimilar problems. Several examples, including both the heat-conduction equation and the boundary-layer equations, are given. The analysis also provides a practical means of estimating the accuracy of finite-difference solutions to parabolic equations.

  2. A non-linear constrained optimization technique for the mimetic finite difference method

    Energy Technology Data Exchange (ETDEWEB)

    Manzini, Gianmarco [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Svyatskiy, Daniil [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Bertolazzi, Enrico [Univ. of Trento (Italy); Frego, Marco [Univ. of Trento (Italy)


    This is a strategy for the construction of monotone schemes in the framework of the mimetic finite difference method for the approximation of diffusion problems on unstructured polygonal and polyhedral meshes.

  3. Application of steady state finite element and transient finite difference theory to sound propagation in a variable area duct: A comparison with experiment (United States)

    Baumeister, K. J.; Eversman, W.; Astley, R. J.; White, J. W.


    Sound propagation without flow in a rectangular duct with a converging-diverging area variation was studied experimentally and theoretically. The area variation was of sufficient magnitude to produce large reflections and induce modal scattering. The rms (root-mean-squared) pressure and phase angle on both the flat and curved surface were measured and tabulated. The steady state finite element theory and the transient finite difference theory are in good agreement with the data. It is concluded that numerical finite difference and finite element theories appear ideally suited for handling duct propagation problems which encounter large area variations.

  4. A finite difference method for nonlinear parabolic-elliptic systems of second order partial differential equations


    Marian Malec; Lucjan Sapa


    This paper deals with a finite difference method for a wide class of weakly coupled nonlinear second-order partial differential systems with initial condition and weakly coupled nonlinear implicit boundary conditions. One part of each system is of the parabolic type (degenerated parabolic equations) and the other of the elliptic type (equations with a parameter) in a cube in \\(\\mathbf{R}^{1+n}\\). A suitable finite difference scheme is constructed. It is proved that the scheme has a unique sol...

  5. Fitted-Stable Finite Difference Method for Singularly Perturbed Two ...

    African Journals Online (AJOL)

    A fitted-stable central difference method is presented for solving singularly perturbed two point boundary value problems with the boundary layer at one end (left or right) of the interval. A fitting factor is introduced in second order stable central difference scheme (SCD Method) and its value is obtained using the theory of ...

  6. On the monotonicity of multidimensional finite difference schemes (United States)

    Kovyrkina, O.; Ostapenko, V.


    The classical concept of monotonicity, introduced by Godunov for linear one-dimensional difference schemes, is extended to multidimensional case. Necessary and sufficient conditions of monotonicity are obtained for linear multidimensional difference schemes of first order. The constraints on the numerical viscosity are given that ensure the monotonicity of a difference scheme in the multidimensional case. It is proposed a modification of the second order multidimensional CABARET scheme that preserves the monotonicity of one-dimensional discrete solutions and, as a result, ensures higher smoothness in the computation of multidimensional discontinuous solutions. The results of two-dimensional test computations illustrating the advantages of the modified CABARET scheme are presented.

  7. Wing-Body Aeroelasticity Using Finite-Difference Fluid/Finite-Element Structural Equations on Parallel Computers (United States)

    Byun, Chansup; Guruswamy, Guru P.; Kutler, Paul (Technical Monitor)


    In recent years significant advances have been made for parallel computers in both hardware and software. Now parallel computers have become viable tools in computational mechanics. Many application codes developed on conventional computers have been modified to benefit from parallel computers. Significant speedups in some areas have been achieved by parallel computations. For single-discipline use of both fluid dynamics and structural dynamics, computations have been made on wing-body configurations using parallel computers. However, only a limited amount of work has been completed in combining these two disciplines for multidisciplinary applications. The prime reason is the increased level of complication associated with a multidisciplinary approach. In this work, procedures to compute aeroelasticity on parallel computers using direct coupling of fluid and structural equations will be investigated for wing-body configurations. The parallel computer selected for computations is an Intel iPSC/860 computer which is a distributed-memory, multiple-instruction, multiple data (MIMD) computer with 128 processors. In this study, the computational efficiency issues of parallel integration of both fluid and structural equations will be investigated in detail. The fluid and structural domains will be modeled using finite-difference and finite-element approaches, respectively. Results from the parallel computer will be compared with those from the conventional computers using a single processor. This study will provide an efficient computational tool for the aeroelastic analysis of wing-body structures on MIMD type parallel computers.

  8. A new fitted operator finite difference method to solve systems of ...

    African Journals Online (AJOL)

    In recent years, fitted operator finite difference methods (FOFDMs) have been developed for numerous types of singularly perturbed ordinary differential equations. The construction of most of these methods differed though the final outcome remained similar. The most crucial aspect was how the difference operator was ...

  9. Modelling Geotechnical Heterogeneities Using Geostatistical Simulation and Finite Differences Analysis

    Directory of Open Access Journals (Sweden)

    Marisa Pinheiro


    Full Text Available Modelling a rock mass in an accurate and realistic way allows researchers to reduce the uncertainty associated with its characterisation and reproduce the intrinsic spatial variability and heterogeneities present in the rock mass. However, there is often a lack of a structured methodology to characterise heterogeneous rock masses using geotechnical information available from the prospection phase. This paper presents a characterization methodology based on the geostatistical simulation of geotechnical variables and the application of a scenario reduction technique aimed at selecting a reduced number of realisations able to statistically represent a large set of realisations obtained by the geostatistical approach. This type of information is useful for a further rock mass behaviour analysis. The methodology is applied to a gold deposit with the goal of understanding its main differences to traditional approaches based on a deterministic modelling of the rock mass. The obtained results show the suitability of the methodology to characterise heterogeneous rock masses, since there were considerable differences between the results of the proposed methodology, mainly concerning the theoretical tunnel displacements, and the ones obtained with a traditional approach.

  10. Accuracy of finite-difference harmonic frequencies in density functional theory. (United States)

    Liu, Kuan-Yu; Liu, Jie; Herbert, John M


    Analytic Hessians are often viewed as essential for the calculation of accurate harmonic frequencies, but the implementation of analytic second derivatives is nontrivial and solution of the requisite coupled-perturbed equations engenders a sizable memory footprint for large systems, given that these equations are not required for energy and gradient calculations in density functional theory. Here, we benchmark the alternative approach to harmonic frequencies based on finite differences of analytic first derivatives, a procedure that is amenable to large-scale parallelization. Not only for absolute frequencies but also for isotopic and conformer-dependent frequency shifts in flexible molecules, we find that the finite-difference approach exhibits mean errors finite-difference error can be larger, but even in these cases the errors can be reduced below 0.1 cm-1 by judicious choice of the displacement step size and a higher-order finite-difference approach. The surprising accuracy and robustness of the finite-difference results suggests that availability of the analytic Hessian is not so important in today's era of commodity processors that are readily available in large numbers. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

  11. Improving sub-grid scale accuracy of boundary features in regional finite-difference models (United States)

    Panday, Sorab; Langevin, Christian D.


    As an alternative to grid refinement, the concept of a ghost node, which was developed for nested grid applications, has been extended towards improving sub-grid scale accuracy of flow to conduits, wells, rivers or other boundary features that interact with a finite-difference groundwater flow model. The formulation is presented for correcting the regular finite-difference groundwater flow equations for confined and unconfined cases, with or without Newton Raphson linearization of the nonlinearities, to include the Ghost Node Correction (GNC) for location displacement. The correction may be applied on the right-hand side vector for a symmetric finite-difference Picard implementation, or on the left-hand side matrix for an implicit but asymmetric implementation. The finite-difference matrix connectivity structure may be maintained for an implicit implementation by only selecting contributing nodes that are a part of the finite-difference connectivity. Proof of concept example problems are provided to demonstrate the improved accuracy that may be achieved through sub-grid scale corrections using the GNC schemes.

  12. Time-domain finite-difference based analysis of induced crosstalk in multiwall carbon nanotube interconnects (United States)

    Kumar, Amit; Nehra, Vikas; Kaushik, Brajesh Kumar


    Graphene rolled-up cylindrical sheets i.e. carbon nanotubes (CNTs) is one of the finest and emerging research area. This paper presents the investigation of induced crosstalk in coupled on-chip multiwalled carbon nanotube (MWCNT) interconnects using finite-difference analysis (FDA) in time-domain i.e. the finite-difference time-domain (FDTD) method. The exceptional properties of versatile MWCNTs profess their candidacy to replace conventional on-chip copper interconnects. Time delay and crosstalk noise have been evaluated for coupled on-chip MWCNT interconnects. With a decrease in CNT length, the obtained results for an MWCNT shows that transmission performance improves as the number of shells increases. It has been observed that the obtained results using the finite-difference time domain (FDTD) technique shows a very close match with the HSPICE simulated results.

  13. Conservative arbitrary order finite difference schemes for shallow-water flows (United States)

    Skiba, Yuri N.; Filatov, Denis M.


    The classical nonlinear shallow-water model (SWM) of an ideal fluid is considered. For the model, a new method for the construction of mass and total energy conserving finite difference schemes is suggested. In fact, it produces an infinite family of finite difference schemes, which are either linear or nonlinear depending on the choice of certain parameters. The developed schemes can be applied in a variety of domains on the plane and on the sphere. The method essentially involves splitting of the model operator by geometric coordinates and by physical processes, which provides substantial benefits in the computational cost of solution. Besides, in case of the whole sphere it allows applying the same algorithms as in a doubly periodic domain on the plane and constructing finite difference schemes of arbitrary approximation order in space. Results of numerical experiments illustrate the skillfulness of the schemes in describing the shallow-water dynamics.

  14. Performance prediction of finite-difference solvers for different computer architectures (United States)

    Louboutin, Mathias; Lange, Michael; Herrmann, Felix J.; Kukreja, Navjot; Gorman, Gerard


    The life-cycle of a partial differential equation (PDE) solver is often characterized by three development phases: the development of a stable numerical discretization; development of a correct (verified) implementation; and the optimization of the implementation for different computer architectures. Often it is only after significant time and effort has been invested that the performance bottlenecks of a PDE solver are fully understood, and the precise details varies between different computer architectures. One way to mitigate this issue is to establish a reliable performance model that allows a numerical analyst to make reliable predictions of how well a numerical method would perform on a given computer architecture, before embarking upon potentially long and expensive implementation and optimization phases. The availability of a reliable performance model also saves developer effort as it both informs the developer on what kind of optimisations are beneficial, and when the maximum expected performance has been reached and optimisation work should stop. We show how discretization of a wave-equation can be theoretically studied to understand the performance limitations of the method on modern computer architectures. We focus on the roofline model, now broadly used in the high-performance computing community, which considers the achievable performance in terms of the peak memory bandwidth and peak floating point performance of a computer with respect to algorithmic choices. A first principles analysis of operational intensity for key time-stepping finite-difference algorithms is presented. With this information available at the time of algorithm design, the expected performance on target computer systems can be used as a driver for algorithm design.

  15. Propagation of 3-D Beams Using a Finite-Difference Algorithm: Practical Considerations (United States)


    difference optical propagation, including non-paraxial methods, was reviewed and augmented by Bekker .2 2. FINITE DIFFERENCE APPROXIMATION TO THE...unstable resonator calculations with laser medium,” Applied Optics 13(11), 2546–2561 (1974). [2] Bekker , E. V., et al., “Wide-angle alternating-direction

  16. Convection in a vertical channel - A finite-difference and an integral method (United States)

    Mata, C. M.; Saraiva, J. A. Gil

    A numerical study of an air vertical solar collector is presented. Two different methods were used: a finite-difference scheme with a rectangular grid and an integral method based on analytic-experimental correlations involving nondimensional parameters. Constant heat flux conditions were assumed, and radiation conditions can be integrated. Each method's advantages are enhanced.

  17. A generalized finite difference method using Coatmèlec lattices (United States)

    García-March, Miguel A.; Arevalillo-Herráez, Miguel; Villatoro, Francisco R.; Giménez, Fernando; de Córdoba, Pedro Fernández


    Generalized finite difference methods require that a properly posed set of nodes exists around each node in the mesh, so that the solution for the corresponding multivariate interpolation problem be unique. In this paper we first show that the construction of these meshes can be computerized using a relatively simple algorithm based on the concept of a Coatmèlec lattice. Then, we present a generalized finite difference method which provides a numerical solution of a partial differential equation over an arbitrary domain, using the generated meshes. The accuracy and mesh adaptivity of the method is evaluated using elliptical equations in several domains.

  18. Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics

    CERN Document Server

    Gedney, Stephen


    Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics provides a comprehensive tutorial of the most widely used method for solving Maxwell's equations -- the Finite Difference Time-Domain Method. This book is an essential guide for students, researchers, and professional engineers who want to gain a fundamental knowledge of the FDTD method. It can accompany an undergraduate or entry-level graduate course or be used for self-study. The book provides all the background required to either research or apply the FDTD method for the solution of Maxwell's equations to p

  19. Numerical solution of a diffusion problem by exponentially fitted finite difference methods. (United States)

    D'Ambrosio, Raffaele; Paternoster, Beatrice


    This paper is focused on the accurate and efficient solution of partial differential differential equations modelling a diffusion problem by means of exponentially fitted finite difference numerical methods. After constructing and analysing special purpose finite differences for the approximation of second order partial derivatives, we employed them in the numerical solution of a diffusion equation with mixed boundary conditions. Numerical experiments reveal that a special purpose integration, both in space and in time, is more accurate and efficient than that gained by employing a general purpose solver.

  20. An implicit logarithmic finite-difference technique for two dimensional coupled viscous Burgers’ equation

    Directory of Open Access Journals (Sweden)

    Vineet K. Srivastava


    Full Text Available This article describes a new implicit finite-difference method: an implicit logarithmic finite-difference method (I-LFDM, for the numerical solution of two dimensional time-dependent coupled viscous Burgers’ equation on the uniform grid points. As the Burgers’ equation is nonlinear, the proposed technique leads to a system of nonlinear systems, which is solved by Newton's iterative method at each time step. Computed solutions are compared with the analytical solutions and those already available in the literature and it is clearly shown that the results obtained using the method is precise and reliable for solving Burgers’ equation.

  1. A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra

    KAUST Repository

    Wheeler, Mary


    In this paper, we develop a new mixed finite element method for elliptic problems on general quadrilateral and hexahedral grids that reduces to a cell-centered finite difference scheme. A special non-symmetric quadrature rule is employed that yields a positive definite cell-centered system for the pressure by eliminating local velocities. The method is shown to be accurate on highly distorted rough quadrilateral and hexahedral grids, including hexahedra with non-planar faces. Theoretical and numerical results indicate first-order convergence for the pressure and face fluxes. © 2011 Springer-Verlag.


    Directory of Open Access Journals (Sweden)

    Chaitanya Goteti


    Full Text Available Abstract Many torque carrying members have circular sections such as shafts. However, there are certain structural members like automotive chassis frames, cross members and machine frames which are often subjected to twisting loads and their cross sections are non circular. several methods were developed to analyze such sections such as Saint Venant’s semi inverse method, Prandtl’s elastic membrane analogy...etc. In this paper, the second order partial differential stress function equation for non-circular torsional members is applied on a rectangular section for different b/h (height /width of section values and the solutions for maximum torsional shear stress are found by employing second order finite difference method. The results are compared to the results obtained from commercial finite element software (ANSYS 10 and by direct solution of the stress function equation using analytical correlations available for rectangular sections. The results obtained by different approaches are in close congruence with a percentage deviation of only 3.22. It is observed that, in implementing second order finite difference scheme, the error in estimating stress is proportional to S2. Where “S” is the grid size.   Keywords: Non-Circular Section, Prandtl’s stress function, Finite difference scheme, Grid size

  3. A fast finite-difference algorithm for topology optimization of permanent magnets (United States)

    Abert, Claas; Huber, Christian; Bruckner, Florian; Vogler, Christoph; Wautischer, Gregor; Suess, Dieter


    We present a finite-difference method for the topology optimization of permanent magnets that is based on the fast-Fourier-transform (FFT) accelerated computation of the stray-field. The presented method employs the density approach for topology optimization and uses an adjoint method for the gradient computation. Comparison to various state-of-the-art finite-element implementations shows a superior performance and accuracy. Moreover, the presented method is very flexible and easy to implement due to various preexisting FFT stray-field implementations that can be used.

  4. Application of 'steady' state finite element and transient finite difference theory to sound propagation in a variable duct - A comparison with experiment (United States)

    Baumeister, K. J.; Eversman, W.; Astley, R. J.; White, J. W.


    Experimental data are presented for sound propagation in a simulated infinite hard wall duct with a large change in duct cross sectional area. The data are conveniently tabulated for further use. The 'steady' state finite element theory of Astley and Eversman (1981) and the transient finite difference theory of White (1981) are in good agreement with the data for both the axial and transverse pressure profiles and the axial phase angle. Therefore, numerical finite difference and finite element theories appear to be ideally suited for handling duct propagation problems which encounter large axial gradients in acoustic parameters. The measured energy reflection coefficient agrees with the values from the Astley-Eversman modal coupling model.

  5. Construction of finite difference schemes having special properties for ordinary and partial differential equations (United States)

    Mickens, R. E.


    Work on the construction of finite difference models of differential equations having zero truncation errors is summarized. Both linear and nonlinear unidirectional wave equations are discussed. Results regarding the construction of zero truncation error schemes for the full wave equation and Burger's equation are also briefly reported.

  6. Efficiency Benchmarking of an Energy Stable High-Order Finite Difference Discretization

    NARCIS (Netherlands)

    van der Weide, Edwin Theodorus Antonius; Giangaspero, G.; Svärd, M


    In this paper, results are presented for a number of benchmark cases, proposed at the 2nd International Workshop on High-Order CFD Methods in Cologne, Germany, in 2013. A robust high-order-accurate finite difference method was used that was developed during the last 10–15 years. The robustness stems

  7. The finite-difference time-domain method for electromagnetics with Matlab simulations

    CERN Document Server

    Elsherbeni, Atef Z


    This book introduces the powerful Finite-Difference Time-Domain method to students and interested researchers and readers. An effective introduction is accomplished using a step-by-step process that builds competence and confidence in developing complete working codes for the design and analysis of various antennas and microwave devices.

  8. A coupled boundary element-finite difference solution of the elliptic modified mild slope equation

    DEFF Research Database (Denmark)

    Naserizadeh, R.; Bingham, Harry B.; Noorzad, A.


    The modified mild slope equation of [5] is solved using a combination of the boundary element method (BEM) and the finite difference method (FDM). The exterior domain of constant depth and infinite horizontal extent is solved by a BEM using linear or quadratic elements. The interior domain...

  9. The finite difference time domain method on a massively parallel computer

    NARCIS (Netherlands)

    Ewijk, L.J. van


    At the Physics and Electronics Laboratory TNO much research is done in the field of computational electromagnetics (CEM). One of the tools in this field is the Finite Difference Time Domain method (FDTD), a method that has been implemented in a program in order to be able to compute electromagnetic

  10. On a Stable and Consistent Finite Difference Scheme for a Time ...

    African Journals Online (AJOL)

    In this paper, a stable and consistent criterion to an explicit finite difference scheme for a time-dependent Schrodinger wave equation (TDSWE) was presented. This paper is a departure from the well-established time independent Schrodinger Wave Equation (SWE). To develop the stability criterion for the scheme, the ...

  11. Finite Difference Study of MHD Stokes Problem for a Vertical Infinite ...

    African Journals Online (AJOL)

    The explicit finite difference method is employed to study the effects of both the Hall and ionslip currents on a free convective flow of a viscous heat generating rotating fluid past an impulsively started infinite vertical plate, to which a strong magnetic field is applied perpendicularly. The velocity (both primary and secondary) ...


    A hybrid of the finite-difference method and the discrete-wavenumber method is developed to calculate radar traces. The method is based on a three-dimensional model defined in the Cartesian coordinate system; the electromag-netic properties of the model are symmetric with respect...

  13. Stability of finite difference schemes for generalized von Foerster equations with renewal

    Directory of Open Access Journals (Sweden)

    Henryk Leszczyński


    Full Text Available We consider a von Foerster-type equation describing the dynamics of a population with the production of offsprings given by the renewal condition. We construct a finite difference scheme for this problem and give sufficient conditions for its stability with respect to \\(l^1\\ and \\(l^\\infty\\ norms.

  14. A smart nonstandard finite difference scheme for second order nonlinear boundary value problems

    NARCIS (Netherlands)

    Erdogan, Utku; Ozis, Turgut


    A new kind of finite difference scheme is presented for special second order nonlinear two point boundary value problems. An artificial parameter is introduced in the scheme. Symbolic computation is proposed for the construction of the scheme. Local truncation error of the method is discussed.

  15. High-order Finite Difference Solution of Euler Equations for Nonlinear Water Waves

    DEFF Research Database (Denmark)

    Christiansen, Torben Robert Bilgrav; Bingham, Harry B.; Engsig-Karup, Allan Peter


    is discretized using arbitrary-order finite difference schemes on a staggered grid with one optional stretching in each coordinate direction. The momentum equations and kinematic free surface condition are integrated in time using the classic fourth-order Runge-Kutta scheme. Mass conservation is satisfied...

  16. Nonuniform grid implicit spatial finite difference method for acoustic wave modeling in tilted transversely isotropic media

    KAUST Repository

    Chu, Chunlei


    Discrete earth models are commonly represented by uniform structured grids. In order to ensure accurate numerical description of all wave components propagating through these uniform grids, the grid size must be determined by the slowest velocity of the entire model. Consequently, high velocity areas are always oversampled, which inevitably increases the computational cost. A practical solution to this problem is to use nonuniform grids. We propose a nonuniform grid implicit spatial finite difference method which utilizes nonuniform grids to obtain high efficiency and relies on implicit operators to achieve high accuracy. We present a simple way of deriving implicit finite difference operators of arbitrary stencil widths on general nonuniform grids for the first and second derivatives and, as a demonstration example, apply these operators to the pseudo-acoustic wave equation in tilted transversely isotropic (TTI) media. We propose an efficient gridding algorithm that can be used to convert uniformly sampled models onto vertically nonuniform grids. We use a 2D TTI salt model to demonstrate its effectiveness and show that the nonuniform grid implicit spatial finite difference method can produce highly accurate seismic modeling results with enhanced efficiency, compared to uniform grid explicit finite difference implementations. © 2011 Elsevier B.V.

  17. Spatial Parallelism of a 3D Finite Difference, Velocity-Stress Elastic Wave Propagation Code

    Energy Technology Data Exchange (ETDEWEB)



    Finite difference methods for solving the wave equation more accurately capture the physics of waves propagating through the earth than asymptotic solution methods. Unfortunately. finite difference simulations for 3D elastic wave propagation are expensive. We model waves in a 3D isotropic elastic earth. The wave equation solution consists of three velocity components and six stresses. The partial derivatives are discretized using 2nd-order in time and 4th-order in space staggered finite difference operators. Staggered schemes allow one to obtain additional accuracy (via centered finite differences) without requiring additional storage. The serial code is most unique in its ability to model a number of different types of seismic sources. The parallel implementation uses the MP1 library, thus allowing for portability between platforms. Spatial parallelism provides a highly efficient strategy for parallelizing finite difference simulations. In this implementation, one can decompose the global problem domain into one-, two-, and three-dimensional processor decompositions with 3D decompositions generally producing the best parallel speed up. Because i/o is handled largely outside of the time-step loop (the most expensive part of the simulation) we have opted for straight-forward broadcast and reduce operations to handle i/o. The majority of the communication in the code consists of passing subdomain face information to neighboring processors for use as ''ghost cells''. When this communication is balanced against computation by allocating subdomains of reasonable size, we observe excellent scaled speed up. Allocating subdomains of size 25 x 25 x 25 on each node, we achieve efficiencies of 94% on 128 processors. Numerical examples for both a layered earth model and a homogeneous medium with a high-velocity blocky inclusion illustrate the accuracy of the parallel code.

  18. A nine-point finite difference scheme for one-dimensional wave equation (United States)

    Szyszka, Barbara


    The paper is devoted to an implicit finite difference method (FDM) for solving initial-boundary value problems (IBVP) for one-dimensional wave equation. The second-order derivatives in the wave equation have been approximated at the four intermediate points, as a consequence, an implicit nine-point difference scheme has been obtained. Von Neumann stability analysis has been conducted and we have demonstrated, that the presented difference scheme is unconditionally stable.

  19. Broadband ground motion simulation using a paralleled hybrid approach of Frequency Wavenumber and Finite Difference method (United States)

    Chen, M.; Wei, S.


    The serious damage of Mexico City caused by the 1985 Michoacan earthquake 400 km away indicates that urban areas may be affected by remote earthquakes. To asses earthquake risk of urban areas imposed by distant earthquakes, we developed a hybrid Frequency Wavenumber (FK) and Finite Difference (FD) code implemented with MPI, since the computation of seismic wave propagation from a distant earthquake using a single numerical method (e.g. Finite Difference, Finite Element or Spectral Element) is very expensive. In our approach, we compute the incident wave field (ud) at the boundaries of the excitation box, which surrounding the local structure, using a paralleled FK method (Zhu and Rivera, 2002), and compute the total wave field (u) within the excitation box using a parallelled 2D FD method. We apply perfectly matched layer (PML) absorbing condition to the diffracted wave field (u-ud). Compared to previous Generalized Ray Theory and Finite Difference (Wen and Helmberger, 1998), Frequency Wavenumber and Spectral Element (Tong et al., 2014), and Direct Solution Method and Spectral Element hybrid method (Monteiller et al., 2013), our absorbing boundary condition dramatically suppress the numerical noise. The MPI implementation of our method can greatly speed up the calculation. Besides, our hybrid method also has a potential use in high resolution array imaging similar to Tong et al. (2014).

  20. High‐order rotated staggered finite difference modeling of 3D elastic wave propagation in general anisotropic media

    KAUST Repository

    Chu, Chunlei


    We analyze the dispersion properties and stability conditions of the high‐order convolutional finite difference operators and compare them with the conventional finite difference schemes. We observe that the convolutional finite difference method has better dispersion properties and becomes more efficient than the conventional finite difference method with the increasing order of accuracy. This makes the high‐order convolutional operator a good choice for anisotropic elastic wave simulations on rotated staggered grids since its enhanced dispersion properties can help to suppress the numerical dispersion error that is inherent in the rotated staggered grid structure and its efficiency can help us tackle 3D problems cost‐effectively.

  1. A Cell-Based Finite Difference Method for the Numerical Solution of PDEs (United States)

    Salih, A.; Barron, R. M.; Friedl, J.


    The governing partial differential equations of fluid motion are usually numerically approximated using one of three methods: Finite Difference (FD), Finite Volume (FV) or Finite Element (FE). Finding practical solutions to the governing equations of fluid mechanics is one of the most challenging problems in engineering because these equations, in most cases, form a set of coupled non-linear partial differential equations. In this research, a new cell-centred Finite Difference (CCFD) formulation is developed that is applied in each individual cell of an arbitrary mesh discretizing the solution domain. This feature allows the application of the proposed FD numerical formulation on arbitrary mesh topologies, i.e., structured, unstructured or hybrid meshes. Initially, a simple test case is investigated to illustrate this method. The numerical results are compared with the analytical solution and/or a traditional FD solution. Lastly, two additional test cases are conducted to illustrate the ability of the CCFD method to handle mixed boundary types and its extendibility to other types of elliptic boundary value problems.

  2. A finite difference method for nonlinear parabolic-elliptic systems of second order partial differential equations

    Directory of Open Access Journals (Sweden)

    Marian Malec


    Full Text Available This paper deals with a finite difference method for a wide class of weakly coupled nonlinear second-order partial differential systems with initial condition and weakly coupled nonlinear implicit boundary conditions. One part of each system is of the parabolic type (degenerated parabolic equations and the other of the elliptic type (equations with a parameter in a cube in \\(\\mathbf{R}^{1+n}\\. A suitable finite difference scheme is constructed. It is proved that the scheme has a unique solution, and the numerical method is consistent, convergent and stable. The error estimate is given. Moreover, by the method, the differential problem has at most one classical solution. The proof is based on the Banach fixed-point theorem, the maximum principle for difference functional systems of the parabolic type and some new difference inequalities. It is a new technique of studying the mixed-type systems. Examples of physical applications and numerical experiments are presented.

  3. Analysis for pressure transient of coalbed methane reservoir based on Laplace transform finite difference method

    Directory of Open Access Journals (Sweden)

    Lei Wang


    Full Text Available Based on fractal geometry, fractal medium of coalbed methane mathematical model is established by Langmuir isotherm adsorption formula, Fick's diffusion law, Laplace transform formula, considering the well bore storage effect and skin effect. The Laplace transform finite difference method is used to solve the mathematical model. With Stehfest numerical inversion, the distribution of dimensionless well bore flowing pressure and its derivative was obtained in real space. According to compare with the results from the analytical method, the result from Laplace transform finite difference method turns out to be accurate. The influence factors are analyzed, including fractal dimension, fractal index, skin factor, well bore storage coefficient, energy storage ratio, interporosity flow coefficient and the adsorption factor. The calculating error of Laplace transform difference method is small. Laplace transform difference method has advantages in well-test application since any moment simulation does not rely on other moment results and space grid.

  4. On the Stability of the Finite Difference based Lattice Boltzmann Method

    KAUST Repository

    El-Amin, Mohamed


    This paper is devoted to determining the stability conditions for the finite difference based lattice Boltzmann method (FDLBM). In the current scheme, the 9-bit two-dimensional (D2Q9) model is used and the collision term of the Bhatnagar- Gross-Krook (BGK) is treated implicitly. The implicitness of the numerical scheme is removed by introducing a new distribution function different from that being used. Therefore, a new explicit finite-difference lattice Boltzmann method is obtained. Stability analysis of the resulted explicit scheme is done using Fourier expansion. Then, stability conditions in terms of time and spatial steps, relaxation time and explicitly-implicitly parameter are determined by calculating the eigenvalues of the given difference system. The determined conditions give the ranges of the parameters that have stable solutions.

  5. An outgoing energy flux boundary condition for finite difference ICRP antenna models

    Energy Technology Data Exchange (ETDEWEB)

    Batchelor, D.B.; Carter, M.D.


    For antennas at the ion cyclotron range of frequencies (ICRF) modeling in vacuum can now be carried out to a high level of detail such that shaping of the current straps, isolating septa, and discrete Faraday shield structures can be included. An efficient approach would be to solve for the fields in the vacuum region near the antenna in three dimensions by finite methods and to match this solution at the plasma-vacuum interface to a solution obtained in the plasma region in one dimension by Fourier methods. This approach has been difficult to carry out because boundary conditions must be imposed at the edge of the finite difference grid on a point-by-point basis, whereas the condition for outgoing energy flux into the plasma is known only in terms of the Fourier transform of the plasma fields. A technique is presented by which a boundary condition can be imposed on the computational grid of a three-dimensional finite difference, or finite element, code by constraining the discrete Fourier transform of the fields at the boundary points to satisfy an outgoing energy flux condition appropriate for the plasma. The boundary condition at a specific grid point appears as a coupling to other grid points on the boundary, with weighting determined by a kemel calctdated from the plasma surface impedance matrix for the various plasma Fourier modes. This boundary condition has been implemented in a finite difference solution of a simple problem in two dimensions, which can also be solved directly by Fourier transformation. Results are presented, and it is shown that the proposed boundary condition does enforce outgoing energy flux and yields the same solution as is obtained by Fourier methods.

  6. Finite difference numerical methods for boundary control problems governed by hyperbolic partial differential equations (United States)

    Chen, G.; Zheng, Q.; Coleman, M.; Weerakoon, S.


    This paper briefly reviews convergent finite difference schemes for hyperbolic initial boundary value problems and their applications to boundary control systems of hyperbolic type which arise in the modelling of vibrations. These difference schemes are combined with the primal and the dual approaches to compute the optimal control in the unconstrained case, as well as the case when the control is subject to inequality constraints. Some of the preliminary numerical results are also presented.

  7. Finite difference analysis of torsional vibrations of pretwisted, rotating, cantilever beams with effects of warping (United States)

    Subrahmanyam, K. B.; Kaza, K. R. V.


    Theoretical natural frequencies of the first three modes of torsional vibration of pretwisted, rotating cantilever beams are determined for various thickness and aspect ratios. Conclusions concerning individual and collective effects of warping, pretwist, tension-torsion coupling and tennis racket effect (twist-rotational coupling) terms on the natural frequencies are drawn from numerical results obtained by using a finite difference procedure with first order central differences. The relative importance of structural warping, inertial warping, pretwist, tension-torsion and twist-rotational coupling terms is discussed for various rotational speeds. The accuracy of results obtained by using the finite difference approach is verified by a comparison with the exact solution for specialized simple cases of the equation of motion used in this paper.

  8. Energy stable and high-order-accurate finite difference methods on staggered grids (United States)

    O'Reilly, Ossian; Lundquist, Tomas; Dunham, Eric M.; Nordström, Jan


    For wave propagation over distances of many wavelengths, high-order finite difference methods on staggered grids are widely used due to their excellent dispersion properties. However, the enforcement of boundary conditions in a stable manner and treatment of interface problems with discontinuous coefficients usually pose many challenges. In this work, we construct a provably stable and high-order-accurate finite difference method on staggered grids that can be applied to a broad class of boundary and interface problems. The staggered grid difference operators are in summation-by-parts form and when combined with a weak enforcement of the boundary conditions, lead to an energy stable method on multiblock grids. The general applicability of the method is demonstrated by simulating an explosive acoustic source, generating waves reflecting against a free surface and material discontinuity.

  9. Stress Analysis of Different Angulations of Implant Installation: The Finite Element Method

    Directory of Open Access Journals (Sweden)

    Ting-Hsun Lan


    Full Text Available Clinically, many implant cases with different angulation over the lower posterior area have been found. The purpose of this study was to analyze the bony stress with different implant tilting during normal masticatory load using the finite element method (FEM, with the hope of discovering a desirable installation of implant. Athree-dimensional finite element method was employed to analyze the bony stress generated by different angulation designs (15° of implant bodies. Eight solid models of the mandibular first and second molars were built up and then transferred to a mesh model in FEM (ANSYS to perform a stress analysis. A simulated load (400N was applied to the splinted crowns with vertical and horizontal forces. The loading sites were on the central fossa of the splinted crowns. For stress distribution, some designs will be better than a parallel installation. The results suggested that not all implant bodies tilting with the splinted crowns lead to stress concentration.

  10. Stability and non-standard finite difference method of the generalized Chua's circuit

    KAUST Repository

    Radwan, Ahmed G.


    In this paper, we develop a framework to obtain approximate numerical solutions of the fractional-order Chua\\'s circuit with Memristor using a non-standard finite difference method. Chaotic response is obtained with fractional-order elements as well as integer-order elements. Stability analysis and the condition of oscillation for the integer-order system are discussed. In addition, the stability analyses for different fractional-order cases are investigated showing a great sensitivity to small order changes indicating the poles\\' locations inside the physical s-plane. The GrnwaldLetnikov method is used to approximate the fractional derivatives. Numerical results are presented graphically and reveal that the non-standard finite difference scheme is an effective and convenient method to solve fractional-order chaotic systems, and to validate their stability. © 2011 Elsevier Ltd. All rights reserved.

  11. Modeling and Simulation of Hamburger Cooking Process Using Finite Difference and CFD Methods

    Directory of Open Access Journals (Sweden)

    J. Sargolzaei


    Full Text Available Unsteady-state heat transfer in hamburger cooking process was modeled using one dimensional finite difference (FD and three dimensional computational fluid dynamic (CFD models. A double-sided cooking system was designed to study the effect of pressure and oven temperature on the cooking process. Three different oven temperatures (114, 152, 204°C and three different pressures (20, 332, 570 pa were selected and 9 experiments were performed. Applying pressure to hamburger increases the contact area of hamburger with heating plate and hence the heat transfer rate to the hamburger was increased and caused the weight loss due to water evaporation and decreasing cooking time, while increasing oven temperature led to increasing weight loss and decreasing cooking time. CFD predicted results were in good agreement with the experimental results than the finite difference (FD ones. But considering the long time needed for CFD model to simulate the cooking process (about 1 hour, using the finite difference model would be more economic.

  12. Thermal Analysis of AC Contactor Using Thermal Network Finite Difference Analysis Method (United States)

    Niu, Chunping; Chen, Degui; Li, Xingwen; Geng, Yingsan

    To predict the thermal behavior of switchgear quickly, the Thermal Network Finite Difference Analysis method (TNFDA) is adopted in thermal analysis of AC contactor in the paper. The thermal network model is built with nodes, thermal resistors and heat generators, and it is solved using finite difference method (FDM). The main circuit and the control system are connected by thermal resistors network, which solves the problem of multi-sources interaction in the application of TNFDA. The temperature of conducting wires is calculated according to the heat transfer process and the fundamental equations of thermal conduction. It provides a method to solve the problem of boundary conditions in applying the TNFDA. The comparison between the results of TNFDA and measurements shows the feasibility and practicability of the method.

  13. Convergence of finite differences schemes for viscous and inviscid conservation laws with rough coefficients

    Energy Technology Data Exchange (ETDEWEB)

    Karlsen, Kenneth Hvistendal; Risebro, Nils Henrik


    We consider the initial value problem for degenerate viscous and inviscid scalar conservation laws where the flux function depends on the spatial location through a ''rough'' coefficient function k(x). we show that the Engquist-Osher (and hence all monotone) finite difference approximations converge to the unique entropy solution of the governing equation if, among other demands, k' is in BV, thereby providing alternative (new) existence proofs for entropy solutions of degenerate convection-diffusion equations as well as new convergence results for their finite difference approximations. In the inviscid case, we also provide a rate of convergence. Our convergence proofs are based on deriving a series of a priori estimates and using a general L{sup p} compactness criterion. (author)

  14. Efficient Energyminimization in Finite-Difference Micromagnetics: Speeding up Hysteresis Computations

    CERN Document Server

    Abert, Claas; Bruckner, Florian; Satz, Armin; Suess, Dieter


    We implement an efficient energy-minimization algorithm for finite-difference micromagnetics that proofs especially usefull for the computation of hysteresis loops. Compared to results obtained by time integration of the Landau-Lifshitz-Gilbert equation, a speedup of up to two orders of magnitude is gained. The method is implemented in a finite-difference code running on CPUs as well as GPUs. This setup enables us to compute accurate hysteresis loops of large systems with a reasonable computational efford. As a benchmark we solve the {\\mu}Mag Standard Problem #1 with a high spatial resolution and compare the results to the solution of the Landau-Lifshitz-Gilbert equation in terms of accuracy and computing time.

  15. Single-cone finite difference scheme for the (2+1)D Dirac von Neumann equation (United States)

    Pötz, Walter; Schreilechner, Magdalena


    An explicit finite difference scheme is presented for the von Neumann equation for (2+1)D Dirac fermions. It is founded upon a staggered space-time grid which ensures a single-cone energy dispersion and performs the time-derivative in one sweep using a three-step leap-frog procedure. It enables a space-time-resolved numerical treatment of the mixed-state dynamics of Dirac fermions within the effective single-particle density matrix formalism. Energy-momentum dispersion, stability and convergence properties are derived. Elementary numerical tests to demonstrate stability properties use parameters which pertain to topological insulator surface states. A method for the simulation of charge injection from an electric contact is presented and tested numerically. Potential extensions of the scheme to a Dirac-Lindblad equation, real-space-time Green's function formulations, and higher-order finite-difference schemes are discussed.

  16. Analysis of Finite Difference Discretization Schemes for Diffusion in Spheres with Variable Diffusivity. (United States)

    Versypt, Ashlee N Ford; Braatz, Richard D


    Two finite difference discretization schemes for approximating the spatial derivatives in the diffusion equation in spherical coordinates with variable diffusivity are presented and analyzed. The numerical solutions obtained by the discretization schemes are compared for five cases of the functional form for the variable diffusivity: (I) constant diffusivity, (II) temporally-dependent diffusivity, (III) spatially-dependent diffusivity, (IV) concentration-dependent diffusivity, and (V) implicitly-defined, temporally- and spatially-dependent diffusivity. Although the schemes have similar agreement to known analytical or semi-analytical solutions in the first four cases, in the fifth case for the variable diffusivity, one scheme produces a stable, physically reasonable solution, while the other diverges. We recommend the adoption of the more accurate and stable of these finite difference discretization schemes to numerically approximate the spatial derivatives of the diffusion equation in spherical coordinates for any functional form of variable diffusivity, especially cases where the diffusivity is a function of position.

  17. Linear finite-difference bond graph model of an ionic polymer actuator (United States)

    Bentefrit, M.; Grondel, S.; Soyer, C.; Fannir, A.; Cattan, E.; Madden, J. D.; Nguyen, T. M. G.; Plesse, C.; Vidal, F.


    With the recent growing interest for soft actuation, many new types of ionic polymers working in air have been developed. Due to the interrelated mechanical, electrical, and chemical properties which greatly influence the characteristics of such actuators, their behavior is complex and difficult to understand, predict and optimize. In light of this challenge, an original linear multiphysics finite difference bond graph model was derived to characterize this ionic actuation. This finite difference scheme was divided into two coupled subparts, each related to a specific physical, electrochemical or mechanical domain, and then converted into a bond graph model as this language is particularly suited for systems from multiple energy domains. Simulations were then conducted and a good agreement with the experimental results was obtained. Furthermore, an analysis of the power efficiency of such actuators as a function of space and time was proposed and allowed to evaluate their performance.

  18. Solving moving interface problems using a higher order accurate finite difference scheme (United States)

    Mittal, H. V. R.; Ray, Rajendra K.


    A new finite difference scheme is applied to solve partial differential equations in domains with discontinuities due to the presence of time dependent moving or deforming interfaces. This scheme is an extension of the finite difference idea developed for solving incompressible, steady stokes equations in discontinuous domains with fixed interfaces [1]. This new idea is applied at the irregular points at each time step in conjunction with the Crank-Nicolson (CN) implicit scheme and a recently developed Higher Order Compact (HOC) scheme at regular points. For validation, Stefan's problem is considered with a moving interface in one dimension. In two dimensions, heat equation is considered on a square domain with a circular interface whose radius is continuously changing with time. HOC scheme is found to produce better results and the order of accuracy is slightly better than that of the CN scheme. However, both the schemes show around second order accuracy and good agreement with the analytical solution.

  19. Full Wave Analysis of Passive Microwave Monolithic Integrated Circuit Devices Using a Generalized Finite Difference Time Domain (GFDTD) Algorithm (United States)

    Lansing, Faiza S.; Rascoe, Daniel L.


    This paper presents a modified Finite-Difference Time-Domain (FDTD) technique using a generalized conformed orthogonal grid. The use of the Conformed Orthogonal Grid, Finite Difference Time Domain (GFDTD) enables the designer to match all the circuit dimensions, hence eliminating a major source o error in the analysis.

  20. Explicit finite difference predictor and convex corrector with applications to hyperbolic partial differential equations (United States)

    Dey, C.; Dey, S. K.


    An explicit finite difference scheme consisting of a predictor and a corrector has been developed and applied to solve some hyperbolic partial differential equations (PDEs). The corrector is a convex-type function which is applied at each time level and at each mesh point. It consists of a parameter which may be estimated such that for larger time steps the algorithm should remain stable and generate a fast speed of convergence to the steady-state solution. Some examples have been given.

  1. Finite difference time domain (FDTD) modeling of implanted deep brain stimulation electrodes and brain tissue. (United States)

    Gabran, S R I; Saad, J H; Salama, M M A; Mansour, R R


    This paper demonstrates the electromagnetic modeling and simulation of an implanted Medtronic deep brain stimulation (DBS) electrode using finite difference time domain (FDTD). The model is developed using Empire XCcel and represents the electrode surrounded with brain tissue assuming homogenous and isotropic medium. The model is created to study the parameters influencing the electric field distribution within the tissue in order to provide reference and benchmarking data for DBS and intra-cortical electrode development.

  2. Direct Simulations of Transition and Turbulence Using High-Order Accurate Finite-Difference Schemes (United States)

    Rai, Man Mohan


    In recent years the techniques of computational fluid dynamics (CFD) have been used to compute flows associated with geometrically complex configurations. However, success in terms of accuracy and reliability has been limited to cases where the effects of turbulence and transition could be modeled in a straightforward manner. Even in simple flows, the accurate computation of skin friction and heat transfer using existing turbulence models has proved to be a difficult task, one that has required extensive fine-tuning of the turbulence models used. In more complex flows (for example, in turbomachinery flows in which vortices and wakes impinge on airfoil surfaces causing periodic transitions from laminar to turbulent flow) the development of a model that accounts for all scales of turbulence and predicts the onset of transition may prove to be impractical. Fortunately, current trends in computing suggest that it may be possible to perform direct simulations of turbulence and transition at moderate Reynolds numbers in some complex cases in the near future. This seminar will focus on direct simulations of transition and turbulence using high-order accurate finite-difference methods. The advantage of the finite-difference approach over spectral methods is that complex geometries can be treated in a straightforward manner. Additionally, finite-difference techniques are the prevailing methods in existing application codes. In this seminar high-order-accurate finite-difference methods for the compressible and incompressible formulations of the unsteady Navier-Stokes equations and their applications to direct simulations of turbulence and transition will be presented.

  3. A Weighted Average Finite Difference Method for the Fractional Convection-Diffusion Equation

    Directory of Open Access Journals (Sweden)

    Lijuan Su


    Full Text Available A weighted average finite difference method for solving the two-sided space-fractional convection-diffusion equation is given, which is an extension of the weighted average method for ordinary convection-diffusion equations. Stability, consistency, and convergence of the new method are analyzed. A simple and accurate stability criterion valid for this method, arbitrary weighted factor, and arbitrary fractional derivative is given. Some numerical examples with known exact solutions are provided.

  4. Generalized energy and potential enstrophy conserving finite difference schemes for the shallow water equations (United States)

    Abramopoulos, Frank


    The conditions under which finite difference schemes for the shallow water equations can conserve both total energy and potential enstrophy are considered. A method of deriving such schemes using operator formalism is developed. Several such schemes are derived for the A-, B- and C-grids. The derived schemes include second-order schemes and pseudo-fourth-order schemes. The simplest B-grid pseudo-fourth-order schemes are presented.

  5. Hexagonal vs. Rectilinear Grids for Explicit Finite Difference Schemes for the Two-dimensional Wave Equation


    Hamilton, Brian; Bilbao, Stefan


    Finite difference schemes for the 2-D wave equation operating on hexagonal grids and the accompanyingnumerical dispersion properties have received little attention in comparison to schemes operating on rectilinear grids. This paper considers the hexagonal tiling of the wavenumber plane in order to show that thehexagonal grid is a more natural choice to emulate the isotropy of the Laplacian operator and the wave equation. Performance of the 7-point scheme on a hexagonal grid is better than pre...

  6. Option Pricing under Risk-Minimization Criterion in an Incomplete Market with the Finite Difference Method

    Directory of Open Access Journals (Sweden)

    Xinfeng Ruan


    Full Text Available We study option pricing with risk-minimization criterion in an incomplete market where the dynamics of the risky underlying asset is governed by a jump diffusion equation with stochastic volatility. We obtain the Radon-Nikodym derivative for the minimal martingale measure and a partial integro-differential equation (PIDE of European option. The finite difference method is employed to compute the European option valuation of PIDE.

  7. Transport and dispersion of pollutants in surface impoundments: a finite difference model

    Energy Technology Data Exchange (ETDEWEB)

    Yeh, G.T.


    A surface impoundment model by finite-difference (SIMFD) has been developed. SIMFD computes the flow rate, velocity field, and the concentration distribution of pollutants in surface impoundments with any number of islands located within the region of interest. Theoretical derivations and numerical algorithm are described in detail. Instructions for the application of SIMFD and listings of the FORTRAN IV source program are provided. Two sample problems are given to illustrate the application and validity of the model.

  8. Direct Calculation of Permeability by High-Accurate Finite Difference and Numerical Integration Methods

    KAUST Repository

    Wang, Yi


    Velocity of fluid flow in underground porous media is 6~12 orders of magnitudes lower than that in pipelines. If numerical errors are not carefully controlled in this kind of simulations, high distortion of the final results may occur [1-4]. To fit the high accuracy demands of fluid flow simulations in porous media, traditional finite difference methods and numerical integration methods are discussed and corresponding high-accurate methods are developed. When applied to the direct calculation of full-tensor permeability for underground flow, the high-accurate finite difference method is confirmed to have numerical error as low as 10-5% while the high-accurate numerical integration method has numerical error around 0%. Thus, the approach combining the high-accurate finite difference and numerical integration methods is a reliable way to efficiently determine the characteristics of general full-tensor permeability such as maximum and minimum permeability components, principal direction and anisotropic ratio. Copyright © Global-Science Press 2016.

  9. Mimetic finite difference method for the stokes problem on polygonal meshes

    Energy Technology Data Exchange (ETDEWEB)

    Lipnikov, K [Los Alamos National Laboratory; Beirao Da Veiga, L [DIPARTIMENTO DI MATE; Gyrya, V [PENNSYLVANIA STATE UNIV; Manzini, G [ISTIUTO DI MATEMATICA


    Various approaches to extend the finite element methods to non-traditional elements (pyramids, polyhedra, etc.) have been developed over the last decade. Building of basis functions for such elements is a challenging task and may require extensive geometry analysis. The mimetic finite difference (MFD) method has many similarities with low-order finite element methods. Both methods try to preserve fundamental properties of physical and mathematical models. The essential difference is that the MFD method uses only the surface representation of discrete unknowns to build stiffness and mass matrices. Since no extension inside the mesh element is required, practical implementation of the MFD method is simple for polygonal meshes that may include degenerate and non-convex elements. In this article, we develop a MFD method for the Stokes problem on arbitrary polygonal meshes. The method is constructed for tensor coefficients, which will allow to apply it to the linear elasticity problem. The numerical experiments show the second-order convergence for the velocity variable and the first-order for the pressure.

  10. Polarization effects on spectra of spherical core/shell nanostructures: Perturbation theory against finite difference approach

    Energy Technology Data Exchange (ETDEWEB)

    Ibral, Asmaa [Equipe d' Optique et Electronique du Solide, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida principale, El Jadida, Royaume du Maroc (Morocco); Laboratoire d' Instrumentation, Mesure et Contrôle, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida principale, El Jadida, Royaume du Maroc (Morocco); Zouitine, Asmaa [Département de Physique, Ecole Nationale Supérieure d' Enseignement Technique, Université Mohammed V Souissi, B. P. 6207 Rabat-Instituts, Rabat, Royaume du Maroc (Morocco); Assaid, El Mahdi, E-mail: [Equipe d' Optique et Electronique du Solide, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida principale, El Jadida, Royaume du Maroc (Morocco); Laboratoire d' Instrumentation, Mesure et Contrôle, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida principale, El Jadida, Royaume du Maroc (Morocco); and others


    Poisson equation is solved analytically in the case of a point charge placed anywhere in a spherical core/shell nanostructure, immersed in aqueous or organic solution or embedded in semiconducting or insulating matrix. Conduction and valence band-edge alignments between core and shell are described by finite height barriers. Influence of polarization charges induced at the surfaces where two adjacent materials meet is taken into account. Original expressions of electrostatic potential created everywhere in the space by a source point charge are derived. Expressions of self-polarization potential describing the interaction of a point charge with its own image–charge are deduced. Contributions of double dielectric constant mismatch to electron and hole ground state energies as well as nanostructure effective gap are calculated via first order perturbation theory and also by finite difference approach. Dependencies of electron, hole and gap energies against core to shell radii ratio are determined in the case of ZnS/CdSe core/shell nanostructure immersed in water or in toluene. It appears that finite difference approach is more efficient than first order perturbation method and that the effect of polarization charge may in no case be neglected as its contribution can reach a significant proportion of the value of nanostructure gap.

  11. A mimetic finite difference method for the Stokes problem with elected edge bubbles

    Energy Technology Data Exchange (ETDEWEB)

    Lipnikov, K [Los Alamos National Laboratory; Berirao, L [DIPARTMENTO DI MATERMATICA


    A new mimetic finite difference method for the Stokes problem is proposed and analyzed. The unstable P{sub 1}-P{sub 0} discretization is stabilized by adding a small number of bubble functions to selected mesh edges. A simple strategy for selecting such edges is proposed and verified with numerical experiments. The discretizations schemes for Stokes and Navier-Stokes equations must satisfy the celebrated inf-sup (or the LBB) stability condition. The stability condition implies a balance between discrete spaces for velocity and pressure. In finite elements, this balance is frequently achieved by adding bubble functions to the velocity space. The goal of this article is to show that the stabilizing edge bubble functions can be added only to a small set of mesh edges. This results in a smaller algebraic system and potentially in a faster calculations. We employ the mimetic finite difference (MFD) discretization technique that works for general polyhedral meshes and can accomodate non-uniform distribution of stabilizing bubbles.

  12. Composite scheme using localized relaxation with non-standard finite difference method for hyperbolic conservation laws (United States)

    Kumar, Vivek; Raghurama Rao, S. V.


    Non-standard finite difference methods (NSFDM) introduced by Mickens [ Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers-Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791-797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250-2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235-276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter ( λ) is chosen locally

  13. Comparison of finite-difference schemes for analysis of shells of revolution. [stress and free vibration analysis (United States)

    Noor, A. K.; Stephens, W. B.


    Several finite difference schemes are applied to the stress and free vibration analysis of homogeneous isotropic and layered orthotropic shells of revolution. The study is based on a form of the Sanders-Budiansky first-approximation linear shell theory modified such that the effects of shear deformation and rotary inertia are included. A Fourier approach is used in which all the shell stress resultants and displacements are expanded in a Fourier series in the circumferential direction, and the governing equations reduce to ordinary differential equations in the meridional direction. While primary attention is given to finite difference schemes used in conjunction with first order differential equation formulation, comparison is made with finite difference schemes used with other formulations. These finite difference discretization models are compared with respect to simplicity of application, convergence characteristics, and computational efficiency. Numerical studies are presented for the effects of variations in shell geometry and lamination parameters on the accuracy and convergence of the solutions obtained by the different finite difference schemes. On the basis of the present study it is shown that the mixed finite difference scheme based on the first order differential equation formulation and two interlacing grids for the different fundamental unknowns combines a number of advantages over other finite difference schemes previously reported in the literature.

  14. A study of unstable rock failures using finite difference and discrete element methods (United States)

    Garvey, Ryan J.

    Case histories in mining have long described pillars or faces of rock failing violently with an accompanying rapid ejection of debris and broken material into the working areas of the mine. These unstable failures have resulted in large losses of life and collapses of entire mine panels. Modern mining operations take significant steps to reduce the likelihood of unstable failure, however eliminating their occurrence is difficult in practice. Researchers over several decades have supplemented studies of unstable failures through the application of various numerical methods. The direction of the current research is to extend these methods and to develop improved numerical tools with which to study unstable failures in underground mining layouts. An extensive study is first conducted on the expression of unstable failure in discrete element and finite difference methods. Simulated uniaxial compressive strength tests are run on brittle rock specimens. Stable or unstable loading conditions are applied onto the brittle specimens by a pair of elastic platens with ranging stiffnesses. Determinations of instability are established through stress and strain histories taken for the specimen and the system. Additional numerical tools are then developed for the finite difference method to analyze unstable failure in larger mine models. Instability identifiers are established for assessing the locations and relative magnitudes of unstable failure through measures of rapid dynamic motion. An energy balance is developed which calculates the excess energy released as a result of unstable equilibria in rock systems. These tools are validated through uniaxial and triaxial compressive strength tests and are extended to models of coal pillars and a simplified mining layout. The results of the finite difference simulations reveal that the instability identifiers and excess energy calculations provide a generalized methodology for assessing unstable failures within potentially complex

  15. Finite difference modelling of dipole acoustic logs in a poroelastic formation with anisotropic permeability (United States)

    He, Xiao; Hu, Hengshan; Wang, Xiuming


    Sedimentary rocks can exhibit strong permeability anisotropy due to layering, pre-stresses and the presence of aligned microcracks or fractures. In this paper, we develop a modified cylindrical finite-difference algorithm to simulate the borehole acoustic wavefield in a saturated poroelastic medium with transverse isotropy of permeability and tortuosity. A linear interpolation process is proposed to guarantee the leapfrog finite difference scheme for the generalized dynamic equations and Darcy's law for anisotropic porous media. First, the modified algorithm is validated by comparison against the analytical solution when the borehole axis is parallel to the symmetry axis of the formation. The same algorithm is then used to numerically model the dipole acoustic log in a borehole with its axis being arbitrarily deviated from the symmetry axis of transverse isotropy. The simulation results show that the amplitudes of flexural modes vary with the dipole orientation because the permeability tensor of the formation is dependent on the wellbore azimuth. It is revealed that the attenuation of the flexural wave increases approximately linearly with the radial permeability component in the direction of the transmitting dipole. Particularly, when the borehole axis is perpendicular to the symmetry axis of the formation, it is possible to estimate the anisotropy of permeability by evaluating attenuation of the flexural wave using a cross-dipole sonic logging tool according to the results of sensitivity analyses. Finally, the dipole sonic logs in a deviated borehole surrounded by a stratified porous formation are modelled using the proposed finite difference code. Numerical results show that the arrivals and amplitudes of transmitted flexural modes near the layer interface are sensitive to the wellbore inclination.

  16. Cell-centered diffusion schemes for Lagrangian radiation hydrodynamics on nonmatched polygonal meshes (United States)

    Liu, Xuezhe; Lin, Zhong; Wang, Ruili


    A cell-centered finite volume scheme to solve diffusion equations on nonmatched meshes which result from the hydrodynamics calculation with slide line treatment is presented. The sliding meshes near the interface are handled as arbitrary polygons together with the internal ones and the hanging nodes can be considered naturally as the vertices of the polygon. A robust and accurate interpolation method based on Taylor expansion is proposed to eliminate the node unknowns including the ones at the hanging nodes.

  17. Simulation of acoustic streaming by means of the finite-difference time-domain method

    DEFF Research Database (Denmark)

    Santillan, Arturo Orozco


    Numerical simulations of acoustic streaming generated by a standing wave in a narrow twodimensional cavity are presented. In this case, acoustic streaming arises from the viscous boundary layers set up at the surfaces of the walls. It is known that streaming vortices inside the boundary layer have...... the finite-difference time-domain method. To simplify the problem, thermal effects are not considered. The motivation of the described investigation has been the possibility of using the numerical method to study acoustic streaming, particularly under non-steady conditions. Results are discussed for channels...

  18. Explicit finite-difference simulation of optical integrated devices on massive parallel computers. (United States)

    Sterkenburgh, T; Michels, R M; Dress, P; Franke, H


    An explicit method for the numerical simulation of optical integrated circuits by means of the finite-difference time-domain (FDTD) method is presented. This method, based on an explicit solution of Maxwell's equations, is well established in microwave technology. Although the simulation areas are small, we verified the behavior of three interesting problems, especially nonparaxial problems, with typical aspects of integrated optical devices. Because numerical losses are within acceptable limits, we suggest the use of the FDTD method to achieve promising quantitative simulation results.

  19. On the convergence of certain finite-difference schemes by an inverse-matrix method (United States)

    Steger, J. L.; Warming, R. F.


    The inverse-matrix method of analyzing the convergence of the solution of a given system of finite-difference equations to the solution of the corresponding system of partial-differential equations is discussed and generalized. The convergence properties of a time- and space-centered differencing of the diffusion equation are analyzed as well as a staggered grid differencing of the Cauchy-Riemann equations. These two schemes are significant since they serve as simplified model algorithms for two recently developed methods used to calculate nonlinear aerodynamic flows.

  20. Finite Difference Time-Domain Modelling of Metamaterials: GPU Implementation of Cylindrical Cloak

    Directory of Open Access Journals (Sweden)

    A. Dawood


    Full Text Available Finite difference time-domain (FDTD technique can be used to model metamaterials by treating them as dispersive material. Drude or Lorentz model can be incorporated into the standard FDTD algorithm for modelling negative permittivity and permeability. FDTD algorithm is readily parallelisable and can take advantage of GPU acceleration to achieve speed-ups of 5x-50x depending on hardware setup. Metamaterial scattering problems are implemented using dispersive FDTD technique on GPU resulting in performance gain of 10x-15x compared to conventional CPU implementation.

  1. Arbitrary Order Mixed Mimetic Finite Differences Method with Nodal Degrees of Freedom

    Energy Technology Data Exchange (ETDEWEB)

    Iaroshenko, Oleksandr [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Gyrya, Vitaliy [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Manzini, Gianmarco [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)


    In this work we consider a modification to an arbitrary order mixed mimetic finite difference method (MFD) for a diffusion equation on general polygonal meshes [1]. The modification is based on moving some degrees of freedom (DoF) for a flux variable from edges to vertices. We showed that for a non-degenerate element this transformation is locally equivalent, i.e. there is a one-to-one map between the new and the old DoF. Globally, on the other hand, this transformation leads to a reduction of the total number of degrees of freedom (by up to 40%) and additional continuity of the discrete flux.

  2. Calculating modes of quantum wire systems using a finite difference technique

    Directory of Open Access Journals (Sweden)

    T Mardani


    Full Text Available  In this paper, the Schrodinger equation for a quantum wire is solved using a finite difference approach. A new aspect in this work is plotting wave function on cross section of rectangular cross-sectional wire in two dimensions, periodically. It is found that the correct eigen energies occur when wave functions have a complete symmetry. If the value of eigen energy has a small increase or decrease in neighborhood of the correct energy the symmetry will be destroyed and aperturbation value at the first of wave function will be observed. In addition, the demand on computer memory varies linearly with the size of the system under investigation.

  3. Varieties of operator manipulation. [for solving differential equations and calculating finite differences (United States)

    Doohovskoy, A.


    A change in MACSYMA syntax is proposed to accommodate the operator manipulators necessary to implement direct and indirect methods for the solution of differential equations, calculus of finite differences, and the fractional calculus, as well as their modern counterparts. To illustrate the benefits and convenience of this syntax extension, an example is given to show how MACSYMA's pattern-matching capability can be used to implement a particular set of operator identities which can then be used to obtain exact solutions to nonlinear differential equations.

  4. Finite-difference solution for turbulent swirling compressible flow in axisymmetric ducts with struts (United States)

    Anderson, O. L.


    A finite-difference procedure for computing the turbulent, swirling, compressible flow in axisymmetric ducts is described. Arbitrary distributions of heat and mass transfer at the boundaries can be treated, and the effects of struts, inlet guide vanes, and flow straightening vanes can be calculated. The calculation procedure is programmed in FORTRAN 4 and has operated successfully on the UNIVAC 1108, IBM 360, and CDC 6600 computers. The analysis which forms the basis of the procedure, a detailed description of the computer program, and the input/output formats are presented. The results of sample calculations performed with the computer program are compared with experimental data.

  5. Scattering analysis of periodic structures using finite-difference time-domain

    CERN Document Server

    ElMahgoub, Khaled; Elsherbeni, Atef Z


    Periodic structures are of great importance in electromagnetics due to their wide range of applications such as frequency selective surfaces (FSS), electromagnetic band gap (EBG) structures, periodic absorbers, meta-materials, and many others. The aim of this book is to develop efficient computational algorithms to analyze the scattering properties of various electromagnetic periodic structures using the finite-difference time-domain periodic boundary condition (FDTD/PBC) method. A new FDTD/PBC-based algorithm is introduced to analyze general skewed grid periodic structures while another algor

  6. Finite-difference time domain solution of light scattering by arbitrarily shaped particles and surfaces

    DEFF Research Database (Denmark)

    Tanev, Stoyan; Sun, Wenbo


    This chapter reviews the fundamental methods and some of the applications of the three-dimensional (3D) finite-difference time-domain (FDTD) technique for the modeling of light scattering by arbitrarily shaped dielectric particles and surfaces. The emphasis is on the details of the FDTD algorithms...... for particle and surface scattering calculations and the uniaxial perfectly matched layer (UPML) absorbing boundary conditions for truncation of the FDTD grid. We show that the FDTD approach has a significant potential for studying the light scattering by cloud, dust, and biological particles. The applications...... of the FDTD approach for beam scattering by arbitrarily shaped surfaces are also discussed....

  7. A note on the stability and accuracy of finite difference approximations to differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Cloutman, L.D.


    There are many finite difference approximations to ordinary and partial differential equations, and these vary in their accuracy and stability properties. We examine selected commonly used methods and illustrate their stability and accuracy using both linear stability analysis and numerical examples. We find that the formal order of accuracy alone gives an incomplete picture of the accuracy of the method. Specifically, the Adams-Bashforth and Crank-Nicholson methods are shown to have some undesirable features for both ordinary and partial differential equations.

  8. Positivity-preserving High Order Finite Difference WENO Schemes for Compressible Euler Equations (United States)


    schemes are preferred, for example, cosmological simulation [5], finite difference WENO scheme [10] is more favored than DG schemes [2, 3] and the...densities, Journal of Computational Physics, 92 (1991), 273-295. [5] L.-L. Feng, C.-W. Shu and M. Zhang, A hybrid cosmological hydrodynamic/N-body code...Cockburn, C. Johnson, C.-W. Shu and E. Tadmor (Editor: A. Quarteroni), Lecture Notes in Mathematics, Springer, 1697 (1998), 325-432. [16] C.-W. Shu and S

  9. WONDY V: a one-dimensional finite-difference wave-propagation code

    Energy Technology Data Exchange (ETDEWEB)

    Kipp, M.E.; Lawrence, R.J.


    WONDY V solves the finite difference analogs to the Lagrangian equations of motion in one spatial dimension (planar, cylindrical, or spherical). Simulations of explosive detonation, energy deposition, plate impact, and dynamic fracture are possible, using a variety of existing material models. In addition, WONDY has proven to be a powerful tool in the evaluation of new constitutive models. A preprocessor is available to allocate storage arrays commensurate with problem size, and automatic rezoning may be employed to improve resolution. This document provides a description of the equations solved, available material models, operating instructions, and sample problems.

  10. Accuracy of spectral and finite difference schemes in 2D advection problems

    DEFF Research Database (Denmark)

    Naulin, V.; Nielsen, A.H.


    In this paper we investigate the accuracy of two numerical procedures commonly used to solve 2D advection problems: spectral and finite difference (FD) schemes. These schemes are widely used, simulating, e.g., neutral and plasma flows. FD schemes have long been considered fast, relatively easy...... that the accuracy of FD schemes can be significantly improved if one is careful in choosing an appropriate FD scheme that reflects conservation properties of the nonlinear terms and in setting up the grid in accordance with the problem....

  11. High-order asynchrony-tolerant finite difference schemes for partial differential equations (United States)

    Aditya, Konduri; Donzis, Diego A.


    Synchronizations of processing elements (PEs) in massively parallel simulations, which arise due to communication or load imbalances between PEs, significantly affect the scalability of scientific applications. We have recently proposed a method based on finite-difference schemes to solve partial differential equations in an asynchronous fashion - synchronization between PEs is relaxed at a mathematical level. While standard schemes can maintain their stability in the presence of asynchrony, their accuracy is drastically affected. In this work, we present a general methodology to derive asynchrony-tolerant (AT) finite difference schemes of arbitrary order of accuracy, which can maintain their accuracy when synchronizations are relaxed. We show that there are several choices available in selecting a stencil to derive these schemes and discuss their effect on numerical and computational performance. We provide a simple classification of schemes based on the stencil and derive schemes that are representative of different classes. Their numerical error is rigorously analyzed within a statistical framework to obtain the overall accuracy of the solution. Results from numerical experiments are used to validate the performance of the schemes.

  12. A finite difference method for space fractional differential equations with variable diffusivity coefficient

    KAUST Repository

    Mustapha, K.


    Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially more difficult the mathematical analysis of these models and the establishment of suitable numerical schemes. This paper proposes and analyzes the first finite difference method for solving {\\\\em variable-coefficient} fractional differential equations, with two-sided fractional derivatives, in one-dimensional space. The proposed scheme combines first-order forward and backward Euler methods for approximating the left-sided fractional derivative when the right-sided fractional derivative is approximated by two consecutive applications of the first-order backward Euler method. Our finite difference scheme reduces to the standard second-order central difference scheme in the absence of fractional derivatives. The existence and uniqueness of the solution for the proposed scheme are proved, and truncation errors of order $h$ are demonstrated, where $h$ denotes the maximum space step size. The numerical tests illustrate the global $O(h)$ accuracy of our scheme, except for nonsmooth cases which, as expected, have deteriorated convergence rates.

  13. On the Definition of Surface Potentials for Finite-Difference Operators (United States)

    Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)


    For a class of linear constant-coefficient finite-difference operators of the second order, we introduce the concepts similar to those of conventional single- and double-layer potentials for differential operators. The discrete potentials are defined completely independently of any notion related to the approximation of the continuous potentials on the grid. We rather use all approach based on differentiating, and then inverting the differentiation of a function with surface discontinuity of a particular kind, which is the most general way of introducing surface potentials in the theory of distributions. The resulting finite-difference "surface" potentials appear to be solutions of the corresponding continuous potentials. Primarily, this pertains to the possibility of representing a given solution to the homogeneous equation on the domain as a variety of surface potentials, with the density defined on the domain's boundary. At the same time the discrete surface potentials can be interpreted as one specific realization of the generalized potentials of Calderon's type, and consequently, their approximation properties can be studied independently in the framework of the difference potentials method by Ryaben'kii. The motivation for introducing and analyzing the discrete surface potentials was provided by the problems of active shielding and control of sound, in which the aforementioned source terms that drive the potentials are interpreted as the acoustic control sources that cancel out the unwanted noise on a predetermined region of interest.

  14. Ground motion simulations in Marmara (Turkey) region from 3D finite difference method (United States)

    Aochi, Hideo; Ulrich, Thomas; Douglas, John


    In the framework of the European project MARSite (2012-2016), one of the main contributions from our research team was to provide ground-motion simulations for the Marmara region from various earthquake source scenarios. We adopted a 3D finite difference code, taking into account the 3D structure around the Sea of Marmara (including the bathymetry) and the sea layer. We simulated two moderate earthquakes (about Mw4.5) and found that the 3D structure improves significantly the waveforms compared to the 1D layer model. Simulations were carried out for different earthquakes (moderate point sources and large finite sources) in order to provide shake maps (Aochi and Ulrich, BSSA, 2015), to study the variability of ground-motion parameters (Douglas & Aochi, BSSA, 2016) as well as to provide synthetic seismograms for the blind inversion tests (Diao et al., GJI, 2016). The results are also planned to be integrated in broadband ground-motion simulations, tsunamis generation and simulations of triggered landslides (in progress by different partners). The simulations are freely shared among the partners via the internet and the visualization of the results is diffused on the project's homepage. All these simulations should be seen as a reference for this region, as they are based on the latest knowledge that obtained during the MARSite project, although their refinement and validation of the model parameters and the simulations are a continuing research task relying on continuing observations. The numerical code used, the models and the simulations are available on demand.

  15. Application of a trigonometric finite difference procedure to numerical analysis of compressive and shear buckling of orthotropic panels (United States)

    Stein, M.; Housner, J. D.


    A numerical analysis developed for the buckling of rectangular orthotropic layered panels under combined shear and compression is described. This analysis uses a central finite difference procedure based on trigonometric functions instead of using the conventional finite differences which are based on polynomial functions. Inasmuch as the buckle mode shape is usually trigonometric in nature, the analysis using trigonometric finite differences can be made to exhibit a much faster convergence rate than that using conventional differences. Also, the trigonometric finite difference procedure leads to difference equations having the same form as conventional finite differences; thereby allowing available conventional finite difference formulations to be converted readily to trigonometric form. For two-dimensional problems, the procedure introduces two numerical parameters into the analysis. Engineering approaches for the selection of these parameters are presented and the analysis procedure is demonstrated by application to several isotropic and orthotropic panel buckling problems. Among these problems is the shear buckling of stiffened isotropic and filamentary composite panels in which the stiffener is broken. Results indicate that a break may degrade the effect of the stiffener to the extent that the panel will not carry much more load than if the stiffener were absent.

  16. Modified Finite Difference Schemes on Uniform Grids for Simulations of the Helmholtz Equation at Any Wave Number

    Directory of Open Access Journals (Sweden)

    Hafiz Abdul Wajid


    Full Text Available We construct modified forward, backward, and central finite difference schemes, specifically for the Helmholtz equation, by using the Bloch wave property. All of these modified finite difference approximations provide exact solutions at the nodes of the uniform grid for the second derivative present in the Helmholtz equation and the first derivative in the radiation boundary conditions for wave propagation. The most important feature of the modified schemes is that they work for large as well as low wave numbers, without the common requirement of a very fine mesh size. The superiority of the modified finite difference schemes is illustrated with the help of numerical examples by making a comparison with standard finite difference schemes.

  17. A parameter-robust finite difference method for singularly perturbed delay parabolic partial differential equations (United States)

    Ansari, A. R.; Bakr, S. A.; Shishkin, G. I.


    A Dirichlet boundary value problem for a delay parabolic differential equation is studied on a rectangular domain in the x-t plane. The second-order space derivative is multiplied by a small singular perturbation parameter, which gives rise to parabolic boundary layers on the two lateral sides of the rectangle. A numerical method comprising a standard finite difference operator (centred in space, implicit in time) on a rectangular piecewise uniform fitted mesh of NxxNt elements condensing in the boundary layers is proved to be robust with respect to the small parameter, or parameter-uniform, in the sense that its numerical solutions converge in the maximum norm to the exact solution uniformly well for all values of the parameter in the half-open interval (0,1]. More specifically, it is shown that the errors are bounded in the maximum norm by , where C is a constant independent not only of Nx and Nt but also of the small parameter. Numerical results are presented, which validate numerically this theoretical result and show that a numerical method consisting of the standard finite difference operator on a uniform mesh of NxxNt elements is not parameter-robust.

  18. Physical and numerical constraints in source modeling for finite difference simulation of room acoustics. (United States)

    Sheaffer, Jonathan; van Walstijn, Maarten; Fazenda, Bruno


    In finite difference time domain simulation of room acoustics, source functions are subject to various constraints. These depend on the way sources are injected into the grid and on the chosen parameters of the numerical scheme being used. This paper addresses the issue of selecting and designing sources for finite difference simulation, by first reviewing associated aims and constraints, and evaluating existing source models against these criteria. The process of exciting a model is generalized by introducing a system of three cascaded filters, respectively, characterizing the driving pulse, the source mechanics, and the injection of the resulting source function into the grid. It is shown that hard, soft, and transparent sources can be seen as special cases within this unified approach. Starting from the mechanics of a small pulsating sphere, a parametric source model is formulated by specifying suitable filters. This physically constrained source model is numerically consistent, does not scatter incoming waves, and is free from zero- and low-frequency artifacts. Simulation results are employed for comparison with existing source formulations in terms of meeting the spectral and temporal requirements on the outward propagating wave.

  19. A fast referenceless PRFS-based MR thermometry by phase finite difference (United States)

    Zou, Chao; Shen, Huan; He, Mengyue; Tie, Changjun; Chung, Yiu-Cho; Liu, Xin


    Proton resonance frequency shift-based MR thermometry is a promising temperature monitoring approach for thermotherapy but its accuracy is vulnerable to inter-scan motion. Model-based referenceless thermometry has been proposed to address this problem but phase unwrapping is usually needed before the model fitting process. In this paper, a referenceless MR thermometry method using phase finite difference that avoids the time consuming phase unwrapping procedure is proposed. Unlike the previously proposed phase gradient technique, the use of finite difference in the new method reduces the fitting error resulting from the ringing artifacts associated with phase discontinuity in the calculation of the phase gradient image. The new method takes into account the values at the perimeter of the region of interest because of their direct relevance to the extrapolated baseline phase of the region of interest (where temperature increase takes place). In simulation study, in vivo and ex vivo experiments, the new method has a root-mean-square temperature error of 0.35 °C, 1.02 °C and 1.73 °C compared to 0.83 °C, 2.81 °C, and 3.76 °C from the phase gradient method, respectively. The method also demonstrated a slightly higher, albeit small, temperature accuracy than the original referenceless MR thermometry method. The proposed method is computationally efficient (∼0.1 s per image), making it very suitable for the real time temperature monitoring.

  20. Biomechanical three-dimensional finite element analysis of monolithic zirconia crown with different cement type (United States)


    PURPOSE The objective of this study was to evaluate the influence of various cement types on the stress distribution in monolithic zirconia crowns under maximum bite force using the finite element analysis. MATERIALS AND METHODS The models of the prepared #46 crown (deep chamfer margin) were scanned and solid models composed of the monolithic zirconia crown, cement layer, and prepared tooth were produced using the computer-aided design technology and were subsequently translated into 3-dimensional finite element models. Four models were prepared according to different cement types (zinc phosphate, polycarboxylate, glass ionomer, and resin). A load of 700 N was applied vertically on the crowns (8 loading points). Maximum principal stress was determined. RESULTS Zinc phosphate cement had a greater stress concentration in the cement layer, while polycarboxylate cement had a greater stress concentration on the distal surface of the monolithic zirconia crown and abutment tooth. Resin cement and glass ionomer cement showed similar patterns, but resin cement showed a lower stress distribution on the lingual and mesial surface of the cement layer. CONCLUSION The test results indicate that the use of different luting agents that have various elastic moduli has an impact on the stress distribution of the monolithic zirconia crowns, cement layers, and abutment tooth. Resin cement is recommended for the luting agent of the monolithic zirconia crowns. PMID:26816578


    Directory of Open Access Journals (Sweden)

    Nuraini Nuraini


    Full Text Available Abstract. Modeling the dynamics of seawater typically uses a shallow water model. The shallow water model is derived from the mass conservation equation and the momentum set into shallow water equations. A two-dimensional shallow water equation alongside the model that is integrated with depth is described in numerical form. This equation can be solved by finite different methods either explicitly or implicitly. In this modeling, the two dimensional shallow water equations are described in discrete form using explicit schemes. Keyword: shallow water equation, finite difference and schema explisit. REFERENSI  1. Bunya, S., Westerink, J. J. dan Yoshimura. 2005. Discontinuous Boundary Implementation for the Shallow Water Equations. Int. J. Numer. Meth. Fluids. 47: 1451-1468. 2. Kampf Jochen. 2009. Ocean Modelling For Beginners. Springer Heidelberg Dordrecht. London New York. 3. Rezolla, L 2011. Numerical Methods for the Solution of Partial Diferential Equations. Trieste. International Schoolfor Advanced Studies. 4. Natakussumah, K. D., Kusuma, S. B. M., Darmawan, H., Adityawan, B. M. Dan  Farid, M. 2007. Pemodelan Hubungan Hujan dan Aliran Permukaan pada Suatu DAS  dengan Metode Beda Hingga. ITB Sain dan Tek. 39: 97-123. 5. Casulli, V. dan Walters, A. R. 2000. An unstructured grid, three-dimensional model based on the shallow water equations. Int. J. Numer. Meth. Fluids. 32: 331-348. 6. Triatmodjo, B. 2002. Metode Numerik  Beta Offset. Yogyakarta.

  2. ATLAS: A Real-Space Finite-Difference Implementation of Orbital-Free Density Functional Theory

    CERN Document Server

    Mi, Wenhui; Sua, Chuanxun; Zhoua, Yuanyuan; Zhanga, Shoutao; Lia, Quan; Wanga, Hui; Zhang, Lijun; Miao, Maosheng; Wanga, Yanchao; Ma, Yanming


    Orbital-free density functional theory (OF-DFT) is a promising method for large-scale quantum mechanics simulation as it provides a good balance of accuracy and computational cost. Its applicability to large-scale simulations has been aided by progress in constructing kinetic energy functionals and local pseudopotentials. However, the widespread adoption of OF-DFT requires further improvement in its efficiency and robustly implemented software. Here we develop a real-space finite-difference method for the numerical solution of OF-DFT in periodic systems. Instead of the traditional self-consistent method, a powerful scheme for energy minimization is introduced to solve the Euler--Lagrange equation. Our approach engages both the real-space finite-difference method and a direct energy-minimization scheme for the OF-DFT calculations. The method is coded into the ATLAS software package and benchmarked using periodic systems of solid Mg, Al, and Al$_{3}$Mg. The test results show that our implementation can achieve ...

  3. Finite element analysis of stress distribution in four different endodontic post systems in a model canine. (United States)

    Chen, Aijie; Feng, Xiaoli; Zhang, Yanli; Liu, Ruoyu; Shao, Longquan


    To investigate the stress distribution in a maxillary canine restored with each of four different post systems at different levels of alveolar bone loss. Two-dimensional finite element analysis (FEA) was performed by modeling a severely damaged canine with four different post systems: CAD/CAM zirconia, CAD/CAM glass fiber, cast titanium, and cast gold. A force of 100 N was applied to the crown, and the von Mises stresses were obtained. FEA revealed that the CAD/CAM zirconia post system produced the lowest maximum von Mises stress in the dentin layer at 115.8 MPa, while the CAD/CAM glass fiber post produced the highest stress in the dentin at 518.2 MPa. For a severely damaged anterior tooth, a zirconia post system is the best choice while a cast gold post ranks second. The CAD/CAM glass fiber post is least recommended in terms of stress level in the dentin.

  4. Transfer-matrix approach for finite-difference time-domain simulation of periodic structures. (United States)

    Deinega, Alexei; Belousov, Sergei; Valuev, Ilya


    Optical properties of periodic structures can be calculated using the transfer-matrix approach, which establishes a relation between amplitudes of the wave incident on a structure with transmitted or reflected waves. The transfer matrix can be used to obtain transmittance and reflectance spectra of finite periodic structures as well as eigenmodes of infinite structures. Traditionally, calculation of the transfer matrix is performed in the frequency domain and involves linear algebra. In this work, we present a technique for calculation of the transfer matrix using the finite-difference time-domain (FDTD) method and show the way of its implementation in FDTD code. To illustrate the performance of our technique we calculate the transmittance spectra for opal photonic crystal slabs consisting of multiple layers of spherical scatterers. Our technique can be used for photonic band structure calculations. It can also be combined with existing FDTD methods for the analysis of periodic structures at an oblique incidence, as well as for modeling point sources in a periodic environment.

  5. Finite element modelling of Plantar Fascia response during running on different surface types (United States)

    Razak, A. H. A.; Basaruddin, K. S.; Salleh, A. F.; Rusli, W. M. R.; Hashim, M. S. M.; Daud, R.


    Plantar fascia is a ligament found in human foot structure located beneath the skin of human foot that functioning to stabilize longitudinal arch of human foot during standing and normal gait. To perform direct experiment on plantar fascia seems very difficult since the structure located underneath the soft tissue. The aim of this study is to develop a finite element (FE) model of foot with plantar fascia and investigate the effect of the surface hardness on biomechanical response of plantar fascia during running. The plantar fascia model was developed using Solidworks 2015 according to the bone structure of foot model that was obtained from Turbosquid database. Boundary conditions were set out based on the data obtained from experiment of ground reaction force response during running on different surface hardness. The finite element analysis was performed using Ansys 14. The results found that the peak of stress and strain distribution were occur on the insertion of plantar fascia to bone especially on calcaneal area. Plantar fascia became stiffer with increment of Young’s modulus value and was able to resist more loads. Strain of plantar fascia was decreased when Young’s modulus increased with the same amount of loading.

  6. Solution to PDEs using radial basis function finite-differences (RBF-FD) on multiple GPUs

    Energy Technology Data Exchange (ETDEWEB)

    Bollig, Evan F., E-mail: [Department of Scientific Computing, Florida State University, 400 Dirac Science Library, Tallahassee, FL 32306 (United States); Flyer, Natasha, E-mail: [Institute for Mathematics Applied to Geosciences, National Center for Atmospheric Research, 1850 Table Mesa Dr., Boulder, CO 80305 (United States); Erlebacher, Gordon, E-mail: [Department of Scientific Computing, Florida State University, 400 Dirac Science Library, Tallahassee, FL 32306 (United States)


    This paper presents parallelization strategies for the radial basis function-finite difference (RBF-FD) method. As a generalized finite differencing scheme, the RBF-FD method functions without the need for underlying meshes to structure nodes. It offers high-order accuracy approximation and scales as O(N) per time step, with N being with the total number of nodes. To our knowledge, this is the first implementation of the RBF-FD method to leverage GPU accelerators for the solution of PDEs. Additionally, this implementation is the first to span both multiple CPUs and multiple GPUs. OpenCL kernels target the GPUs and inter-processor communication and synchronization is managed by the Message Passing Interface (MPI). We verify our implementation of the RBF-FD method with two hyperbolic PDEs on the sphere, and demonstrate up to 9x speedup on a commodity GPU with unoptimized kernel implementations. On a high performance cluster, the method achieves up to 7x speedup for the maximum problem size of 27,556 nodes.

  7. On the computational noise of finite-difference schemes used in ocean models (United States)

    Batteen, M. L.; Han, Y.-J.


    Different distributions of variables over the horizontal array of grid points in an ocean circulation model are investigated, using the shallow water equations as a guide in the choice of finite-difference schemes for use in ocean modeling. It is shown that the scheme with diffusive dissipation, in which the horizontal velocity is carried at the center and the height field is carried at each corner of a rectangular grid, successively suppresses numerical noise in a coarse (greater than 100 km) grid ocean model. For resolutions smaller than 50 km, it is shown that the scheme in which zonal velocity is carried at points to the east and west of the point of a rectangular grid where the height is carried, with meridional velocity carried to the north and south of the height point, can be free of noise for the gravest mode.

  8. A two-dimensional finite difference solution for the transient thermal behavior of tubular solar collector (United States)

    Lansing, F. L.


    A numerical procedure was established using the finite-difference technique in the determination of the time-varying temperature distribution of a tubular solar collector under changing solar radiancy and ambient temperature. Three types of spatial discretization processes were considered and compared for their accuracy of computations and for selection of the shortest computer time and cost. The stability criteria of this technique was analyzed in detail to give the critical time increment to ensure stable computations. The results of the numerical analysis were in good agreement with the analytical solution previously reported. The numerical method proved to be a powerful tool in the investigation of the collector sensitivity to two different flow patterns and several flow control mechanisms.

  9. Exact finite-size corrections for the spanning-tree model under different boundary conditions (United States)

    Izmailian, N. Sh.; Kenna, R.


    We express the partition functions of the spanning tree on finite square lattices under five different sets of boundary conditions in terms of a principal partition function with twisted-boundary conditions. Based on these expressions, we derive the exact asymptotic expansions of the logarithm of the partition function for each case. We have also established several groups of identities relating spanning-tree partition functions for the different boundary conditions. We also explain an apparent discrepancy between logarithmic correction terms in the free energy for a two-dimensional spanning-tree model with periodic and free-boundary conditions and conformal field theory predictions. We have obtained corner free energy for the spanning tree under free-boundary conditions in full agreement with conformal field theory predictions.

  10. Linear and nonlinear Stability analysis for finite difference discretizations of higher order Boussinesq equations

    DEFF Research Database (Denmark)

    Fuhrmann, David R.; Bingham, Harry B.; Madsen, Per A.


    This paper considers a method of lines stability analysis for finite difference discretizations of a recently published Boussinesq method for the study of highly nonlinear and extremely dispersive water waves. The analysis demonstrates the near-equivalence of classical linear Fourier (von Neumann......) techniques with matrix-based methods for formulations in both one and two horizontal dimensions. The matrix-based method is also extended to show the local de-stabilizing effects of the nonlinear terms, as well as the stabilizing effects of numerical dissipation. A comparison of the relative stability...... of rotational and irrotational formulations in two horizontal dimensions provides evidence that the irrotational formulation has significantly better stability properties when the deep-water nonlinearity is high, particularly on refined grids. Computation of matrix pseudospectra shows that the system is only...

  11. Efficient ferromagnetic core impedance model with application to finite-difference time-domain simulation

    Directory of Open Access Journals (Sweden)

    T. C. Genoni


    Full Text Available A frequency-dependent impedance model for laminated ferromagnetic cores is presented and analyzed. The model assumes a multiple-winding ferromagnetic induction core composed of multiple thin layers with linear material response. This model builds on the analysis presented by Rose et al. [Phys. Rev. ST Accel. Beams 13, 090401 (2010PRABFM1098-440210.1103/PhysRevSTAB.13.090401], that determined an equivalent time-dependent resistance that was used to successfully model the loss currents in a linear transformer device cavity containing ferromagnetic cores. The new core impedance model is more general and has been implemented as a surface-impedance boundary condition [K. S. Oh and J. E. Schutt-Aine, IEEE Trans. Antennas Propag. 43, 660 (1995IETPAK0018-926X10.1109/8.391136] which is suitable for use in multidimensional finite-difference time-domain codes.

  12. Full-wave finite-difference time-domain simulation of electromagnetic cloaking structures. (United States)

    Zhao, Yan; Argyropoulos, Christos; Hao, Yang


    This paper proposes a radial dependent dispersive finite-difference time-domain method for the modeling of electromagnetic cloaking structures. The permittivity and permeability of the cloak are mapped to the Drude dispersion model and taken into account in dispersive FDTD simulations. Numerical simulations demonstrate that under ideal conditions, objects placed inside the cloak are 'invisible' to external electromagnetic fields. However for the simplified cloak based on linear transformations, the back scattering has a similar level to the case of a PEC cylinder without any cloak, rendering the object still being 'visible'. It is also demonstrated numerically that the simplified cloak based on high-order transformations can indeed improve the cloaking performance.

  13. Solution of the Porous Media Equation by a Compact Finite Difference Method

    Directory of Open Access Journals (Sweden)

    Murat Sari


    Full Text Available Accurate solutions of the porous media equation that usually occurs in nonlinear problems of heat and mass transfer and in biological systems are obtained using a compact finite difference method in space and a low-storage total variation diminishing third-order Runge-Kutta scheme in time. In the calculation of the numerical derivatives, only a tridiagonal band matrix algorithm is encountered. Therefore, this scheme causes to less accumulation of numerical errors and less use of storage space. The computed results obtained by this way have been compared with the exact solutions to show the accuracy of the method. The approximate solutions to the equation have been computed without transforming the equation and without using linearization. Comparisons indicate that there is a very good agreement between the numerical solutions and the exact solutions in terms of accuracy. This method is seen to be a very good alternative method to some existing techniques for such realistic problems.

  14. Black-Scholes finite difference modeling in forecasting of call warrant prices in Bursa Malaysia (United States)

    Mansor, Nur Jariah; Jaffar, Maheran Mohd


    Call warrant is a type of structured warrant in Bursa Malaysia. It gives the holder the right to buy the underlying share at a specified price within a limited period of time. The issuer of the structured warrants usually uses European style to exercise the call warrant on the maturity date. Warrant is very similar to an option. Usually, practitioners of the financial field use Black-Scholes model to value the option. The Black-Scholes equation is hard to solve analytically. Therefore the finite difference approach is applied to approximate the value of the call warrant prices. The central in time and central in space scheme is produced to approximate the value of the call warrant prices. It allows the warrant holder to forecast the value of the call warrant prices before the expiry date.

  15. Dispersive finite-difference time-domain (FDTD) analysis of the elliptic cylindrical cloak

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Y. Y.; Ahn, D. [University of Seoul, Seoul (Korea, Republic of)


    A dispersive full-wave finite-difference time-domain (FDTD) model is used to calculate the performance of elliptic cylindrical cloaking devices. The permittivity and the permeability tensors for the cloaking structure are derived by using an effective medium approach in general relativity. The elliptic cylindrical invisibility devices are found to show imperfect cloaking, and the cloaking performance is found to depend on the polarization of the incident waves, the direction of the propagation of those waves, the semi-focal distances and the loss tangents of the meta-material. When the semifocal distance of the elliptic cylinder decreases, the performance of the cloaking becomes very good, with neither noticeable scatterings nor field penetrations. For a larger semi-focal distance, only the TM wave with a specific propagation direction shows good cloaking performance. Realistic cloaking materials with loss still show a cloak that is working, but attenuated back-scattering waves exist.

  16. Finite-Difference Simulation of Elastic Wave with Separation in Pure P- and S-Modes

    Directory of Open Access Journals (Sweden)

    Ke-Yang Chen


    Full Text Available Elastic wave equation simulation offers a way to study the wave propagation when creating seismic data. We implement an equivalent dual elastic wave separation equation to simulate the velocity, pressure, divergence, and curl fields in pure P- and S-modes, and apply it in full elastic wave numerical simulation. We give the complete derivations of explicit high-order staggered-grid finite-difference operators, stability condition, dispersion relation, and perfectly matched layer (PML absorbing boundary condition, and present the resulting discretized formulas for the proposed elastic wave equation. The final numerical results of pure P- and S-modes are completely separated. Storage and computing time requirements are strongly reduced compared to the previous works. Numerical testing is used further to demonstrate the performance of the presented method.

  17. Implementation of the asymptotic corrugation boundary condition in the finite difference time domain method (United States)

    Simon, Andrew E.; Kishk, Ahmed A.


    Geometry description in the finite difference time domain method is a tedious task if the geometry contains fine details, such as the case of corrugated objects. Such fine details constrain the cell size. The corrugated object can be modeled using the asymptotic corrugation boundary condition (ACBC) with a correction due to the width-over-period ratio. The ACBC forces certain field distributions inside the corrugation and allows for the removal of the corrugation teeth to have a homogeneous region with enforced field behavior that represents the actual corrugations. The ACBC approach is found to be accurate when the number of corrugations per wavelength is large (typically around 10 corrugations per wavelength). Computed results using ACBC are in good agreement with detailed simulations, which demonstrates the validity of the asymptotic approximations. Last, a major improvement in the computation time is achieved when using the ACBC to model structures that have a large number of corrugations per wavelength.

  18. Numerical simulation of the second-order Stokes theory using finite difference method

    Directory of Open Access Journals (Sweden)

    M.A. Maâtoug


    Full Text Available The nonlinear water waves problem is of great importance because, according to the mechanical modeling of this problem, a relationship exists between the potential flow and pressure exerted by water waves. The difficulty of this problem comes not only from the fact that the kinematic and dynamic conditions are nonlinear in relation to the velocity potential, but especially because they are applied at an unknown and variable free surface. To overcome this difficulty, Stokes used an approach consisting of perturbations series around the still water level to develop a nonlinear theory. This paper deals with computation of the second-order Stokes theory in order to simulate the potential flow and the surface elevation and then to deduct the pressure loads. The Crank–Nicholson scheme and the finite difference method are used. The modeling accuracy was proved and is of order two in time and in space. Some computational results are presented and discussed.

  19. Analyses on the finite difference method by Gibou et al. for Poisson equation (United States)

    Yoon, Gangjoon; Min, Chohong


    Gibou et al. in [4] introduced a finite difference method for solving the Poisson equation in irregular domains with the Dirichlet boundary condition. Contrary to its great importance, its properties have not been mathematically analyzed, but have just been numerically observed. In this article, we present two analyses for the method. One proves that its solution is second order accurate, and the other estimates the condition number of its linear system. According to our estimation, the condition number of the unpreconditioned linear system is of size O (1 / (h ṡhmin)), and each of Jacobi, SGS, and ILU preconditioned systems is of size O (h-2). Furthermore, our analysis shows that the condition number of MILU is of size O (h-1), the most successful one.

  20. The mimetic finite difference method for the Landau-Lifshitz equation (United States)

    Kim, Eugenia; Lipnikov, Konstantin


    The Landau-Lifshitz equation describes the dynamics of the magnetization inside ferromagnetic materials. This equation is highly nonlinear and has a non-convex constraint (the magnitude of the magnetization is constant) which poses interesting challenges in developing numerical methods. We develop and analyze explicit and implicit mimetic finite difference schemes for this equation. These schemes work on general polytopal meshes which provide enormous flexibility to model magnetic devices with various shapes. A projection on the unit sphere is used to preserve the magnitude of the magnetization. We also provide a proof that shows the exchange energy is decreasing in certain conditions. The developed schemes are tested on general meshes that include distorted and randomized meshes. The numerical experiments include a test proposed by the National Institute of Standard and Technology and a test showing formation of domain wall structures in a thin film.

  1. Finite difference method to find period-one gait cycles of simple passive walkers (United States)

    Dardel, Morteza; Safartoobi, Masoumeh; Pashaei, Mohammad Hadi; Ghasemi, Mohammad Hassan; Navaei, Mostafa Kazemi


    Passive dynamic walking refers to a class of bipedal robots that can walk down an incline with no actuation or control input. These bipeds are sensitive to initial conditions due to their style of walking. According to small basin of attraction of passive limit cycles, it is important to start with an initial condition in the basin of attraction of stable walking (limit cycle). This paper presents a study of the simplest passive walker with point and curved feet. A new approach is proposed to find proper initial conditions for a pair of stable and unstable period-one gait limit cycles. This methodology is based on finite difference method which can solve the nonlinear differential equations of motion on a discrete time. Also, to investigate the physical configurations of the walkers and the environmental influence such as the slope angle, the parameter analysis is applied. Numerical simulations reveal the performance of the presented method in finding two stable and unstable gait patterns.

  2. The analysis of reactively loaded microstrip antennas by finite difference time domain modelling (United States)

    Hilton, G. S.; Beach, M. A.; Railton, C. J.


    In recent years, much interest has been shown in the use of printed circuit antennas in mobile satellite and communications terminals at microwave frequencies. Although such antennas have many advantages in weight and profile size over more conventional reflector/horn configurations, they do, however, suffer from an inherently narrow bandwidth. A way of optimizing the bandwidth of such antennas by an electronic tuning technique using a loaded probe mounted within the antenna structure is examined, and the resulting far-field radiation patterns are shown. Simulation results from a 2D finite difference time domain (FDTD) model for a rectangular microstrip antenna loaded with shorting pins are given and compared to results obtained with an actual antenna. It is hoped that this work will result in a design package for the analysis of microstrip patch antenna elements.

  3. FDiff3: a finite-difference solver for facilitating understanding of heat conduction and numerical analysis

    Energy Technology Data Exchange (ETDEWEB)

    Russell, M.B. [University of Hertfordshire, Hatfield (United Kingdom). Department of Aerospace, Automotive and Design Engineering; Probert, S.D. [Cranfield University, Bedfordshire (United Kingdom). School of Engineering


    The growing requirement for energy thrift and hence the increasing emphasis on 'low-purchased-energy' designs are stimulating the need for more accurate insights into the thermal behaviours of buildings and their components. This better understanding is preferably achieved, rather than by using 'closed software' or teaching the relevant mathematics outside heat-transfer lessons, but from embedding the pertinent tutoring while dealing with heat-transfer problems using an open-source code approach. Hence a finite-difference software program (FDiff3) has been composed to show the principles of numerical analysis as well as improve the undergraduates' perception of transient conduction. The pedagogic approach behind the development, its present capabilities and applications to sample test-cases are discussed. (author)

  4. An efficient finite-difference strategy for sensitivity analysis of stochastic models of biochemical systems. (United States)

    Morshed, Monjur; Ingalls, Brian; Ilie, Silvana


    Sensitivity analysis characterizes the dependence of a model's behaviour on system parameters. It is a critical tool in the formulation, characterization, and verification of models of biochemical reaction networks, for which confident estimates of parameter values are often lacking. In this paper, we propose a novel method for sensitivity analysis of discrete stochastic models of biochemical reaction systems whose dynamics occur over a range of timescales. This method combines finite-difference approximations and adaptive tau-leaping strategies to efficiently estimate parametric sensitivities for stiff stochastic biochemical kinetics models, with negligible loss in accuracy compared with previously published approaches. We analyze several models of interest to illustrate the advantages of our method. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

  5. Finite difference time domain method for simulation of damage initiation in thin film coatings (United States)

    Smalakys, Linas; Momgaudis, Balys; Grigutis, Robertas; Melninkaitis, Andrius


    Time resolved digital holography (TRDH) is a versatile tool that provides valuable insights into the dynamics of femtosecond damage initiation by providing spatiotemporal information of excited material. However, interpreting of TRDH data in thin film dielectric coatings is rather complicated without appropriate theoretical models that are able to correctly describe underlying nature of damage formation. Therefore, a model based on finite difference time domain (FDTD) method with complete Keldysh theory for nonlinear ionization of atoms and multiple rate equation (MRE) method for conduction band electrons was developed. The model was used to reproduce both temporal and spatial characteristics of TRDH experiment performed on Ta2O5 dielectric coating. Fitted material parameters were then applied to indirectly estimate LIDT of the coating.

  6. Finite difference Hermite WENO schemes for the Hamilton-Jacobi equations (United States)

    Zheng, Feng; Shu, Chi-Wang; Qiu, Jianxian


    In this paper, a new type of finite difference Hermite weighted essentially non-oscillatory (HWENO) schemes are constructed for solving Hamilton-Jacobi (HJ) equations. Point values of both the solution and its first derivatives are used in the HWENO reconstruction and evolved via time advancing. While the evolution of the solution is still through the classical numerical fluxes to ensure convergence to weak solutions, the evolution of the first derivatives of the solution is through a simple dimension-by-dimension non-conservative procedure to gain efficiency. The main advantages of this new scheme include its compactness in the spatial field and its simplicity in the reconstructions. Extensive numerical experiments in one and two dimensional cases are performed to verify the accuracy, high resolution and efficiency of this new scheme.

  7. Finite-Difference Time-Domain Simulation for Three-dimensional Polarized Light Imaging

    CERN Document Server

    Menzel, Miriam; De Raedt, Hans; Michielsen, Kristel


    Three-dimensional Polarized Light Imaging (3D-PLI) is a promising technique to reconstruct the nerve fiber architecture of human post-mortem brains from birefringence measurements of histological brain sections with micrometer resolution. To better understand how the reconstructed fiber orientations are related to the underlying fiber structure, numerical simulations are employed. Here, we present two complementary simulation approaches that reproduce the entire 3D-PLI analysis: First, we give a short review on a simulation approach that uses the Jones matrix calculus to model the birefringent myelin sheaths. Afterwards, we introduce a more sophisticated simulation tool: a 3D Maxwell solver based on a Finite-Difference Time-Domain algorithm that simulates the propagation of the electromagnetic light wave through the brain tissue. We demonstrate that the Maxwell solver is a valuable tool to better understand the interaction of polarized light with brain tissue and to enhance the accuracy of the fiber orientati...

  8. Analysis and modeling of different topologies for linear switched reluctance motor using finite element method

    Directory of Open Access Journals (Sweden)

    Babak Ganji


    Full Text Available In the present paper, an electromagnetic simulation model is introduced for the conventional type of linear switched reluctance motor (LSRM in which the dynamic characteristics of the motor are predicted precisely by carrying out 2D finite element (FE transient analysis using ANSYS FE package. The simulation model is created totally in ANSYS parametric design language (APDL as a parametric model and it can be used easily for different designs of the conventional LSRMs. Introducing linear switched reluctance motor with segmental translator as a new type of LSRM, performance principles and design criteria are presented for two various topologies of this motor. Carrying out 2D FE transient analysis, dynamic characteristics of these two motors are predicted and compared to those obtained for the conventional LSRM.

  9. Thermal Analysis of Ball screw Systems by Explicit Finite Difference Method

    Energy Technology Data Exchange (ETDEWEB)

    Min, Bog Ki [Hanyang Univ., Seoul (Korea, Republic of); Park, Chun Hong; Chung, Sung Chong [KIMM, Daejeon (Korea, Republic of)


    Friction generated from balls and grooves incurs temperature rise in the ball screw system. Thermal deformation due to the heat degrades positioning accuracy of the feed drive system. To compensate for the thermal error, accurate prediction of the temperature distribution is required first. In this paper, to predict the temperature distribution according to the rotational speed, solid and hollow cylinders are applied for analysis of the ball screw shaft and nut, respectively. Boundary conditions such as the convective heat transfer coefficient, friction torque, and thermal contact conductance (TCC) between balls and grooves are formulated according to operating and fabrication conditions of the ball screw. Explicit FDM (finite difference method) is studied for development of a temperature prediction simulator. Its effectiveness is verified through numerical analysis.

  10. Finite difference solution for transient cooling of a radiating-conducting semitransparent layer (United States)

    Siegel, Robert


    Transient solutions were obtained for cooling a semitransparent material by radiation and conduction. The layer is in a vacuum environment so the only means for heat dissipation is by radiation from within the medium leaving through the boundaries. Heat conduction serves only to partially equalize temperatures across the layer. As the optical thickness is increased, steep temperature gradients exist near the boundaries when conduction is relatively small. A solution procedure is required that will provide accurate temperature distributions adjacent to the boundaries, or radiative heat losses will be in error. The approach utilized numerical Gaussian integration to obtain the local radiative source term, and a finite difference procedure with variable space and time increments to solve the transient energy equation.

  11. Finite difference solution for transient radiative cooling of a conducting semitransparent square region (United States)

    Siegel, R.; Molls, F. B.


    Transient solutions were obtained for a square region of heat conducting semitransparent material cooling by thermal radiation. The region is in a vacuum environment, so energy is dissipated only by radiation from within the medium leaving through its boundaries. The effect of heat conduction during the transient is to partially equalize the internal temperature distribution. As the optical thickness of the region is increased, the temperature gradients increase near the boundaries and corners, unless heat conduction is large. The solution procedure must provide accurate temperature distributions in these regions to prevent error in the calculated radiation losses. Two-dimensional numerical Gaussian integration is used to obtain the local radiative source term. A finite difference procedure with variable space and time increments is used to solve the transient energy equation. Variable spacing was used to concentrate grid points in regions with large temperature gradients.

  12. Linear discontinuous finite difference formulation for synthetic coarse-mesh few-group diffusion calculations

    Energy Technology Data Exchange (ETDEWEB)

    Aragones, J.M.; Ahnert, C.


    A linear discontinuous finite difference formulation to solve the diffusion equations in coarse mesh and few groups is developed. The correction factors for heterogeneities, coarse mesh, and spectral effects are general interface flux discontinuity factors that can be explicitly calculated (synthetized) from detailed diffusion or transport solutions in fine mesh (heterogeneous) and multigroups, preserving the integrated fluxes and interface net currents. The stability is explicitly established for general synthetizations and for specific fine to coarse mesh and group reductions. Computing methods have been implemented for one-group (grey) synthetic diffusion acceleration, two-dimensional nodal/local solutions, and three-dimensional nodal simulation of pressurized water reactor cores. Results demonstrate the simplicity and stability of the formulation, a regular behaviour of the correction factors, an outstanding acceleration performance, and high potential for parallel and vector computing.

  13. A Comparison of Different Finite Element Methods in the Thermal Analysis of Friction Stir Welding (FSW

    Directory of Open Access Journals (Sweden)

    Bahman Meyghani


    Full Text Available Friction Stir Welding (FSW is a novel kind of welding for joining metals that are impossible or difficult to weld by conventional methods. Three-dimensional nature of FSW makes the experimental investigation more complex. Moreover, experimental observations are often costly and time consuming, and usually there is an inaccuracy in measuring the data during experimental tests. Thus, Finite Element Methods (FEMs has been employed to overcome the complexity, to increase the accuracy and also to reduce costs. It should be noted that, due to the presence of large deformations of the material during FSW, strong distortions of mesh might be happened in the numerical simulation. Therefore, one of the most significant considerations during the process simulation is the selection of the best numerical approach. It must be mentioned that; the numerical approach selection determines the relationship between the finite grid (mesh and deforming continuum of computing zones. Also, numerical approach determines the ability of the model to overcome large distortions of mesh and provides an accurate resolution of boundaries and interfaces. There are different descriptions for the algorithms of continuum mechanics include Lagrangian and Eulerian. Moreover, by combining the above-mentioned methods, an Arbitrary Lagrangian–Eulerian (ALE approach is proposed. In this paper, a comparison between different numerical approaches for thermal analysis of FSW at both local and global scales is reviewed and the applications of each method in the FSW process is discussed in detail. Observations showed that, Lagrangian method is usually used for modelling thermal behavior in the whole structure area, while Eulerian approach is seldom employed for modelling of the thermal behavior, and it is usually employed for modelling the material flow. Additionally, for modelling of the heat affected zone, ALE approach is found to be as an appropriate approach. Finally, several

  14. Finite volume hydromechanical simulation in porous media. (United States)

    Nordbotten, Jan Martin


    Cell-centered finite volume methods are prevailing in numerical simulation of flow in porous media. However, due to the lack of cell-centered finite volume methods for mechanics, coupled flow and deformation is usually treated either by coupled finite-volume-finite element discretizations, or within a finite element setting. The former approach is unfavorable as it introduces two separate grid structures, while the latter approach loses the advantages of finite volume methods for the flow equation. Recently, we proposed a cell-centered finite volume method for elasticity. Herein, we explore the applicability of this novel method to provide a compatible finite volume discretization for coupled hydromechanic flows in porous media. We detail in particular the issue of coupling terms, and show how this is naturally handled. Furthermore, we observe how the cell-centered finite volume framework naturally allows for modeling fractured and fracturing porous media through internal boundary conditions. We support the discussion with a set of numerical examples: the convergence properties of the coupled scheme are first investigated; second, we illustrate the practical applicability of the method both for fractured and heterogeneous media.

  15. Different geometric patterns of pacifiers compared on the basis of finite element analysis. (United States)

    Levrini, L; Merlo, P; Paracchini, L


    This study was carried out with the purpose to show on a virtual model of oral cavity the mechanical behaviour of different kinds of pacifiers with different pressure levels that can be likened to a condition of rest and deglutition. Three different types of dummies, orthodontic- (A), cherry- (B) and drop- (C) shaped from an anatomical point of view, were inserted between the palate and the tongue in a virtual system by means of a finite element simulation. The palatal structure was recreated through tridimensional laser scanning, while the tongue structure was reconstructed by a software suitable for reproducing solids. Also the image of the pacifiers was developed by computer-aided scanning and reproduction. Suitable constraints were inserted and high and low pressure levels were exerted on these systems. FEA simulation allowed us to distribute the strain on the palate according to the different geometrical structures of the objects. Dummy A shows a more uniform and wider crosswise stress distribution with also a lesser load on the anterior palatal crest. Dummy B and C, on the contrary, show a more dot-like behaviour inducing a higher stress due to contact on restricted points. The characteristics of dummy A, although they have not been clinically investigated yet, seem to be the fittest ones to guarantee the maintenance of the transversal diameters of the premaxilla and reduce the risk of open bite.

  16. A three-dimensional finite element study on anterior laminate veneers with different incisal preparations. (United States)

    Li, Zhongjie; Yang, Zheng; Zuo, Ling; Meng, Yukun


    Mechanical properties are important in the long-term success of restorations, but whether different incisal preparations can affect the behavior of veneers remains controversial. The purpose of this study was to evaluate the influence of different preparation designs on stress distribution in a maxillary incisor restored with veneers and with regard to different restorative materials and loading conditions. Based on the cone beam computed tomography scanning of a maxillary incisor, 3-dimensional finite element models for 2 different designs were developed. A static load of 50 N was applied with angulations of 60 degrees and 125 degrees to the longitudinal axis at the level of the incisal margin, simulating functional movements. Both porcelain laminate veneer and composite resin veneer were considered. The maximum stress values and stress distribution of the veneer, cement layer, and tooth structure were calculated and analyzed. The maximum stress values in the veneer and tooth were higher with the butt-joint design. Stresses were distributed more uniformly in the cement layer in the palatal chamfer design for porcelain laminate veneers, whereas a better stress distribution under protrusive movement was observed in the butt-joint design for composite resin veneers. The palatal chamfer design for porcelain laminate veneers tolerated stress better, whereas the butt-joint design was favored for composite resin veneers, particularly under protrusive movement. Copyright © 2014 Editorial Council for the Journal of Prosthetic Dentistry. Published by Elsevier Inc. All rights reserved.

  17. A Family of Sixth-Order Compact Finite-Difference Schemes for the Three-Dimensional Poisson Equation

    Directory of Open Access Journals (Sweden)

    Yaw Kyei


    Full Text Available We derive a family of sixth-order compact finite-difference schemes for the three-dimensional Poisson's equation. As opposed to other research regarding higher-order compact difference schemes, our approach includes consideration of the discretization of the source function on a compact finite-difference stencil. The schemes derived approximate the solution to Poisson's equation on a compact stencil, and thus the schemes can be easily implemented and resulting linear systems are solved in a high-performance computing environment. The resulting discretization is a one-parameter family of finite-difference schemes which may be further optimized for accuracy and stability. Computational experiments are implemented which illustrate the theoretically demonstrated truncation errors.

  18. Numerical stability of an explicit finite difference scheme for the solution of transient conduction in composite media (United States)

    Campbell, W.


    A theoretical evaluation of the stability of an explicit finite difference solution of the transient temperature field in a composite medium is presented. The grid points of the field are assumed uniformly spaced, and media interfaces are either vertical or horizontal and pass through grid points. In addition, perfect contact between different media (infinite interfacial conductance) is assumed. A finite difference form of the conduction equation is not valid at media interfaces; therefore, heat balance forms are derived. These equations were subjected to stability analysis, and a computer graphics code was developed that permitted determination of a maximum time step for a given grid spacing.

  19. Finite difference method and algebraic polynomial interpolation for numerically solving Poisson's equation over arbitrary domains

    Directory of Open Access Journals (Sweden)

    Tsugio Fukuchi


    Full Text Available The finite difference method (FDM based on Cartesian coordinate systems can be applied to numerical analyses over any complex domain. A complex domain is usually taken to mean that the geometry of an immersed body in a fluid is complex; here, it means simply an analytical domain of arbitrary configuration. In such an approach, we do not need to treat the outer and inner boundaries differently in numerical calculations; both are treated in the same way. Using a method that adopts algebraic polynomial interpolations in the calculation around near-wall elements, all the calculations over irregular domains reduce to those over regular domains. Discretization of the space differential in the FDM is usually derived using the Taylor series expansion; however, if we use the polynomial interpolation systematically, exceptional advantages are gained in deriving high-order differences. In using the polynomial interpolations, we can numerically solve the Poisson equation freely over any complex domain. Only a particular type of partial differential equation, Poisson's equations, is treated; however, the arguments put forward have wider generality in numerical calculations using the FDM.

  20. A novel and accurate finite difference method for the fractional Laplacian and the fractional Poisson problem (United States)

    Duo, Siwei; van Wyk, Hans Werner; Zhang, Yanzhi


    In this paper, we develop a novel finite difference method to discretize the fractional Laplacian (- Δ) α / 2 in hypersingular integral form. By introducing a splitting parameter, we formulate the fractional Laplacian as the weighted integral of a weak singular function, which is then approximated by the weighted trapezoidal rule. Compared to other existing methods, our method is more accurate and simpler to implement, and moreover it closely resembles the central difference scheme for the classical Laplace operator. We prove that for u ∈C 3 , α / 2 (R), our method has an accuracy of O (h2)uniformly for any α ∈ (0 , 2), while for u ∈C 1 , α / 2 (R), the accuracy is O (h 1 - α / 2). The convergence behavior of our method is consistent with that of the central difference approximation of the classical Laplace operator. Additionally, we apply our method to solve the fractional Poisson equation and study the convergence of its numerical solutions. The extensive numerical examples that accompany our analysis verify our results, as well as give additional insights into the convergence behavior of our method.

  1. Acceleration of Linear Finite-Difference Poisson-Boltzmann Methods on Graphics Processing Units. (United States)

    Qi, Ruxi; Botello-Smith, Wesley M; Luo, Ray


    Electrostatic interactions play crucial roles in biophysical processes such as protein folding and molecular recognition. Poisson-Boltzmann equation (PBE)-based models have emerged as widely used in modeling these important processes. Though great efforts have been put into developing efficient PBE numerical models, challenges still remain due to the high dimensionality of typical biomolecular systems. In this study, we implemented and analyzed commonly used linear PBE solvers for the ever-improving graphics processing units (GPU) for biomolecular simulations, including both standard and preconditioned conjugate gradient (CG) solvers with several alternative preconditioners. Our implementation utilizes the standard Nvidia CUDA libraries cuSPARSE, cuBLAS, and CUSP. Extensive tests show that good numerical accuracy can be achieved given that the single precision is often used for numerical applications on GPU platforms. The optimal GPU performance was observed with the Jacobi-preconditioned CG solver, with a significant speedup over standard CG solver on CPU in our diversified test cases. Our analysis further shows that different matrix storage formats also considerably affect the efficiency of different linear PBE solvers on GPU, with the diagonal format best suited for our standard finite-difference linear systems. Further efficiency may be possible with matrix-free operations and integrated grid stencil setup specifically tailored for the banded matrices in PBE-specific linear systems.

  2. Finite-difference theory for sound propagation in a lined duct with uniform flow using the wave envelope concept (United States)

    Baumeister, K. J.


    Finite difference equations are derived for sound propagation in a two dimensional, straight, soft wall duct with a uniform flow by using the wave envelope concept. This concept reduces the required number of finite difference grid points by one to two orders of magnitude depending on the length of the duct and the frequency of the sound. The governing acoustic difference equations in complex notation are derived. An exit condition is developed that allows a duct of finite length to simulate the wave propagation in an infinitely long duct. Sample calculations presented for a plane wave incident upon the acoustic liner show the numerical theory to be in good agreement with closed form analytical theory. Complete pressure and velocity printouts are given to some sample problems and can be used to debug and check future computer programs.

  3. Finite element analysis of thermal stress distribution in different restorative materials used in class V cavities. (United States)

    Guler, M S; Guler, C; Cakici, F; Cakici, E B; Sen, S


    Cervical lesions are restored with class V preparation. The aim of this study was to use a three-dimensional finite element method to carry out a thermal analysis of the temperature and stress distributions of three different restorative materials used for class V cavities of maxillary molar teeth. A maxillary left first molar tooth was modeled and a class V cavity was prepared on the cervical 1/3 of the buccal surface. This cavity was restored with three different materials (Group I: Resin composite, Group II: Glass ionomer cement, and Group III: Amalgam). Loads of 400 N were applied at an angle of 90° to the longitudinal axis of the tooth on the restorative material at 5 and 55°C temperatures. Von Mises and thermal stress distributions were evaluated. In all groups, the von Mises stress values increased with temperature. The highest von Mises stress distribution was observed at 55°C in Group II (144.53 MPa). The lowest von Mises stress distribution was observed at 5°C in Group III (70.81 MPa). Amalgam is the most suitable restorative material for class V restorations because of minimal stress distribution.

  4. Memory-optimized shift operator alternating direction implicit finite difference time domain method for plasma (United States)

    Song, Wanjun; Zhang, Hou


    Through introducing the alternating direction implicit (ADI) technique and the memory-optimized algorithm to the shift operator (SO) finite difference time domain (FDTD) method, the memory-optimized SO-ADI FDTD for nonmagnetized collisional plasma is proposed and the corresponding formulae of the proposed method for programming are deduced. In order to further the computational efficiency, the iteration method rather than Gauss elimination method is employed to solve the equation set in the derivation of the formulae. Complicated transformations and convolutions are avoided in the proposed method compared with the Z transforms (ZT) ADI FDTD method and the piecewise linear JE recursive convolution (PLJERC) ADI FDTD method. The numerical dispersion of the SO-ADI FDTD method with different plasma frequencies and electron collision frequencies is analyzed and the appropriate ratio of grid size to the minimum wavelength is given. The accuracy of the proposed method is validated by the reflection coefficient test on a nonmagnetized collisional plasma sheet. The testing results show that the proposed method is advantageous for improving computational efficiency and saving computer memory. The reflection coefficient of a perfect electric conductor (PEC) sheet covered by multilayer plasma and the RCS of the objects coated by plasma are calculated by the proposed method and the simulation results are analyzed.

  5. Analysis of different bicruciate-retaining tibial prosthesis design using a three dimension finite element model. (United States)

    He, Peiheng; Li, Xing; Huang, Shuai; Liu, Minghao; Chen, Weizhi; Xu, Dongliang


    The recent interest in bicruciate-retaining prostheses has aimed to address the need for an implant that can mimic a natural knee. Arguments have always existed about survivorship, including loosening and subsidence, as well as tibial preparation in bicruciate-retaining tibial prostheses. The aim of this study was to investigate the biomechanics of a new modular design and other bicruciate-retaining designs using a three-dimensional finite element model under different load conditions to discover which prosthesis was more suitable. We also evaluated related parameters (the third principal stress, shear stress, micromotion, and von Mises stresses) to compare the characteristics of different bicruciate-retaining designs. The biomechanics of the bicruciate-retaining tibial prosthesis can be influenced by the style of the designed prosthesis and gait loading. The new modular design showed stability and moderated the third principal stress, leading to less shear stress and stress shield, suggesting that this type of design can avoid knee prosthesis loosening and subsidence. Therefore, the new design may be used as a more suitable prosthesis for future bicruciate-retaining implant application.

  6. Finite difference analysis and experimental validation of 3D photonic crystals for structural health monitoring (United States)

    Piccolo, Valentina; Chiappini, Andrea; Vaccari, Alessandro; Calà Lesina, Antonino; Ferrari, Maurizio; Deseri, Luca; Perry, Marcus; Zonta, Daniele


    In this work, we validate the behavior of 3D Photonic Crystals for Structural Health Monitoring applications. A Finite Difference Time Domain (FDTD) analysis has been performed and compared to experimental data. We demonstrate that the photonic properties of a crystal (comprised of sub-micrometric polystyrene colloidal spheres embedded in a PDMS matrix) change as a function of the axial strain applied to a rubber substrate. The change in the reflected wavelength, detected through our laboratory experiments and equivalent to a visible change in crystal color, is assumed to be caused by changes in the interplanar spacing of the polystyrene beads. This behavior is captured by our full wave 3D FDTD model. This contains different wavelengths in the visible spectrum and the wave amplitudes of the reflected and transmitted secondary beams are then computed. A change in the reflectance or transmittance is observed at every programmed step in which we vary the distance between the spheres. These investigations are an important tool to predict, study and validate our understanding of the behavior of this highly complex physical system. In this context, we have developed a versatile and robust parallelized code, able to numerically model the interaction of light with matter, by directly solving Maxwell's equations in their strong form. The ability to describe the physical behavior of such systems is an important and fundamental capability which will aid the design and validation of innovative photonic sensors.

  7. Evaluation of load transfer characteristics of five different implants in compact bone at different load levels by finite elements analysis. (United States)

    Bozkaya, Dincer; Muftu, Sinan; Muftu, Ali


    The external contour of an implant and the magnitude of occlusal loading can have significant effects on the load transfer characteristics and may result in different bone failure rates for different implant systems. The goal of this study was to investigate the effects of external geometry and occlusal load magnitude on bone failure modes for 5 commercially available dental implant systems. Five different implant systems; Ankylos, Astra, Bicon, ITI, and Nobel Biocare, comparable in size, but different in thread profile and crest module shapes, were compared using the finite element method. Type II bone quality was approximated and complete osseous integration was assumed. Occlusal loads of varying magnitudes (0 to 2000 N) were applied on the abutments supporting single tooth restorations at 11.3 degrees from the vertical axis with a 1-mm offset. Total overloaded bone area, where tensile and compressive normal stresses fell outside of the recommended limits of 100 and 170 MPa, respectively, was investigated for different load levels. For moderate levels of occlusal loads up to 300 N, the compact bone was not overloaded by any of the implant systems. At the extreme end of the occlusal load range (1000 N or more) the overloading characteristics of implants may be dependent on geometric shape. In general, overloading occurs near the superior region of compact bone, in compression, and it is primarily caused by the normal and lateral components of the occlusal load. At the region of intersection of compact and trabecular bone, overloading occurs in tension due to the vertical component of the occlusal load. For excessive forces greater than 1000 N, the overloaded areas of the bone varied considerably among 5 different implants systems evaluated.

  8. Finite difference method for inner-layer equations in the resistive MagnetoHydroDynamic stability analysis

    Energy Technology Data Exchange (ETDEWEB)

    Tokuda, Shinji [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Watanabe, Tomoko


    The matching problem in resistive MagnetoHydroDynamic stability analysis by the asymptotic matching method has been reformulated as an initial-boundary value problem for the inner-layer equations describing the plasma dynamics in the thin layer around a rational surface. The third boundary conditions at boundaries of a finite interval are imposed on the inner layer equations in the formulation instead of asymptotic conditions at infinities. The finite difference method for this problem has been applied to model equations whose solutions are known in a closed form. It has been shown that the initial value problem and the associated eigenvalue problem for the model equations can be solved by the finite difference method with numerical stability. The formulation presented here enables the asymptotic matching method to be a practical method for the resistive MHD stability analysis. (author)

  9. The transient response for different types of erodable surface thermocouples using finite element analysis

    Directory of Open Access Journals (Sweden)

    Mohammed Hussein


    Full Text Available The transient response of erodable surface thermocouples has been numerically assessed by using a two dimensional finite element analysis. Four types of base metal erodable surface thermocouples have been examined in this study, included type-K (alumel-chromel, type-E (chromel-constantan, type-T (copper-constantan, and type-J (iron-constantan with 50 mm thick- ness for each. The practical importance of these types of thermocouples is to be used in internal combustion engine studies and aerodynamics experiments. The step heat flux was applied at the surface of the thermocouple model. The heat flux from the measurements of the surface temperature can be commonly identified by assuming that the heat transfer within these devices is one-dimensional. The surface temperature histories at different positions along the thermocouple are presented. The normalized surface temperature histories at the center of the thermocouple for different types at different response time are also depicted. The thermocouple response to different heat flux variations were considered by using a square heat flux with 2 ms width, a sinusoidal surface heat flux variation width 10 ms period and repeated heat flux variation with 2 ms width. The present results demonstrate that the two dimensional transient heat conduction effects have a significant influence on the surface temperature history measurements made with these devices. It was observed that the surface temperature history and the transient response for thermocouple type-E are higher than that for other types due to the thermal properties of this thermocouple. It was concluded that the thermal properties of the surrounding material do have an impact, but the properties of the thermocouple and the insulation materials also make an important contribution to the net response.

  10. Effect of Different Treatment Options on Biomechanics of Immature Teeth: A Finite Element Stress Analysis Study. (United States)

    Belli, Sema; Eraslan, Oğuz; Eskitaşcıoğlu, Gürcan


    Immature teeth (IT) can be managed by using several treatment options, depending on the vitality of the tooth. The aim of this finite element stress analysis study was to evaluate the effect of different treatment procedures on the stresses in three-dimensional IT models. Three-dimensional finite element stress analysis premolar tooth model was created as control (model 1), modified to simulate IT. Eleven models were created to simulate IT filled with (model 2) calcium hydroxide (CH), (model 3) mineral trioxide aggregate (MTA), (model 4) Biodentine (B), (models 5 and 6) MTA plug and B plug without root-filling, (models 7 and 8) MTA plug and B plug with root-filling with composite restoration, and amputation by using (model 9) CH, (model 10) MTA, and (model 11) B. Materials and structures were assumed to be homogenous and isotropic. A 300 N load was applied to the models from the functional cusps and central fossa with a 135° angle. Cosmosworks structural analysis program was used. The results were presented considering the von Mises criteria, and the scale range was limited to 0-10 + MPa. CH use in comparison with temporary filling increased the stresses within the root. MTA filling showed less stresses when compared with B filling. MTA and B plug increased the stresses at apical and root; however, when the roots were filled using gutta-percha and the crowns were restored with composite resin, the stresses at the coronal side of the roots were reduced. The stresses were distributed more favorably in the models simulating CH, MTA, or B amputation. Amputation by using MTA and B showed similar stresses with natural tooth model. CH is not a favorable dressing material for IT when compared with MTA and B. MTA or B plug increases the stresses at apical, whereas root-filling reduces the stresses within the root. Amputation by using CH, MTA, and B in combination with composite resin restoration may save both the coronal and root structure of IT. Copyright © 2017

  11. One-Dimensional Vacuum Steady Seepage Model of Unsaturated Soil and Finite Difference Solution

    Directory of Open Access Journals (Sweden)

    Feng Huang


    Full Text Available Vacuum tube dewatering method and light well point method have been widely used in engineering dewatering and foundation treatment. However, there is little research on the calculation method of unsaturated seepage under the effect of vacuum pressure which is generated by the vacuum well. In view of this, the one-dimensional (1D steady seepage law of unsaturated soil in vacuum field has been analyzed based on Darcy’s law, basic equations, and finite difference method. First, the gravity drainage ability is analyzed. The analysis presents that much unsaturated water can not be drained off only by gravity effect because of surface tension. Second, the unsaturated vacuum seepage equations are built up in conditions of flux boundary and waterhead boundary. Finally, two examples are analyzed based on the relationship of matric suction and permeability coefficient after boundary conditions are determined. The results show that vacuum pressure will significantly enhance the drainage ability of unsaturated water by improving the hydraulic gradient of unsaturated water.

  12. Finite-difference time-domain modelling of through-the-Earth radio signal propagation (United States)

    Ralchenko, M.; Svilans, M.; Samson, C.; Roper, M.


    This research seeks to extend the knowledge of how a very low frequency (VLF) through-the-Earth (TTE) radio signal behaves as it propagates underground, by calculating and visualizing the strength of the electric and magnetic fields for an arbitrary geology through numeric modelling. To achieve this objective, a new software tool has been developed using the finite-difference time-domain method. This technique is particularly well suited to visualizing the distribution of electromagnetic fields in an arbitrary geology. The frequency range of TTE radio (400-9000 Hz) and geometrical scales involved (1 m resolution for domains a few hundred metres in size) involves processing a grid composed of millions of cells for thousands of time steps, which is computationally expensive. Graphics processing unit acceleration was used to reduce execution time from days and weeks, to minutes and hours. Results from the new modelling tool were compared to three cases for which an analytic solution is known. Two more case studies were done featuring complex geologic environments relevant to TTE communications that cannot be solved analytically. There was good agreement between numeric and analytic results. Deviations were likely caused by numeric artifacts from the model boundaries; however, in a TTE application in field conditions, the uncertainty in the conductivity of the various geologic formations will greatly outweigh these small numeric errors.

  13. Calculation of incompressible and compressible unsteady boundary layers by a noniterative finite difference method (United States)

    Kim, J. S.; Chang, K. S.


    Transient as well as oscillating two-dimensional boundary layers are solved numerically by using a noniterative implicit finite difference scheme which is second-order accurate both in time and space. To obtain the exact spatial initial condition, the solution is obtained of parabolic partial differential equations at the initial plane which are reduced from the full biparabolic equations valid in the main time-space domain. Formulations are made first for incompressible flow, and then for compressible boundary layers so that the effect of temperature-induced compressibility can be considered. The method is applied to the unsteady laminar boundary layers with large temporal flow disturbances. Examples are transition to Falkner-Skan flow, oscillatory Blasius flow, constantly accelerated stagnation point flow and harmonically fluctuating flow past a circular cylinder, with or without the compressibility effect taken into account for the last two cases. Comparison with the existing data has demonstrated the excellency of the present method both in accuracy and computer-time economy.

  14. Finite-difference time-domain synthesis of infrasound propagation through an absorbing atmosphere. (United States)

    de Groot-Hedlin, C


    Equations applicable to finite-difference time-domain (FDTD) computation of infrasound propagation through an absorbing atmosphere are derived and examined in this paper. It is shown that over altitudes up to 160 km, and at frequencies relevant to global infrasound propagation, i.e., 0.02-5 Hz, the acoustic absorption in dB/m varies approximately as the square of the propagation frequency plus a small constant term. A second-order differential equation is presented for an atmosphere modeled as a compressible Newtonian fluid with low shear viscosity, acted on by a small external damping force. It is shown that the solution to this equation represents pressure fluctuations with the attenuation indicated above. Increased dispersion is predicted at altitudes over 100 km at infrasound frequencies. The governing propagation equation is separated into two partial differential equations that are first order in time for FDTD implementation. A numerical analysis of errors inherent to this FDTD method shows that the attenuation term imposes additional stability constraints on the FDTD algorithm. Comparison of FDTD results for models with and without attenuation shows that the predicted transmission losses for the attenuating media agree with those computed from synthesized waveforms.

  15. Electromagnetic Wave Propagation in Body Area Networks Using the Finite-Difference-Time-Domain Method

    Directory of Open Access Journals (Sweden)

    Raj Mittra


    Full Text Available A rigorous full-wave solution, via the Finite-Difference-Time-Domain (FDTD method, is performed in an attempt to obtain realistic communication channel models for on-body wireless transmission in Body-Area-Networks (BANs, which are local data networks using the human body as a propagation medium. The problem of modeling the coupling between body mounted antennas is often not amenable to attack by hybrid techniques owing to the complex nature of the human body. For instance, the time-domain Green’s function approach becomes more involved when the antennas are not conformal. Furthermore, the human body is irregular in shape and has dispersion properties that are unique. One consequence of this is that we must resort to modeling the antenna network mounted on the body in its entirety, and the number of degrees of freedom (DoFs can be on the order of billions. Even so, this type of problem can still be modeled by employing a parallel version of the FDTD algorithm running on a cluster. Lastly, we note that the results of rigorous simulation of BANs can serve as benchmarks for comparison with the abundance of measurement data.

  16. A comparison between different finite elements for elastic and aero-elastic analyses. (United States)

    Mahran, Mohamed; ELsabbagh, Adel; Negm, Hani


    In the present paper, a comparison between five different shell finite elements, including the Linear Triangular Element, Linear Quadrilateral Element, Linear Quadrilateral Element based on deformation modes, 8-node Quadrilateral Element, and 9-Node Quadrilateral Element was presented. The shape functions and the element equations related to each element were presented through a detailed mathematical formulation. Additionally, the Jacobian matrix for the second order derivatives was simplified and used to derive each element's strain-displacement matrix in bending. The elements were compared using carefully selected elastic and aero-elastic bench mark problems, regarding the number of elements needed to reach convergence, the resulting accuracy, and the needed computation time. The best suitable element for elastic free vibration analysis was found to be the Linear Quadrilateral Element with deformation-based shape functions, whereas the most suitable element for stress analysis was the 8-Node Quadrilateral Element, and the most suitable element for aero-elastic analysis was the 9-Node Quadrilateral Element. Although the linear triangular element was the last choice for modal and stress analyses, it establishes more accurate results in aero-elastic analyses, however, with much longer computation time. Additionally, the nine-node quadrilateral element was found to be the best choice for laminated composite plates analysis.

  17. Parallel 3d Finite-Difference Time-Domain Method on Multi-Gpu Systems (United States)

    Du, Liu-Ge; Li, Kang; Kong, Fan-Min; Hu, Yuan

    Finite-difference time-domain (FDTD) is a popular but computational intensive method to solve Maxwell's equations for electrical and optical devices simulation. This paper presents implementations of three-dimensional FDTD with convolutional perfect match layer (CPML) absorbing boundary conditions on graphics processing unit (GPU). Electromagnetic fields in Yee cells are calculated in parallel millions of threads arranged as a grid of blocks with compute unified device architecture (CUDA) programming model and considerable speedup factors are obtained versus sequential CPU code. We extend the parallel algorithm to multiple GPUs in order to solve electrically large structures. Asynchronous memory copy scheme is used in data exchange procedure to improve the computation efficiency. We successfully use this technique to simulate pointwise source radiation and validate the result by comparison to high precision computation, which shows favorable agreements. With four commodity GTX295 graphics cards on a single personal computer, more than 4000 million Yee cells can be updated in one second, which is hundreds of times faster than traditional CPU computation.

  18. A finite-difference modeling of Love channel waves in transversely isotropic medium

    Energy Technology Data Exchange (ETDEWEB)

    Cho, D.H. [Inha Univ., Incheon (Korea, Republic of); Lee, S.S. [Korea Mining Promotion Corp., Seoul (Korea, Republic of)


    The present paper deals with numerical modeling of Love channel waves in transversely isotropic elastic medium. First, an explicit finite-difference scheme of second order approximation is formulated with the wave equation of SH particle displacement in transversely isotropic medium. Since it is a heterogeneous formulation, it should enable efficient modeling of complex model structures without additional treatment of the internal boundary matching. With a model of isotropic coal seam embedded in high velocity host rock, seismograms are synthesized and turn out to be essentially identical with published ones of Korn and Stockl. Next, anisotropic coal seams are investigated. It is found that the horizontal velocity of the seam appears to play a major role of determining the group velocity of Love channel waves. The group velocity increases with the increase of the horizontal velocity or vice versa. However, further study will be needed to exploit fully Love channel waves for the determination of lithology, stratification, fracture in sedimentary rocks, for instance, for hydrocarbon exploration and development. (author). 21 refs., 3 tabs., 10 figs.

  19. A Finite-Difference Solution of Solute Transport through a Membrane Bioreactor

    Directory of Open Access Journals (Sweden)

    B. Godongwana


    Full Text Available The current paper presents a theoretical analysis of the transport of solutes through a fixed-film membrane bioreactor (MBR, immobilised with an active biocatalyst. The dimensionless convection-diffusion equation with variable coefficients was solved analytically and numerically for concentration profiles of the solutes through the MBR. The analytical solution makes use of regular perturbation and accounts for radial convective flow as well as axial diffusion of the substrate species. The Michaelis-Menten (or Monod rate equation was assumed for the sink term, and the perturbation was extended up to second-order. In the analytical solution only the first-order limit of the Michaelis-Menten equation was considered; hence the linearized equation was solved. In the numerical solution, however, this restriction was lifted. The solution of the nonlinear, elliptic, partial differential equation was based on an implicit finite-difference method (FDM. An upwind scheme was employed for numerical stability. The resulting algebraic equations were solved simultaneously using the multivariate Newton-Raphson iteration method. The solution allows for the evaluation of the effect on the concentration profiles of (i the radial and axial convective velocity, (ii the convective mass transfer rates, (iii the reaction rates, (iv the fraction retentate, and (v the aspect ratio.

  20. M2Di: MATLAB 2D Stokes solvers using the Finite Difference method (United States)

    Räss, Ludovic; Duretz, Thibault; Schmalholz, Stefan; Podladchikov, Yury


    The study of coupled processes in Earth Sciences leads to the development of multiphysics modelling tools. Mechanical solvers represent the essential ingredient of any of these tools such that their performance and robustness is generally dictated by that of the mechanical solver. Here, we present M2Di, a collection of MATLAB routines designed for studying 2D linear and power law incompressible viscous flow using Finite Difference discretisation. The scripts are written in a concise vectorised MATLAB fashion and rely on fast and robust linear and non-linear solvers (Picard and Newton iterations). As a result, time to solution of 22 seconds for linear viscous flow with 104 viscosity jump on 10002 grid points can be achieved on a standard personal computer. We will present a numerous example of applications that span from high resolution crystal-melt dynamics, deformation of heterogeneous power law viscous fluids, instantaneous mantle flow patterns in cylindrical coordinates, and calculation of pressure gradients around inclusions using variable grid spacing. We use analytical solution for linear viscous flow with highly variable viscosity to validate the linear flow solver. Validation of the non-linear solver is achieved by comparing numerical solution to analytic and benchmark solutions of power law viscous folding and necking. The M2Di codes are open source and can hence be used for research or educational purposes.

  1. Multiscale Finite-Difference-Diffusion-Monte-Carlo Method for Simulating Dendritic Solidification (United States)

    Plapp, Mathis; Karma, Alain


    We present a novel hybrid computational method to simulate accurately dendritic solidification in the low undercooling limit where the dendrite tip radius is one or more orders of magnitude smaller than the characteristic spatial scale of variation of the surrounding thermal or solutal diffusion field. The first key feature of this method is an efficient multiscale diffusion Monte Carlo (DMC) algorithm which allows off-lattice random walkers to take longer and concomitantly rarer steps with increasing distance away from the solid-liquid interface. As a result, the computational cost of evolving the large-scale diffusion field becomes insignificant when compared to that of calculating the interface evolution. The second key feature is that random walks are only permitted outside of a thin liquid layer surrounding the interface. Inside this layer and in the solid, the diffusion equation is solved using a standard finite difference algorithm that is interfaced with the DMC algorithm using the local conservation law for the diffusing quantity. Here we combine this algorithm with a previously developed phase-field formulation of the interface dynamics and demonstrate that it can accurately simulate three-dimensional dendritic growth in a previously unreachable range of low undercoolings that is of direct experimental relevance.

  2. [Response of a finite element model of the pelvis to different side impact loads]. (United States)

    Ruan, Shijie; Zheng, Huijing; Li, Haiyan; Zhao, Wei


    The pelvis is one of the most likely affected areas of the human body in case of side impact, especially while people suffer from motor vehicle crashes. With the investigation of pelvis injury on side impact, the injury biomechanical behavior of pelvis can be found, and the data can help design the vehicle security devices to keep the safety of the occupants. In this study, a finite element (FE) model of an isolated human pelvis was used to study the pelvic dynamic response under different side impact conditions. Fracture threshold was established by applying lateral loads of 1000, 2000, 3000, 4000 and 5000 N, respectively, to the articular surface of the right acetabulum. It was observed that the smaller the lateral loads were, the smaller the von Mises stress and the displacement in the direction of impact were. It was also found that the failure threshold load was near 3000 N, based on the fact that the peak stress would not exceed the average compressive strength of the cortical bone. It could well be concluded that with better design of car-door and hip-pad so that the side impact force was brought down to 3000 N or lower, the pelvis would not be injured.

  3. A comparison between different finite elements for elastic and aero-elastic analyses

    Directory of Open Access Journals (Sweden)

    Mohamed Mahran


    Full Text Available In the present paper, a comparison between five different shell finite elements, including the Linear Triangular Element, Linear Quadrilateral Element, Linear Quadrilateral Element based on deformation modes, 8-node Quadrilateral Element, and 9-Node Quadrilateral Element was presented. The shape functions and the element equations related to each element were presented through a detailed mathematical formulation. Additionally, the Jacobian matrix for the second order derivatives was simplified and used to derive each element’s strain-displacement matrix in bending. The elements were compared using carefully selected elastic and aero-elastic bench mark problems, regarding the number of elements needed to reach convergence, the resulting accuracy, and the needed computation time. The best suitable element for elastic free vibration analysis was found to be the Linear Quadrilateral Element with deformation-based shape functions, whereas the most suitable element for stress analysis was the 8-Node Quadrilateral Element, and the most suitable element for aero-elastic analysis was the 9-Node Quadrilateral Element. Although the linear triangular element was the last choice for modal and stress analyses, it establishes more accurate results in aero-elastic analyses, however, with much longer computation time. Additionally, the nine-node quadrilateral element was found to be the best choice for laminated composite plates analysis.

  4. Accelerated cardiac cine MRI using locally low rank and finite difference constraints. (United States)

    Miao, Xin; Lingala, Sajan Goud; Guo, Yi; Jao, Terrence; Usman, Muhammad; Prieto, Claudia; Nayak, Krishna S


    To evaluate the potential value of combining multiple constraints for highly accelerated cardiac cine MRI. A locally low rank (LLR) constraint and a temporal finite difference (FD) constraint were combined to reconstruct cardiac cine data from highly undersampled measurements. Retrospectively undersampled 2D Cartesian reconstructions were quantitatively evaluated against fully-sampled data using normalized root mean square error, structural similarity index (SSIM) and high frequency error norm (HFEN). This method was also applied to 2D golden-angle radial real-time imaging to facilitate single breath-hold whole-heart cine (12 short-axis slices, 9-13s single breath hold). Reconstruction was compared against state-of-the-art constrained reconstruction methods: LLR, FD, and k-t SLR. At 10 to 60 spokes/frame, LLR+FD better preserved fine structures and depicted myocardial motion with reduced spatio-temporal blurring in comparison to existing methods. LLR yielded higher SSIM ranking than FD; FD had higher HFEN ranking than LLR. LLR+FD combined the complimentary advantages of the two, and ranked the highest in all metrics for all retrospective undersampled cases. Single breath-hold multi-slice cardiac cine with prospective undersampling was enabled with in-plane spatio-temporal resolutions of 2×2mm(2) and 40ms. Highly accelerated cardiac cine is enabled by the combination of 2D undersampling and the synergistic use of LLR and FD constraints. Copyright © 2016 Elsevier Inc. All rights reserved.

  5. An Efficient Explicit Finite-Difference Scheme for Simulating Coupled Biomass Growth on Nutritive Substrates

    Directory of Open Access Journals (Sweden)

    G. F. Sun


    Full Text Available A novel explicit finite-difference (FD method is presented to simulate the positive and bounded development process of a microbial colony subjected to a substrate of nutrients, which is governed by a nonlinear parabolic partial differential equations (PDE system. Our explicit FD scheme is uniquely designed in such a way that it transfers the nonlinear terms in the original PDE into discrete sets of linear ones in the algebraic equation system that can be solved very efficiently, while ensuring the stability and the boundedness of the solution. This is achieved through (1 a proper design of intertwined FD approximations for the diffusion function term in both time and spatial variations and (2 the control of the time-step through establishing theoretical stability criteria. A detailed theoretical stability analysis is conducted to reveal that our FD method is indeed stable. Our examples verified the fact that the numerical solution can be ensured nonnegative and bounded to simulate the actual physics. Numerical examples have also been presented to demonstrate the efficiency of the proposed scheme. The present scheme is applicable for solving similar systems of PDEs in the investigation of the dynamics of biological films.

  6. Data assimilation method for fractured reservoirs using mimetic finite differences and ensemble Kalman filter

    KAUST Repository

    Ping, Jing


    Optimal management of subsurface processes requires the characterization of the uncertainty in reservoir description and reservoir performance prediction. For fractured reservoirs, the location and orientation of fractures are crucial for predicting production characteristics. With the help of accurate and comprehensive knowledge of fracture distributions, early water/CO 2 breakthrough can be prevented and sweep efficiency can be improved. However, since the rock property fields are highly non-Gaussian in this case, it is a challenge to estimate fracture distributions by conventional history matching approaches. In this work, a method that combines vector-based level-set parameterization technique and ensemble Kalman filter (EnKF) for estimating fracture distributions is presented. Performing the necessary forward modeling is particularly challenging. In addition to the large number of forward models needed, each model is used for sampling of randomly located fractures. Conventional mesh generation for such systems would be time consuming if possible at all. For these reasons, we rely on a novel polyhedral mesh method using the mimetic finite difference (MFD) method. A discrete fracture model is adopted that maintains the full geometry of the fracture network. By using a cut-cell paradigm, a computational mesh for the matrix can be generated quickly and reliably. In this research, we apply this workflow on 2D two-phase fractured reservoirs. The combination of MFD approach, level-set parameterization, and EnKF provides an effective solution to address the challenges in the history matching problem of highly non-Gaussian fractured reservoirs.

  7. Methods for compressible fluid simulation on GPUs using high-order finite differences (United States)

    Pekkilä, Johannes; Väisälä, Miikka S.; Käpylä, Maarit J.; Käpylä, Petri J.; Anjum, Omer


    We focus on implementing and optimizing a sixth-order finite-difference solver for simulating compressible fluids on a GPU using third-order Runge-Kutta integration. Since graphics processing units perform well in data-parallel tasks, this makes them an attractive platform for fluid simulation. However, high-order stencil computation is memory-intensive with respect to both main memory and the caches of the GPU. We present two approaches for simulating compressible fluids using 55-point and 19-point stencils. We seek to reduce the requirements for memory bandwidth and cache size in our methods by using cache blocking and decomposing a latency-bound kernel into several bandwidth-bound kernels. Our fastest implementation is bandwidth-bound and integrates 343 million grid points per second on a Tesla K40t GPU, achieving a 3 . 6 × speedup over a comparable hydrodynamics solver benchmarked on two Intel Xeon E5-2690v3 processors. Our alternative GPU implementation is latency-bound and achieves the rate of 168 million updates per second.

  8. Design and development of an air humidifier using finite difference method for a solar desalination plant (United States)

    Chiranjeevi, C.; Srinivas, T.


    Humidifier is an important component in air humidification-dehumidification desalination plant for fresh water production. Liquid to air flow rate ratio is optimization is reported for an industrial cooling towers but for an air humidifier it is not addressed. The current work is focused on the design and analysis of an air humidifier for solar desalination plant to maximize the yield with better humidification, using finite difference method (FDM). The outlet conditions of air from the humidifier are theoretically predicted by FDM with the given inlet conditions, which will be further used in the design calculation of the humidifier. Hot water to air flow rate ratio and inlet hot water temperature are identified as key operating parameters to evaluate the humidifier performance. The maximum and optimal values of mass flow rate ratio of water to air are found to be 2.15 and 1.5 respectively using packing function and Merkel Integral. The height of humidifier is constrained to 1.5 m and the diameter of the humidifier is found as 0.28m. The performance of humidifier and outlet conditions of air are simulated using FDM and compared with experimental results. The obtained results are within an agreeable range of deviation.

  9. Auralization of concert hall acoustics using finite difference time domain methods and wave field synthesis (United States)

    Hochgraf, Kelsey

    Auralization methods have been used for a long time to simulate the acoustics of a concert hall for different seat positions. The goal of this thesis was to apply the concept of auralization to a larger audience area that the listener could walk through to compare differences in acoustics for a wide range of seat positions. For this purpose, the acoustics of Rensselaer's Experimental Media and Performing Arts Center (EMPAC) Concert Hall were simulated to create signals for a 136 channel wave field synthesis (WFS) system located at Rensselaer's Collaborative Research Augmented Immersive Virtual Environment (CRAIVE) Laboratory. By allowing multiple people to dynamically experience the concert hall's acoustics at the same time, this research gained perspective on what is important for achieving objective accuracy and subjective plausibility in an auralization. A finite difference time domain (FDTD) simulation on a three-dimensional face-centered cubic grid, combined at a crossover frequency of 800 Hz with a CATT-Acoustic(TM) simulation, was found to have a reverberation time, direct to reverberant sound energy ratio, and early reflection pattern that more closely matched measured data from the hall compared to a CATT-Acoustic(TM) simulation and other hybrid simulations. In the CRAIVE lab, nine experienced listeners found all hybrid auralizations (with varying source location, grid resolution, crossover frequency, and number of loudspeakers) to be more perceptually plausible than the CATT-Acoustic(TM) auralization. The FDTD simulation required two days to compute, while the CATT-Acoustic(TM) simulation required three separate TUCT(TM) computations, each taking four hours, to accommodate the large number of receivers. Given the perceptual advantages realized with WFS for auralization of a large, inhomogeneous sound field, it is recommended that hybrid simulations be used in the future to achieve more accurate and plausible auralizations. Predictions are made for a

  10. A finite difference approach to despiking in-stationary velocity data - tested on a triple-lidar

    DEFF Research Database (Denmark)

    Meyer Forsting, Alexander Raul; Troldborg, Niels


    A novel despiking method is presented for in-stationary wind lidar velocity measurements. A finite difference approach yields the upper and lower bounds for a valid velocity reading. The sole input to the algorithm is the velocity series and optionally a far- field reference to the temporal...

  11. Application of the finite-difference contrast-source inversion algorithm to seismic full-waveform data

    NARCIS (Netherlands)

    Abubakar, A.; Hu, W.; Habashy, T.M.; Van den Berg, P.M.


    We have applied the finite-difference contrast-source inversion (FDCSI) method to seismic full-waveform inversion problems. The FDCSI method is an iterative nonlinear inversion algorithm. However, unlike the nonlinear conjugate gradient method and the Gauss-Newton method, FDCSI does not solve any

  12. High-Accuracy Approximation of High-Rank Derivatives: Isotropic Finite Differences Based on Lattice-Boltzmann Stencils

    Directory of Open Access Journals (Sweden)

    Keijo Kalervo Mattila


    Full Text Available We propose isotropic finite differences for high-accuracy approximation of high-rank derivatives. These finite differences are based on direct application of lattice-Boltzmann stencils. The presented finite-difference expressions are valid in any dimension, particularly in two and three dimensions, and any lattice-Boltzmann stencil isotropic enough can be utilized. A theoretical basis for the proposed utilization of lattice-Boltzmann stencils in the approximation of high-rank derivatives is established. In particular, the isotropy and accuracy properties of the proposed approximations are derived directly from this basis. Furthermore, in this formal development, we extend the theory of Hermite polynomial tensors in the case of discrete spaces and present expressions for the discrete inner products between monomials and Hermite polynomial tensors. In addition, we prove an equivalency between two approaches for constructing lattice-Boltzmann stencils. For the numerical verification of the presented finite differences, we introduce 5th-, 6th-, and 8th-order two-dimensional lattice-Boltzmann stencils.

  13. High-accuracy approximation of high-rank derivatives: isotropic finite differences based on lattice-Boltzmann stencils. (United States)

    Mattila, Keijo Kalervo; Hegele Júnior, Luiz Adolfo; Philippi, Paulo Cesar


    We propose isotropic finite differences for high-accuracy approximation of high-rank derivatives. These finite differences are based on direct application of lattice-Boltzmann stencils. The presented finite-difference expressions are valid in any dimension, particularly in two and three dimensions, and any lattice-Boltzmann stencil isotropic enough can be utilized. A theoretical basis for the proposed utilization of lattice-Boltzmann stencils in the approximation of high-rank derivatives is established. In particular, the isotropy and accuracy properties of the proposed approximations are derived directly from this basis. Furthermore, in this formal development, we extend the theory of Hermite polynomial tensors in the case of discrete spaces and present expressions for the discrete inner products between monomials and Hermite polynomial tensors. In addition, we prove an equivalency between two approaches for constructing lattice-Boltzmann stencils. For the numerical verification of the presented finite differences, we introduce 5th-, 6th-, and 8th-order two-dimensional lattice-Boltzmann stencils.

  14. A Moving Mesh Finite Difference Method for Non-Monotone Solutions of Non-Equilibrium Equations in Porous Media

    NARCIS (Netherlands)

    Zhang, Hong; Zegeling, Paul Andries


    An adaptive moving mesh finite difference method is presented to solve two types of equations with dynamic capillary pressure effect in porous media. One is the non-equilibrium Richards Equation and the other is the modified Buckley-Leverett equation. The governing equations are discretized with an

  15. Solving the maxwell equations by the Chebyshev method : A one-step finite-difference time-domain algorithm

    NARCIS (Netherlands)

    de Raedt, H.A.; Michielsen, K.F L; Kole, J.S.; Figge, M.T


    We present a one-step algorithm that solves the Maxwell equations for systems with spatially varying permittivity and permeability by the Chebyshev method. We demonstrate that this algorithm may be orders of magnitude more efficient than current finite-difference time-domain (FDTD) algorithms.

  16. An Adaptive Finite Difference Method for Hyperbolic Systems in OneSpace Dimension

    Energy Technology Data Exchange (ETDEWEB)

    Bolstad, John H. [Stanford Univ., CA (United States); Univ. of California, Berkeley, CA (United States)


    Many problems of physical interest have solutions which are generally quite smooth in a large portion of the region of interest, but have local phenomena such as shocks, discontinuities or large gradients which require much more accurate approximations or finer grids for reasonable accuracy. Examples are atmospheric fronts, ocean currents, and geological discontinuities. In this thesis we develop and partially analyze an adaptive finite difference mesh refinement algorithm for the initial boundary value problem for hyperbolic systems in one space dimension. The method uses clusters of uniform grids which can ''move'' along with pulses or steep gradients appearing in the calculation, and which are superimposed over a uniform coarse grid. Such refinements are created, destroyed, merged, separated, recursively nested or moved based on estimates of the local truncation error. We use a four-way linked tree and sequentially allocated deques (double-ended queues) to perform these operations efficiently. The local truncation error in the interior of the region is estimated using a three-step Richardson extrapolation procedure, which can also be considered a deferred correction method. At the boundaries we employ differences to estimate the error. Our algorithm was implemented using a portable, extensible Fortran preprocessor, to which we added records and pointers. The method is applied to three model problems: the first order wave equation, the second order wave equation, and the inviscid Burgers equation. For the first two model problems our algorithm is shown to be three to five times more efficient (in computing time) than the use of a uniform coarse mesh, for the same accuracy. Furthermore, to our knowledge, our algorithm is the only one which adaptively treats time-dependent boundary conditions for hyperbolic systems.

  17. Finite-Difference Algorithm for 3D Orthorhombic Elastic Wave Propagation (United States)

    Jensen, R.; Preston, L. A.; Aldridge, D. F.


    Many geophysicists concur that an orthorhombic elastic medium, characterized by three mutually orthogonal symmetry planes, constitutes a realistic representation of seismic anisotropy in shallow crustal rocks. This symmetry condition typically arises via a dense system of vertically-aligned microfractures superimposed on a finely-layered horizontal geology. Mathematically, the elastic stress-strain constitutive relations for an orthorhombic body contain nine independent moduli. In turn, these moduli can be determined by observing (or prescribing) nine independent P-wave and S-wave phase speeds along different propagation directions. We are developing an explicit time-domain finite-difference (FD) algorithm for simulating 3D elastic wave propagation in a heterogeneous orthorhombic medium. The components of the particle velocity vector and the stress tensor are governed by a set of nine, coupled, first-order, linear, partial differential equations (PDEs) called the velocity-stress system. All time and space derivatives are discretized with centered and staggered FD operators possessing second- and fourth-order numerical accuracy, respectively. Simplified FD updating formulae (with significantly reduced operation counts) for stress components are obtained by restricting the principle axes of the modulus tensor to be parallel to the global rectangular coordinate axes. Moreover, restriction to a piecewise homogeneous earth model reduces computational memory demand for storing the ten (including mass density) model parameters. These restrictions will be relaxed in the future. Novel perfectly matched layer (PML) absorbing boundary conditions, specifically designed for orthorhombic media, effectively suppress grid boundary reflections. Initial modeling results reveal the well-established anisotropic seismic phenomena of complex wavefront shapes, split (fast and slow) S-waves, and shear waves generated by a spherically-symmetric explosion in a homogeneous body.

  18. Analysis of attenuation and dispersion of Rayleigh waves in viscoelastic media by finite-difference modeling (United States)

    Yuan, Shichuan; Song, Xianhai; Cai, Wei; Hu, Ying


    Viscoelasticity of Earth media has an important influence on Rayleigh-wave propagation. Therefore, it is necessary to study the attenuation and dispersion of Rayleigh-wave by numerical modeling to better understand Rayleigh-wave behaviors in Earth media. Modeling adopts a staggered finite-difference (FD) scheme, which calculates the spatial derivatives by a 12th-order operator and the time derivatives by the fourth-order Runge-Kutta method. In time-space domain, the accuracy of FD method is demonstrated through comparing the modeling results with the analytical solution in an elastic half-space. In frequency-velocity domain, the correctness of modeling results is verified via comparing the dispersive images with the theoretical dispersion curves of Rayleigh-wave. The attenuation and dispersion of Rayleigh-wave are analyzed by comparisons between elastic and viscoelastic modeling results in the homogeneous half-space models in terms of the wave field snapshots, the synthetic seismograms, and the dispersive images, respectively. The two-layer models are also simulated to further investigate the attenuation and dispersion of Rayleigh-wave in viscoelastic layered media. Results show that the viscoelastic Rayleigh-wave presents substantial differences in amplitude and phase velocity compared with the elastic case. Viscoelasticity of media arouses amplitude attenuation of Rayleigh-wave. The high-frequency waves are attenuated more severely than the lower-frequency waves, and the attenuation degree is severe increasingly with offset increasing. Viscoelasticity of media also causes the phase velocity dispersion of Rayleigh-wave. The phase velocity ratio of viscoelastic Rayleigh-wave respecting to the corresponding elastic one increases with frequency, and the resolution of dispersion energy is lower than the elastic one. The attenuation and dispersion of Rayleigh-wave are prominent increasingly with Q decreasing.

  19. Biomechanical evaluation of different abutment-implant connections - A nonlinear finite element analysis (United States)

    Ishak, Muhammad Ikman; Shafi, Aisyah Ahmad; Rosli, M. U.; Khor, C. Y.; Zakaria, M. S.; Rahim, Wan Mohd Faizal Wan Abd; Jamalludin, Mohd Riduan


    The success of dental implant surgery is majorly dependent on the stability of prosthesis to anchor to implant body as well as the integration of implant body to bone. The attachment between dental implant body and abutment plays a vital role in attributing to the stability of dental implant system. A good connection between implant body cavity to abutment may minimize the complications of abutment loosening and implant fractures as widely reported in clinical findings. The aim of this paper is to investigate the effect of different abutment-implant connections on stress dispersion within the abutment and implant bodies as well as displacement of implant body via three-dimensional (3-D) finite element analysis (FEA). A 3-D model of mandible was reconstructed from computed tomography (CT) image datasets using an image-processing software with the selected region of interest was the left side covering the second premolar, first molar and second molar regions. The bone was modelled as compact (cortical) and porous (cancellous) structures. Besides, three implant bodies and three generic models of abutment with different types of connections - tapered interference fit (TIF), tapered integrated screwed-in (TIS) and screw retention (SR) were created using computer-aided design (CAD) software and all models were then analysed via 3D FEA software. Occlusal forces of 114.6 N, 17.2 N and 23.4 N were applied in the axial, lingual and mesio-distal directions, respectively, on the top surface of first molar crown. All planes of the mandibular bone model were rigidly fixed. The result exhibited that abutment with TIS connection produced the most favourable stress and displacement outcomes as compared to other attachment types. This is due to the existence of integrated screw at the bottom portion of tapered abutment which increases the motion resistance.

  20. Finite difference analysis of an advance core pre-reinforcement system for Toulon's south tube

    Directory of Open Access Journals (Sweden)

    Fethi Kitchah


    Full Text Available The stability of shallow tunnels excavated in full face has been a major challenge to the scientific community for a long time. In recent years, new techniques based on the installation of a pre-reinforcement system ahead of the tunnel face were developed to control the deformations and surface settlements induced by the excavation and to ensure the sustainability of the tunnel in the long term. In this paper, a finite difference numerical simulation was conducted to study the behaviors and effects of two pre-reinforcement systems, i.e. the face bolting and the umbrella arch system installed in a section of southern Toulon tunnel in France. For this purpose, two approaches were taken and compared: a two-dimensional (2D approach based on the convergence–confinement method, and a three-dimensional (3D approach taking into account the complete modeling of the tunnel. A 2D numerical back-analysis was performed to identify the geomechanical parameters that offer satisfactory agreement with the measurement results. The limit of this method lies in the exact choice of the stress relaxation ratio λ. To overcome this uncertainty, a 3D model was developed, which permitted to study the influence of different pre-support systems on the reaction of ground mass. Both 2D and 3D numerical approaches have been fitted to measurements recorded in a section of the Toulon tunnel and the very satisfactory correspondence has allowed validating the simulations. The results show that the 3D numerical analysis with a full discretization of the inclusions seems unquestionably the most reliable approach.

  1. The analytic coarse-mesh finite-difference method for multigroup and multidimensional diffusion calculations

    Energy Technology Data Exchange (ETDEWEB)

    Aragones, J.M.; Ahnert, C.; Garcia-Herranz, N. [Madrid Universidad Politecnica, Dept. of Nuclear Engineering (Spain)


    In this work we develop and demonstrate the Analytic Coarse-Mesh Finite-Difference (ACMFD) method for multigroup, with any number of groups, and multidimensional diffusion calculations of steady-state and kinetics and external source problems. The first step in this method is to reduce the coupled system of the G multigroup diffusion equations, inside any homogenized region (or node) of any size, to the G independent modal equations in the real or complex Eigen-space of the G*G multigroup matrix. The mathematical and numerical analysis of this step is discussed for several reactor media and number of groups. As second step, we discuss the analytical solutions in the general (complex) modal Eigen-space for 1-dimensional plane geometry, deriving the generalized Chao's relation among the surface fluxes and the net currents, at a given interface, and the node average fluxes, essential in the ACMFD method. We also introduce here the treatment of heterogeneous nodes, through modal interface flux discontinuity factors, and show the analytical and numerical application to core-reflector problems, for a single infinite reflector and for reflectors with two layers of different materials. Then, we address the general multidimensional case, with both rectangular X-Y-Z and triangular-Z geometries considered, showing the equivalency of the methods of transverse integration and incomplete expansion of the multidimensional fluxes, in the real or complex modal Eigen-space of the multigroup matrix. A non-linear iteration scheme is implemented to solve the multigroup multidimensional nodal problem, which has shown a fast and robust convergence in proof-of-principle numerical applications to realistic PWR cores, with heterogeneous fuel assemblies and reflectors. (authors)

  2. Finite Automata


    Rogač, Luka Viktor


    In this diploma work the concept of formal language is presented, introducing the ideas related to the concept of formal language and operations over languages. Informal and formal recognition of the concept of the finite state automata is given together with the similarities and differences between deterministic and nondeterministic finite state automata. The concept of regular expression and regular language is described, enabling a transparent and shorter form at writing of the language...

  3. Poroelastic finite-difference modeling for ultrasonic waves in digital porous cores (United States)

    Fu, Li-Yun; Zhang, Yan; Pei, Zhenglin; Wei, Wei; Zhang, Luxin


    Scattering attenuation in short wavelengths has long been interesting to geophysicists. Ultrasonic coda waves, observed as the tail portion of ultrasonic wavetrains in laboratory ultrasonic measurements, are important for such studies where ultrasonic waves interact with small-scale random heterogeneities on a scale of micrometers, but often ignored as noises because of the contamination of boundary reflections from the side ends of a sample core. Numerical simulations with accurate absorbing boundary can provide insight into the effect of boundary reflections on coda waves in laboratory experiments. The simulation of wave propagation in digital and heterogeneous porous cores really challenges numerical techniques by digital image of poroelastic properties, numerical dispersion at high frequency and strong heterogeneity, and accurate absorbing boundary schemes at grazing incidence. To overcome these difficulties, we present a staggered-grid high-order finite-difference (FD) method of Biot's poroelastic equations, with an arbitrary even-order (2 L) accuracy to simulate ultrasonic wave propagation in digital porous cores with strong heterogeneity. An unsplit convolutional perfectly matched layer (CPML) absorbing boundary, which improves conventional PML methods at grazing incidence with less memory and better computational efficiency, is employed in the simulation to investigate the influence of boundary reflections on ultrasonic coda waves. Numerical experiments with saturated poroelastic media demonstrate that the 2 L FD scheme with the CPML for ultrasonic wave propagation significantly improves stability conditions at strong heterogeneity and absorbing performance at grazing incidence. The boundary reflections from the artificial boundary surrounding the digital core decay fast with the increase of CPML thicknesses, almost disappearing at the CPML thickness of 15 grids. Comparisons of the resulting ultrasonic coda Q sc values between the numerical and experimental

  4. M2Di: Concise and efficient MATLAB 2-D Stokes solvers using the Finite Difference Method (United States)

    Räss, Ludovic; Duretz, Thibault; Podladchikov, Yury Y.; Schmalholz, Stefan M.


    Recent development of many multiphysics modeling tools reflects the currently growing interest for studying coupled processes in Earth Sciences. The core of such tools should rely on fast and robust mechanical solvers. Here we provide M2Di, a set of routines for 2-D linear and power law incompressible viscous flow based on Finite Difference discretizations. The 2-D codes are written in a concise vectorized MATLAB fashion and can achieve a time to solution of 22 s for linear viscous flow on 10002 grid points using a standard personal computer. We provide application examples spanning from finely resolved crystal-melt dynamics, deformation of heterogeneous power law viscous fluids to instantaneous models of mantle flow in cylindrical coordinates. The routines are validated against analytical solution for linear viscous flow with highly variable viscosity and compared against analytical and numerical solutions of power law viscous folding and necking. In the power law case, both Picard and Newton iterations schemes are implemented. For linear Stokes flow and Picard linearization, the discretization results in symmetric positive-definite matrix operators on Cartesian grids with either regular or variable grid spacing allowing for an optimized solving procedure. For Newton linearization, the matrix operator is no longer symmetric and an adequate solving procedure is provided. The reported performance of linear and power law Stokes flow is finally analyzed in terms of wall time. All MATLAB codes are provided and can readily be used for educational as well as research purposes. The M2Di routines are available from Bitbucket and the University of Lausanne Scientific Computing Group website, and are also supplementary material to this article.

  5. Stress and deformation of rocket gas turbine disc under different loads using finite element modelling

    Directory of Open Access Journals (Sweden)

    Amr Elhefny


    Full Text Available Gas turbine discs have numerous applications in the aerospace industry, such as in liquid rocket engines. In this study, the stresses and deformations of a turbine disc were studied. The goal was to highlight the stress and deformation distribution to assist in the design of a disc as well as to demonstrate the importance of using finite element (FE analysis in simulating an actual design case. Then, to present the real model, a two-dimensional (2D axisymmetric model for a non-uniform disc was analysed using FE analysis. The stresses and deformations developed as a result of the disc operating conditions at high rotational speeds and thermal gradients were evaluated using two types of heat transfer modes—conduction and convection, taking into consideration the material behaviour at elevated temperatures. The FE model revealed that the weight of the disc should be reduced optimally by using a non-uniform thickness because this results in a huge increase in the applied stresses. The greatest stresses in the disc result from the thermal load caused by conduction, and they are located at the centre of the disc. In addition, an analytical method was used to evaluate and predict the stresses along the disc, and it gave a good estimate of the stress values compared to the FE model. Based on this estimate, a parametric study was conducted for a range of rotational velocities under high temperature loads for a series of disc radii. Finally, it was found that this method can be used for the preliminary design of different turbines.

  6. RSW Fully Tet Coarse Cell-Centered Mesh (United States)

    National Aeronautics and Space Administration — This is the RSW fully tetrahedral unstructured mesh dataset for a cell-centered code, including the viscous wind tunnel wall. UG3 : Grid File Name =...

  7. RSW Fully Tet Cell-Centered Fine Mesh (United States)

    National Aeronautics and Space Administration — This is the RSW dataset for a fine fully tetrahedral grid designed for a cell-centered unstructured solver. UG3 : Grid File Name = rsw_fine_tetcc.b8.ugrid UG3 : Quad...

  8. RSW Mixed Element Cell-Centered Medium Mesh (United States)

    National Aeronautics and Space Administration — This RSW gridset is designed as the medium size mixed element grid for use with cell-centered unstructured meshes. UG3 : Grid File Name = rsw_med_mixedcc.b8.ugrid...

  9. RSW Fully Tet Medium Cell-Centered Mesh (United States)

    National Aeronautics and Space Administration — This is the RSW Fully tetrahedral medium cell-centered unstructured grid with a viscous wall. UG3 : Grid File Name = rsw_med_tetcc.b8.ugrid UG3 : Quad Surface Faces=...

  10. Inverse Interpolation: The Rate of Enzymatic Reaction based Finite differences, Formulas for obtaining intermediate values of Temperature, Substrate Concentration, Enzyme Concentration and their Estimation of Errors


    Nizam Uddin


    Inverse interpolation is the process of finding the values of the argument corresponding to a given value of the function when the latter is intermediate between two tabulated values. The finite differences are differences between the values of the function or the difference between the past differences. Finite differences are forward difference, backward difference and divide difference. Temperature, concentration of substrate, concentration of enzyme and other factors are affected the rate ...

  11. Statistical parameters of random heterogeneity estimated by analysing coda waves based on finite difference method (United States)

    Emoto, K.; Saito, T.; Shiomi, K.


    Short-period (seismic waves and randomly distributed small-scale heterogeneities. Statistical properties of the random heterogeneities have been estimated by analysing short-period seismograms. However, generally, the small-scale random heterogeneity is not taken into account for the modelling of long-period (>2 s) seismograms. We found that the energy of the coda of long-period seismograms shows a spatially flat distribution. This phenomenon is well known in short-period seismograms and results from the scattering by small-scale heterogeneities. We estimate the statistical parameters that characterize the small-scale random heterogeneity by modelling the spatiotemporal energy distribution of long-period seismograms. We analyse three moderate-size earthquakes that occurred in southwest Japan. We calculate the spatial distribution of the energy density recorded by a dense seismograph network in Japan at the period bands of 8-16 s, 4-8 s and 2-4 s and model them by using 3-D finite difference (FD) simulations. Compared to conventional methods based on statistical theories, we can calculate more realistic synthetics by using the FD simulation. It is not necessary to assume a uniform background velocity, body or surface waves and scattering properties considered in general scattering theories. By taking the ratio of the energy of the coda area to that of the entire area, we can separately estimate the scattering and the intrinsic absorption effects. Our result reveals the spectrum of the random inhomogeneity in a wide wavenumber range including the intensity around the corner wavenumber as P(m) = 8πε2a3/(1 + a2m2)2, where ε = 0.05 and a = 3.1 km, even though past studies analysing higher-frequency records could not detect the corner. Finally, we estimate the intrinsic attenuation by modelling the decay rate of the energy. The method proposed in this study is suitable for quantifying the statistical properties of long-wavelength subsurface random inhomogeneity, which

  12. Numerical simulation of particulate flows using a hybrid of finite difference and boundary integral methods. (United States)

    Bhattacharya, Amitabh; Kesarkar, Tejas


    A combination of finite difference (FD) and boundary integral (BI) methods is used to formulate an efficient solver for simulating unsteady Stokes flow around particles. The two-dimensional (2D) unsteady Stokes equation is being solved on a Cartesian grid using a second order FD method, while the 2D steady Stokes equation is being solved near the particle using BI method. The two methods are coupled within the viscous boundary layer, a few FD grid cells away from the particle, where solutions from both FD and BI methods are valid. We demonstrate that this hybrid method can be used to accurately solve for the flow around particles with irregular shapes, even though radius of curvature of the particle surface is not resolved by the FD grid. For dilute particle concentrations, we construct a virtual envelope around each particle and solve the BI problem for the flow field located between the envelope and the particle. The BI solver provides velocity boundary condition to the FD solver at "boundary" nodes located on the FD grid, adjacent to the particles, while the FD solver provides the velocity boundary condition to the BI solver at points located on the envelope. The coupling between FD method and BI method is implicit at every time step. This method allows us to formulate an O(N) scheme for dilute suspensions, where N is the number of particles. For semidilute suspensions, where particles may cluster, an envelope formation method has been formulated and implemented, which enables solving the BI problem for each individual particle cluster, allowing efficient simulation of hydrodynamic interaction between particles even when they are in close proximity. The method has been validated against analytical results for flow around a periodic array of cylinders and for Jeffrey orbit of a moving ellipse in shear flow. Simulation of multiple force-free irregular shaped particles in the presence of shear in a 2D slit flow has been conducted to demonstrate the robustness of

  13. Acoustic Wave Propagation Modeling by a Two-dimensional Finite-difference Summation-by-parts Algorithm

    Energy Technology Data Exchange (ETDEWEB)

    Kim, K. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Petersson, N. A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Rodgers, A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)


    Acoustic waveform modeling is a computationally intensive task and full three-dimensional simulations are often impractical for some geophysical applications such as long-range wave propagation and high-frequency sound simulation. In this study, we develop a two-dimensional high-order accurate finite-difference code for acoustic wave modeling. We solve the linearized Euler equations by discretizing them with the sixth order accurate finite difference stencils away from the boundary and the third order summation-by-parts (SBP) closure near the boundary. Non-planar topographic boundary is resolved by formulating the governing equation in curvilinear coordinates following the interface. We verify the implementation of the algorithm by numerical examples and demonstrate the capability of the proposed method for practical acoustic wave propagation problems in the atmosphere.

  14. Newton's method applied to finite-difference approximations for the steady-state compressible Navier-Stokes equations (United States)

    Bailey, Harry E.; Beam, Richard M.


    Finite-difference approximations for steady-state compressible Navier-Stokes equations, whose two spatial dimensions are written in generalized curvilinear coordinates and strong conservation-law form, are presently solved by means of Newton's method in order to obtain a lifting-airfoil flow field under subsonic and transonnic conditions. In addition to ascertaining the computational requirements of an initial guess ensuring convergence and the degree of computational efficiency obtainable via the approximate Newton method's freezing of the Jacobian matrices, attention is given to the need for auxiliary methods assessing the temporal stability of steady-state solutions. It is demonstrated that nonunique solutions of the finite-difference equations are obtainable by Newton's method in conjunction with a continuation method.

  15. A Fast Implicit Finite Difference Method for Fractional Advection-Dispersion Equations with Fractional Derivative Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Taohua Liu


    Full Text Available Fractional advection-dispersion equations, as generalizations of classical integer-order advection-dispersion equations, are used to model the transport of passive tracers carried by fluid flow in a porous medium. In this paper, we develop an implicit finite difference method for fractional advection-dispersion equations with fractional derivative boundary conditions. First-order consistency, solvability, unconditional stability, and first-order convergence of the method are proven. Then, we present a fast iterative method for the implicit finite difference scheme, which only requires storage of O(K and computational cost of O(Klog⁡K. Traditionally, the Gaussian elimination method requires storage of O(K2 and computational cost of O(K3. Finally, the accuracy and efficiency of the method are checked with a numerical example.

  16. Single-cone finite-difference schemes for the (2+1)-dimensional Dirac equation in general electromagnetic textures (United States)

    Pötz, Walter


    A single-cone finite-difference lattice scheme is developed for the (2+1)-dimensional Dirac equation in presence of general electromagnetic textures. The latter is represented on a (2+1)-dimensional staggered grid using a second-order-accurate finite difference scheme. A Peierls-Schwinger substitution to the wave function is used to introduce the electromagnetic (vector) potential into the Dirac equation. Thereby, the single-cone energy dispersion and gauge invariance are carried over from the continuum to the lattice formulation. Conservation laws and stability properties of the formal scheme are identified by comparison with the scheme for zero vector potential. The placement of magnetization terms is inferred from consistency with the one for the vector potential. Based on this formal scheme, several numerical schemes are proposed and tested. Elementary examples for single-fermion transport in the presence of in-plane magnetization are given, using material parameters typical for topological insulator surfaces.

  17. A Radial Basis Function (RBF)-Finite Difference (FD) Method for Diffusion and Reaction-Diffusion Equations on Surfaces


    Shankar, Varun; Wright, Grady B.; Kirby, Robert M.; Fogelson, Aaron L.


    In this paper, we present a method based on Radial Basis Function (RBF)-generated Finite Differences (FD) for numerically solving diffusion and reaction-diffusion equations (PDEs) on closed surfaces embedded in $\\mathbb{R}^d$. Our method uses a method-of-lines formulation, in which surface derivatives that appear in the PDEs are approximated locally using RBF interpolation. The method requires only scattered nodes representing the surface and normal vectors at those scattered nodes. All compu...

  18. Estimation of State of Charge for Lithium-Ion Battery Based on Finite Difference Extended Kalman Filter


    Ze Cheng; Jikao Lv; Yanli Liu; Zhihao Yan


    An accurate estimation of the state of charge (SOC) of the battery is of great significance for safe and efficient energy utilization of electric vehicles. Given the nonlinear dynamic system of the lithium-ion battery, the parameters of the second-order RC equivalent circuit model were calibrated and optimized using a nonlinear least squares algorithm in the Simulink parameter estimation toolbox. A comparison was made between this finite difference extended Kalman filter (FDEKF) and the stand...

  19. SBP-SAT finite difference discretization of acoustic wave equations on staggered block-wise uniform grids

    KAUST Repository

    Gao, Longfei


    We consider the numerical simulation of the acoustic wave equations arising from seismic applications, for which staggered grid finite difference methods are popular choices due to their simplicity and efficiency. We relax the uniform grid restriction on finite difference methods and allow the grids to be block-wise uniform with nonconforming interfaces. In doing so, variations in the wave speeds of the subterranean media can be accounted for more efficiently. Staggered grid finite difference operators satisfying the summation-by-parts (SBP) property are devised to approximate the spatial derivatives appearing in the acoustic wave equation. These operators are applied within each block independently. The coupling between blocks is achieved through simultaneous approximation terms (SATs), which impose the interface condition weakly, i.e., by penalty. Ratio of the grid spacing of neighboring blocks is allowed to be rational number, for which specially designed interpolation formulas are presented. These interpolation formulas constitute key pieces of the simultaneous approximation terms. The overall discretization is shown to be energy-conserving and examined on test cases of both theoretical and practical interests, delivering accurate and stable simulation results.

  20. Serpentine: Finite Difference Methods for Wave Propagation in Second Order Formulation

    Energy Technology Data Exchange (ETDEWEB)

    Petersson, N A; Sjogreen, B


    second order system is significantly smaller. Another issue with re-writing a second order system into first order form is that compatibility conditions often must be imposed on the first order form. These (Saint-Venant) conditions ensure that the solution of the first order system also satisfies the original second order system. However, such conditions can be difficult to enforce on the discretized equations, without introducing additional modeling errors. This project has previously developed robust and memory efficient algorithms for wave propagation including effects of curved boundaries, heterogeneous isotropic, and viscoelastic materials. Partially supported by internal funding from Lawrence Livermore National Laboratory, many of these methods have been implemented in the open source software WPP, which is geared towards 3-D seismic wave propagation applications. This code has shown excellent scaling on up to 32,768 processors and has enabled seismic wave calculations with up to 26 Billion grid points. TheWPP calculations have resulted in several publications in the field of computational seismology, e.g.. All of our current methods are second order accurate in both space and time. The benefits of higher order accurate schemes for wave propagation have been known for a long time, but have mostly been developed for first order hyperbolic systems. For second order hyperbolic systems, it has not been known how to make finite difference schemes stable with free surface boundary conditions, heterogeneous material properties, and curvilinear coordinates. The importance of higher order accurate methods is not necessarily to make the numerical solution more accurate, but to reduce the computational cost for obtaining a solution within an acceptable error tolerance. This is because the accuracy in the solution can always be improved by reducing the grid size h. However, in practice, the available computational resources might not be large enough to solve the problem with a

  1. Investigation of contact acoustic nonlinearity in delaminations by shearographic imaging, laser doppler vibrometric scanning and finite difference modeling. (United States)

    Sarens, Bart; Verstraeten, Bert; Glorieux, Christ; Kalogiannakis, Georgios; Van Hemelrijck, Danny


    Full-field dynamic shearography and laser Doppler vibrometric scanning are used to investigate the local contact acoustic nonlinear generation of delamination-induced effects on the vibration of a harmonically excited composite plate containing an artificial defect. Nonlinear elastic behavior caused by the stress-dependent boundary conditions at the delamination interfaces of a circular defect is also simulated by a 3-D second-order, finite-difference, staggered-grid model (displacement-stress formulation). Both the experimental and simulated data reveal an asymmetric motion of the layer above the delamination, which acts as a membrane vibrating with enhanced displacement amplitude around a finite offset displacement. The spectrum of the membrane motion is enriched with clapping-induced harmonics of the excitation frequency. In case of a sufficiently thin and soft membrane, the simulations reveal clear modal behavior at sub-harmonic frequencies caused by inelastic clapping.

  2. Different Finite Durations of Anticoagulation and Outcomes following Idiopathic Venous Thromboembolism: A Meta-Analysis

    Directory of Open Access Journals (Sweden)

    Aaron B. Holley


    Full Text Available Introduction. Controversy remains over the optimal length of anticoagulation following idiopathic venous thromboembolism. We sought to determine if a longer, finite course of anticoagulation offered additional benefit over a short course in the initial treatment of the first episode of idiopathic venous thromboembolism. Data Extraction. Rates of deep venous thrombosis, pulmonary embolism, combined venous thromboembolism, major bleeding, and mortality were extracted from prospective trials enrolling patients with first time, idiopathic venous thromboembolism. Data was pooled using random effects meta-regression. Results. Ten trials, with a total of 3225 patients, met inclusion criteria. For each additional month of initial anticoagulation, once therapy was stopped, recurrent venous thromboembolism (0.03 (95% CI: −0.28 to 0.35; =.24, mortality (−0.10 (95% CI: −0.24 to 0.04; =.15, and major bleeding (−0.01 (95% CI: −0.05 to 0.02; =.44 rates measured in percent per patient years, did not significantly change. Conclusions: Patients with an initial idiopathic venous thromboembolism should be treated with 3 to 6 months of secondary prophylaxis with vitamin K antagonists. At that time, a decision between continuing with indefinite therapy can be made, but there is no benefit to a longer (but finite course of therapy.

  3. Development of the software Conden 1.0 in finite differences to model electrostatics problems 2D

    Directory of Open Access Journals (Sweden)

    Wilson Rodríguez Calderón


    Full Text Available The present work consists on the development and implementation of the finite differences method for over-relaxation adapted to irregular meshes to determine the influence of the air frontiers on the potencial values and field electricians, calculated inside a badges parallel condenser, using GID like a pre/post-process platform and Fortran like a programming language of the calculation motor of differences Conden 1.0. The problem domain is constituted by two rectangles that represent the condenser and the air layer that covers it, divided in rectangular meshes no standardize.

  4. One-dimensional coupled Burgers’ equation and its numerical solution by an implicit logarithmic finite-difference method

    Directory of Open Access Journals (Sweden)

    Vineet K. Srivastava


    Full Text Available In this paper, an implicit logarithmic finite difference method (I-LFDM is implemented for the numerical solution of one dimensional coupled nonlinear Burgers’ equation. The numerical scheme provides a system of nonlinear difference equations which we linearise using Newton's method. The obtained linear system via Newton's method is solved by Gauss elimination with partial pivoting algorithm. To illustrate the accuracy and reliability of the scheme, three numerical examples are described. The obtained numerical solutions are compared well with the exact solutions and those already available.

  5. Development of the software Conden 1.0 in finite differences to model electrostatics problems 2D

    Directory of Open Access Journals (Sweden)

    Wilson Rodríguez Calderón


    Full Text Available The present work consists on the development and implementation of the finite differences method for over-relaxation adapted to irregular meshes to determine the influence of the air frontiers on the potencial values and field electricians, calculated inside a badges parallel condenser, using GID like a pre/post-process platform and Fortran like a programming language of the calculation motor of differences Conden 1.0. The problem domain is constituted by two rectangles that represent the condenser and the air layer that covers it, divided in rectangular meshes no standardize.

  6. High-order weighted essentially nonoscillatory finite-difference formulation of the lattice Boltzmann method in generalized curvilinear coordinates. (United States)

    Hejranfar, Kazem; Saadat, Mohammad Hossein; Taheri, Sina


    In this work, a high-order weighted essentially nonoscillatory (WENO) finite-difference lattice Boltzmann method (WENOLBM) is developed and assessed for an accurate simulation of incompressible flows. To handle curved geometries with nonuniform grids, the incompressible form of the discrete Boltzmann equation with the Bhatnagar-Gross-Krook (BGK) approximation is transformed into the generalized curvilinear coordinates and the spatial derivatives of the resulting lattice Boltzmann equation in the computational plane are solved using the fifth-order WENO scheme. The first-order implicit-explicit Runge-Kutta scheme and also the fourth-order Runge-Kutta explicit time integrating scheme are adopted for the discretization of the temporal term. To examine the accuracy and performance of the present solution procedure based on the WENOLBM developed, different benchmark test cases are simulated as follows: unsteady Taylor-Green vortex, unsteady doubly periodic shear layer flow, steady flow in a two-dimensional (2D) cavity, steady cylindrical Couette flow, steady flow over a 2D circular cylinder, and steady and unsteady flows over a NACA0012 hydrofoil at different flow conditions. Results of the present solution are compared with the existing numerical and experimental results which show good agreement. To show the efficiency and accuracy of the solution methodology, the results are also compared with the developed second-order central-difference finite-volume lattice Boltzmann method and the compact finite-difference lattice Boltzmann method. It is shown that the present numerical scheme is robust, efficient, and accurate for solving steady and unsteady incompressible flows even at high Reynolds number flows.

  7. Computer Simulation and Experimental Study of Deformation in a Radial Tire under Different Static Loads Using Finite Element Method

    Directory of Open Access Journals (Sweden)

    Mir Hamid Reza Ghoreishy


    Full Text Available This research work is devoted to the simulation of a steel-belted radial tire under different static loads. The nonlinear finite element calculations were performed using the MSC.MARC code, installed on a computer system equipped with a parallel processing technology. Hybrid elements in conjunction with two hyperelastic models, namely Marlow and Yeoh, and rebar layer implemented in surface elements were used for the modeling of rubbery and reinforcing parts, respectively. Linear elastic material models were also used for the modeling of the reinforcing elements including steel cord in belts, polyester cord in carcass and nylon cord in cap ply section. Two-dimensional axisymmetric elements were used for the modeling of rim-mounting and inflation and three-dimensional models were developed for the application of the radial, tangential, lateral and torsional loads. Different finite element models were developed, in which both linear and quadratic elements were used in conjunction with different mesh densities in order to find the optimum finite element model. Based on the results of the load deflection (displacement data, the tire stiffness under radial, tangential, lateral and torsional loads were calculated and compared with their corresponding experimentally measured values. The comparison was verified by the accuracy of the measured radial stiffness. However, due to the neglecting of the stiffness in shear and bending modes in cord-rubber composites, modeled with rebar layer methodology, the difference between computed values and real data are not small enough so that a more robust material models and element formulation are required to be developed.

  8. Finite element analysis of heat generation from different light-polymerization sources during cementation of all-ceramic crowns. (United States)

    Tunc, Elif Pak


    Exothermic composite resin chemical reactions and visible light generators can produce heat during a restorative polymerization process. These thermal changes in restored teeth may cause pain and irreversible pulpitis. The purpose of this study was to analyze the temperature distribution and heat flow patterns of a crowned mandibular second premolar tooth model using 3 different light-polymerization technologies and a finite element technique. A 2-dimensional finite element model was used to simulate a clinical condition. Heat flow and thermal stress distribution in a tooth during cementation of an all-ceramic crown using 4 commercially available light-polymerization units (LPUs), each with different wavelengths (Elipar TriLight, Elipar Freelight, Apollo 95 E, and ADT 1000 PAC), were investigated. The temperature values were measured at 3, 10, 12, and 40 seconds for each light-polymerizing unit (LPU) at 6 different finite element nodes. Two-dimensional temporal and spatial distribution of the thermal stress within the tooth, including the thermal coefficients and boundary conditions of the dental materials, were obtained and evaluated. The temperature at the nodal points did not exceed 42 degrees C, which is a threshold value for tissue vitality within the recommended operating periods at the dentin and pulp surface for all LPUs, except for Elipar TriLight. In the case of Elipar TriLlight, the temperatures at the dentin and pulp surfaces were 47 degrees C and 42 degrees C, respectively. When the light-polymerization units were used according to the manufacturers' operating procedures and without prolonged operating periods, with the exception of Elipar TriLight, the investigated LPUs did not produce significant heat. However, when the operating periods were prolonged, unacceptable temperature increases were observed, especially with the high-intensity LPUs.

  9. Development of a Finite-Difference Time Domain (FDTD) Model for Propagation of Transient Sounds in Very Shallow Water. (United States)

    Sprague, Mark W; Luczkovich, Joseph J


    This finite-difference time domain (FDTD) model for sound propagation in very shallow water uses pressure and velocity grids with both 3-dimensional Cartesian and 2-dimensional cylindrical implementations. Parameters, including water and sediment properties, can vary in each dimension. Steady-state and transient signals from discrete and distributed sources, such as the surface of a vibrating pile, can be used. The cylindrical implementation uses less computation but requires axial symmetry. The Cartesian implementation allows asymmetry. FDTD calculations compare well with those of a split-step parabolic equation. Applications include modeling the propagation of individual fish sounds, fish aggregation sounds, and distributed sources.

  10. An efficient realization of frequency dependent boundary conditions in an acoustic finite-difference time-domain model

    DEFF Research Database (Denmark)

    Escolano-Carrasco, José; Jacobsen, Finn; López, J.J.


    The finite-difference time-domain (FDTD) method provides a simple and accurate way of solving initial boundary value problems. However, most acoustic problems involve frequency dependent boundary conditions, and it is not easy to include such boundary conditions in an FDTD model. Although solutions...... to this problem exist, most of them have high computational costs, and stability cannot always be ensured. In this work, a solution is proposed based on "mixing modelling strategies"; this involves separating the FDTD mesh and the boundary conditions (a digital filter representation of the impedance...

  11. Study on optimized upwind schemes for computational areoacoustics and extension of a fully conservative Chimera to finite difference schemes (United States)

    Chen, Rangfu

    A computational methodology has been developed in the first part of the thesis for the simulations of acoustic radiation, propagation and reflection. The developed methodology is high order accurate, uses less grid points per wave length comparing to standard high order accurate numerical methods, and automatically damps out spurious short waves. Furthermore, the methodology can be applied to acoustic problems in the presence of objects with curved geometries. To achieve these results, high order accurate optimized upwind schemes, which are applied to discretize spatial derivatives on interior grid points, have been developed. High order accurate optimized one- side biased schemes, which are only applied to discretize the spatial derivatives on grid points near computational boundaries, have also been constructed. The developed schemes are combined with a time difference scheme to fully discretize acoustic field equations in multi- dimension in arbitrary curvilinear coordinates. Numerical boundary conditions are investigated and intuitively illustrated. Applications of the developed methodology to a sequence of one-dimensional and multi-dimensional acoustic problems are performed. The numerical results have validated the developed methodology and demonstrated advantages of the methodology over central-difference Dispersion-Relation-Preserving method. Numerical results have also shown that the optimized upwind schemes minimize not only the dissipation error but also the dissipation error, while retaining the numerical stability. The second part of the thesis deals with a fully conservative Chimera methodology. The fully conservative Chimera was originally developed based on a finite volume approach. A finite difference scheme is shown to be identical to a finite volume scheme with proper definition of control volumes and metrics. The fully conservative Chimera has been successfully extended to finite difference schemes for viscous flows including turbulence models


    Directory of Open Access Journals (Sweden)

    Gabbasov Radek Fatykhovich


    It is noteworthy that the algorithm of the analysis is developed with a view to the employment of computer-aided methods and with due account for a substantial number of subsettings. The examples provided in the article are solely designated to illustrate the operation of the proposed algorithm. They demonstrate that even if the number of subsettings is minimal, generalized equations of the method of finite differences are capable of generating the results that make it possible to assess the stress-strained state of a slab.

  13. Quintic hyperbolic nonpolynomial spline and finite difference method for nonlinear second order differential equations and its application

    Directory of Open Access Journals (Sweden)

    Navnit Jha


    Full Text Available An efficient numerical method based on quintic nonpolynomial spline basis and high order finite difference approximations has been presented. The scheme deals with the space containing hyperbolic and polynomial functions as spline basis. With the help of spline functions we derive consistency conditions and high order discretizations of the differential equation with the significant first order derivative. The error analysis of the new method is discussed briefly. The new method is analyzed for its efficiency using the physical problems. The order and accuracy of the proposed method have been analyzed in terms of maximum errors and root mean square errors.

  14. A convergent 2D finite-difference scheme for the Dirac-Poisson system and the simulation of graphene

    KAUST Repository

    Brinkman, Daniel


    We present a convergent finite-difference scheme of second order in both space and time for the 2D electromagnetic Dirac equation. We apply this method in the self-consistent Dirac-Poisson system to the simulation of graphene. The model is justified for low energies, where the particles have wave vectors sufficiently close to the Dirac points. In particular, we demonstrate that our method can be used to calculate solutions of the Dirac-Poisson system where potentials act as beam splitters or Veselago lenses. © 2013 Elsevier Inc.

  15. RSW Mixed Element Cell-Centered Fine Mesh (United States)

    National Aeronautics and Space Administration — This is a RSW mixed-element unstructured fine mesh for cell-centered solvers. UG3 : Grid File Name = rsw_fine_mixedcc.b8.ugrid UG3 : Quad Surface Faces= 28968 UG3 :...

  16. Tridimensional finite element analysis of teeth movement induced by different headgear forces. (United States)

    Maruo, Ivan Toshio; Maruo, Hiroshi; Saga, Armando Yukio; de Oliveira, Dauro Douglas; Argenta, Marco André; Tanaka, Orlando Motohiro


    This study aimed to simulate the actions of low-pull (LP), high-pull (HP), and combined pull (CP) headgears (HGs) and to analyze tooth movement tendencies through finite element analysis. Tomographic slices of a human maxilla with complete permanent dentition were processed by reconstruction software, and the triangular surface mesh was converted into non-uniform rational B-spline (NURBS) curves. An HG facial bow was also modulated in 3D. The teeth and bone were considered to have isotropic and linear behavior, whereas the periodontal ligament was considered to have non-linear and hyperelastic behavior. Data regarding the application points, directions and magnitudes of forces were obtained from the literature and from a dolichofacial patient with class II, division 1 malocclusion, who was treated with a CP HG. The CP HG promoted 37.1 to 41.1 %, and the HP HG promoted 19.1 to 31.9 % of LP distalization. The HP HG presented the highest intrusion, and the LP HG presented the highest extrusion of the first molar. The LP HG contracted the distal side, and the HP and CP HGs contracted the lingual and distobuccal roots of the second molar to a lesser degree. The LP HG promotes the greatest distalization, followed by the CP and HP HGs; the LP HG causes greater extrusion of the first molar, and the HP HG causes greater intrusion of the first molar. The LP HG causes greater contraction of the second molar than the HP HG.

  17. Performance analysis of a finite radon transform in OFDM system under different channel models

    Energy Technology Data Exchange (ETDEWEB)

    Dawood, Sameer A.; Anuar, M. S.; Fayadh, Rashid A. [School of Computer and Communication Engineering, Universiti Malaysia Perlis (UniMAP) Pauh Putra, 02000 Arau, Parlis (Malaysia); Malek, F.; Abdullah, Farrah Salwani [School of Electrical System Engineering, Universiti Malaysia Perlis (UniMAP) Pauh Putra, 02000 Arau, Parlis (Malaysia)


    In this paper, a class of discrete Radon transforms namely Finite Radon Transform (FRAT) was proposed as a modulation technique in the realization of Orthogonal Frequency Division Multiplexing (OFDM). The proposed FRAT operates as a data mapper in the OFDM transceiver instead of the conventional phase shift mapping and quadrature amplitude mapping that are usually used with the standard OFDM based on Fast Fourier Transform (FFT), by the way that ensure increasing the orthogonality of the system. The Fourier domain approach was found here to be the more suitable way for obtaining the forward and inverse FRAT. This structure resulted in a more suitable realization of conventional FFT- OFDM. It was shown that this application increases the orthogonality significantly in this case due to the use of Inverse Fast Fourier Transform (IFFT) twice, namely, in the data mapping and in the sub-carrier modulation also due to the use of an efficient algorithm in determining the FRAT coefficients called the optimal ordering method. The proposed approach was tested and compared with conventional OFDM, for additive white Gaussian noise (AWGN) channel, flat fading channel, and multi-path frequency selective fading channel. The obtained results showed that the proposed system has improved the bit error rate (BER) performance by reducing inter-symbol interference (ISI) and inter-carrier interference (ICI), comparing with conventional OFDM system.

  18. Finite element analysis of residual stress in cold expanded plate with different thickness and expansion ratio (United States)

    Arifin Shariffudin, Kamarul; Karuppanan, Saravanan; Patil, Santosh S.


    Cold expansion of fastener/rivet holes is a common way to generate beneficial compressive residual stress around the fastener hole. In this study, cold expansion process was simulated by finite-element method in order to determine the residual stress field around two cold expanded holes by varying the plate thickness and expansion ratio of the hole. The model was developed in ANSYS and assigned to aluminium alloy 7475-T61 material model. The results showed that the residual stress become more compressive as the plate thickness is increased up to t/d = 2.6 and decreased for further level of thickness. In addition, the residual stress at the edge of the hole become more compressive as the expansion ratio is increased up to 4.5% and decreased for further level of expansion. This study also found that the residual stresses near the entrance and the exit face of the plate are less compressive than the residual stresses on the mid-thickness of the plate.

  19. An Analysis Technique/Automated Tool for Comparing and Tracking Analysis Modes of Different Finite Element Models (United States)

    Towner, Robert L.; Band, Jonathan L.


    An analysis technique was developed to compare and track mode shapes for different Finite Element Models. The technique may be applied to a variety of structural dynamics analyses, including model reduction validation (comparing unreduced and reduced models), mode tracking for various parametric analyses (e.g., launch vehicle model dispersion analysis to identify sensitivities to modal gain for Guidance, Navigation, and Control), comparing models of different mesh fidelity (e.g., a coarse model for a preliminary analysis compared to a higher-fidelity model for a detailed analysis) and mode tracking for a structure with properties that change over time (e.g., a launch vehicle from liftoff through end-of-burn, with propellant being expended during the flight). Mode shapes for different models are compared and tracked using several numerical indicators, including traditional Cross-Orthogonality and Modal Assurance Criteria approaches, as well as numerical indicators obtained by comparing modal strain energy and kinetic energy distributions. This analysis technique has been used to reliably identify correlated mode shapes for complex Finite Element Models that would otherwise be difficult to compare using traditional techniques. This improved approach also utilizes an adaptive mode tracking algorithm that allows for automated tracking when working with complex models and/or comparing a large group of models.

  20. Model for describing plasmonic nanolasers using Maxwell-Liouville equations with finite-difference time-domain calculations (United States)

    Trivedi, Dhara J.; Wang, Danqing; Odom, Teri W.; Schatz, George C.


    We present a theoretical study of lasing action when plasmonic metallic structures that show lattice plasmon resonances are embedded in a gain medium. Our model combines classical electrodynamics for arrays of gold nanoparticles with a four-level quantum Liouville model of the laser dye photophysics. A numerical solution was implemented using finite-difference time-domain calculations coupled with a finite-difference solution to the Liouville equation. A particular focus of this work is the influence of dephasing in the quantum dynamics on the emission intensity at the threshold for lasing. We find that dephasing in the quantum system leads to reduced lasing emission, but with little effect on the long-term population inversion. Both electronic and vibrational dephasing is considered, but only electronic dephasing is significant, with the fully dephased result appearing for dephasing times comparable to plasmon dephasing (˜10 fs) while fully coherent results involve >100 ps dephasing times as determined by the rate of stimulated emission. There are factor-of-2 differences between the Maxwell-Liouville results (greater emission intensities and narrower widths) compared to the corresponding results of rate-equation models of the dye states, which indicates the importance of using the Maxwell-Liouville approach in modeling these systems. We also examine rate-equation models with and without constraints arising from the Pauli exclusion principle, and we find relatively small effects.

  1. Tridimensional finite element analysis of teeth movement induced by different headgear forces

    Directory of Open Access Journals (Sweden)

    Ivan Toshio Maruo


    Full Text Available Abstract Background This study aimed to simulate the actions of low-pull (LP, high-pull (HP, and combined pull (CP headgears (HGs and to analyze tooth movement tendencies through finite element analysis. Methods Tomographic slices of a human maxilla with complete permanent dentition were processed by reconstruction software, and the triangular surface mesh was converted into non-uniform rational B-spline (NURBS curves. An HG facial bow was also modulated in 3D. The teeth and bone were considered to have isotropic and linear behavior, whereas the periodontal ligament was considered to have non-linear and hyperelastic behavior. Data regarding the application points, directions and magnitudes of forces were obtained from the literature and from a dolichofacial patient with class II, division 1 malocclusion, who was treated with a CP HG. Results The CP HG promoted 37.1 to 41.1 %, and the HP HG promoted 19.1 to 31.9 % of LP distalization. The HP HG presented the highest intrusion, and the LP HG presented the highest extrusion of the first molar. The LP HG contracted the distal side, and the HP and CP HGs contracted the lingual and distobuccal roots of the second molar to a lesser degree. Conclusions The LP HG promotes the greatest distalization, followed by the CP and HP HGs; the LP HG causes greater extrusion of the first molar, and the HP HG causes greater intrusion of the first molar. The LP HG causes greater contraction of the second molar than the HP HG.

  2. Influence of Different Boundary Conditions in Finite Element Analysis on Pelvic Biomechanical Load Transmission. (United States)

    Hu, Pan; Wu, Tao; Wang, Hui-Zhi; Qi, Xin-Zheng; Yao, Jie; Cheng, Xiao-Dong; Chen, Wei; Zhang, Ying-Ze


    To observe the effects of boundary conditions and connect conditions on biomechanics predictions in finite element (FE) pelvic models. Three FE pelvic models were constructed to analyze the effect of boundary conditions and connect conditions in the hip joint: an intact pelvic model assumed contact of the hip joint on both sides (Model I); and a pelvic model assumed the hip joint connecting surfaces fused together with (Model II) or without proximal femurs (Model III). The model was validated by bone surface strains obtained from strain gauges in an in vitro pelvic experiment. Vertical load was applied to the pelvic specimen, and the same load was simulated in the FE model. There was a strong correlation between the FE analysis results of Model I and the experimental results (R 2 = 0.979); meanwhile, the correlation coefficient and the linear regression function increased slightly with increasing load force. Comparing the three models, the stress values in the point near the pubic symphysis in Model III were 48.52 and 39.1% lower, respectively, in comparison with Models I and II. Furthermore, the stress values on the dome region of the acetabulum in Models II and III were 103.61 and 390.53% less than those of Model I. Besides, the posterior acetabular wall stress values of Model II were 197.15 and 305.17% higher than those of Models I and III, respectively. These findings suggest that the effect of the connect condition in the hip joint should not be neglected, especially in studies related to clinical applications. © 2017 Chinese Orthopaedic Association and John Wiley & Sons Australia, Ltd.

  3. Rehabilitation of the atrophic mandible with short implants in different positions: A finite elements study. (United States)

    Peixoto, Hugo E; Camati, Paulo R; Faot, Fernanda; Sotto-Maior, Bruno S; Martinez, Elizabeth F; Peruzzo, Daiane C


    The aim of this study was to analyze whether the use of inclined short implants without lower transcortical involvement (test model - SI), thus preserving the mandibular lower cortical bone, could optimize stress distribution. Six identical atrophic mandible models were created featuring 8mm of height at the symphysis. Two study factors were evaluated: implant length and angulation. Implant length was represented either by short implants (7mm) with preservation of the mandibular lower cortical bone or standard implants (9mm) with a bicortical approach and 3 possible implant positioning configurations: 4 distally-inclined implants at 45° (experimental model), all-on-four, 4 vertical implants. All tridimensional (3D) models were analyzed using the Finite Element Method (FEM) and the Ansys Workbench software. The maximum stress on the bone at the cervical region of the implants in the experimental model was 132MPa and transcortical involvement with implant inclination yielded higher values (171MPa). Regarding von Mises stress on the retaining screw of the prosthesis, 61MPa was recorded for the experimental model while upright implants had the highest values (223MPa). At the acrylic base, 4MPa was recorded for the experimental model whereas models with upright implants showed the highest stress values (11MPa). Rehabilitation of severely resorbed mandibles with 4 short implants placed distally at 45°, without lower transcortical involvement, were biomechanically more favorable, generating lower stress peaks, than the models with short implants on an all-on-four, or on an upright configuration, with or without lower transcortical involvement. Copyright © 2017. Published by Elsevier B.V.

  4. Comparison of five different fixation techniques of sagittal split ramus osteotomy using three-dimensional finite elements analysis. (United States)

    Sato, F R L; Asprino, L; Noritomi, P Y; da Silva, J V L; de Moraes, M


    The aim of this study was to compare the mechanical stress over hemimandible substrate and hardware after sagittal split ramus osteotomy (SSRO) fixed with five different techniques using three-dimensional (3D) finite element analysis. A 3D finite element model of a hemimandible was created and a 5mm advancement SSRO was simulated on a computer model. The model was fixed with five different techniques: 3 linear 60° screw arrangement; 3 linear 90° screw arrangement; 3 inverted L screw arrangement; 1 conventional miniplate; and 1 locking miniplate with four monocortical screws. Load was applied until 3mm displacement was reached and the results were compared with previous mechanical and photoelastic tests, thus analysing the mechanical stresses developed in the proximity of miniplates and screws and within the fixation system itself. The maximum principal stress values demonstrate a lower mechanical stress rate in bone and in the fixation system with the inverted L arrangement, followed by the linear 90° and linear 60° arrangements. The locking miniplate/screw system presented lower maximum principal stress and better stress distribution compared with the conventional system. Under the conditions tested, the reversed L arrangement provided the most favourable stress dissipation behaviour. Crown Copyright © 2012. Published by Elsevier Ltd. All rights reserved.

  5. Three-Dimensional Finite Difference Simulation of Ground Motions from the August 24, 2014 South Napa Earthquake

    Energy Technology Data Exchange (ETDEWEB)

    Rodgers, Arthur J. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Univ. of California, Berkeley, CA (United States); Dreger, Douglas S. [Univ. of California, Berkeley, CA (United States); Pitarka, Arben [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)


    We performed three-dimensional (3D) anelastic ground motion simulations of the South Napa earthquake to investigate the performance of different finite rupture models and the effects of 3D structure on the observed wavefield. We considered rupture models reported by Dreger et al. (2015), Ji et al., (2015), Wei et al. (2015) and Melgar et al. (2015). We used the SW4 anelastic finite difference code developed at Lawrence Livermore National Laboratory (Petersson and Sjogreen, 2013) and distributed by the Computational Infrastructure for Geodynamics. This code can compute the seismic response for fully 3D sub-surface models, including surface topography and linear anelasticity. We use the 3D geologic/seismic model of the San Francisco Bay Area developed by the United States Geological Survey (Aagaard et al., 2008, 2010). Evaluation of earlier versions of this model indicated that the structure can reproduce main features of observed waveforms from moderate earthquakes (Rodgers et al., 2008; Kim et al., 2010). Simulations were performed for a domain covering local distances (< 25 km) and resolution providing simulated ground motions valid to 1 Hz.

  6. Pricing derivatives under Lévy models modern finite-difference and pseudo-differential operators approach

    CERN Document Server

    Itkin, Andrey


    This monograph presents a novel numerical approach to solving partial integro-differential equations arising in asset pricing models with jumps, which greatly exceeds the efficiency of existing approaches. The method, based on pseudo-differential operators and several original contributions to the theory of finite-difference schemes, is new as applied to the Lévy processes in finance, and is herein presented for the first time in a single volume. The results within, developed in a series of research papers, are collected and arranged together with the necessary background material from Lévy processes, the modern theory of finite-difference schemes, the theory of M-matrices and EM-matrices, etc., thus forming a self-contained work that gives the reader a smooth introduction to the subject. For readers with no knowledge of finance, a short explanation of the main financial terms and notions used in the book is given in the glossary. The latter part of the book demonstrates the efficacy of the method by solvin...

  7. Stress analysis of different prosthesis materials in implant-supported fixed dental prosthesis using 3D finite element method

    Directory of Open Access Journals (Sweden)

    Pedram Iranmanesh


    Full Text Available Introduction: In the present study, the finite element method (FEM was used to investigate the effects of prosthesis material types on stress distribution of the bone surrounding implants and to evaluate stress distribution in three-unit implant-supported fixed dental prosthesis (FDP. Materials and Methods: A three-dimensional (3D finite element FDP model of the maxillary second premolar to the second molar was designed. Three load conditions were statically applied on the functional cusps in horizontal (57.0 N, vertical (200.0 N, and oblique (400.0 N, θ = 120° directions. Four standard framework materials were evaluated: Polymethyl methacrylate (PMMA, base-metal, porcelain fused to metal, andporcelain. Results: The maximum of von Mises stress in the oblique direction was higher than the vertical and horizontal directions in all conditions. In the bone-crestal section, the maximum von Mises stress (53.78 MPa was observed in PMMA within oblique load. In FDPs, the maximum stress was generated at the connector region in all conditions. Conclusion: A noticeable difference was not observed in the bone stress distribution pattern with different prosthetic materials. Although, higher stress value could be seen in polymethyl methacrylate, all types of prosthesis yielded the same stress distribution pattern in FDP. More clinical studies are needed to evaluate the survival rate of these materials.

  8. Finite-difference method Stokes solver (FDMSS) for 3D pore geometries: Software development, validation and case studies

    KAUST Repository

    Gerke, Kirill M.


    Permeability is one of the fundamental properties of porous media and is required for large-scale Darcian fluid flow and mass transport models. Whilst permeability can be measured directly at a range of scales, there are increasing opportunities to evaluate permeability from pore-scale fluid flow simulations. We introduce the free software Finite-Difference Method Stokes Solver (FDMSS) that solves Stokes equation using a finite-difference method (FDM) directly on voxelized 3D pore geometries (i.e. without meshing). Based on explicit convergence studies, validation on sphere packings with analytically known permeabilities, and comparison against lattice-Boltzmann and other published FDM studies, we conclude that FDMSS provides a computationally efficient and accurate basis for single-phase pore-scale flow simulations. By implementing an efficient parallelization and code optimization scheme, permeability inferences can now be made from 3D images of up to 109 voxels using modern desktop computers. Case studies demonstrate the broad applicability of the FDMSS software for both natural and artificial porous media.

  9. Simulation of natural convection in an inclined polar cavity using a finite-difference lattice Boltzmann method

    Energy Technology Data Exchange (ETDEWEB)

    Yang, Fan; Yang, Haicheng; Guo, Xueyan; Ren Dai [University of Shanghai for Science and Technology, Shanghai (China); Yan, Yonghua [Shanghai Key Laboratory of Multiphase Flow and Heat Transfer in Power Engineering, Shanghai (China); Liu, Chaoqun [University of Texas at Arlington, Arlington (United States)


    Natural convection heat transfer in an inclined polar cavity was studied using a Finite-difference lattice Boltzmann method (FDLBM) based on a double-population approach for body-fitted coordinates. A D2G9 model coupled with the simplest TD2Q4 lattice model was applied to determine the velocity field and temperature field. For both velocity and temperature fields, the discrete spatial derivatives were obtained by combining the upwind scheme with the central scheme, and the discrete temporal term is obtained using a fourth-order Runge-Kutta scheme. Studies were carried out for different Rayleigh numbers and different inclination angles. The results in terms of streamlines, isotherms, and Nusselt numbers explain the heat transfer mechanism of natural convection in an inclined polar cavity due to the change of Rayleigh number and inclination angle.

  10. Finite-Difference Algorithm for Simulating 3D Electromagnetic Wavefields in Conductive Media (United States)

    Aldridge, D. F.; Bartel, L. C.; Knox, H. A.


    Electromagnetic (EM) wavefields are routinely used in geophysical exploration for detection and characterization of subsurface geological formations of economic interest. Recorded EM signals depend strongly on the current conductivity of geologic media. Hence, they are particularly useful for inferring fluid content of saturated porous bodies. In order to enhance understanding of field-recorded data, we are developing a numerical algorithm for simulating three-dimensional (3D) EM wave propagation and diffusion in heterogeneous conductive materials. Maxwell's equations are combined with isotropic constitutive relations to obtain a set of six, coupled, first-order partial differential equations governing the electric and magnetic vectors. An advantage of this system is that it does not contain spatial derivatives of the three medium parameters electric permittivity, magnetic permeability, and current conductivity. Numerical solution methodology consists of explicit, time-domain finite-differencing on a 3D staggered rectangular grid. Temporal and spatial FD operators have order 2 and N, where N is user-selectable. We use an artificially-large electric permittivity to maximize the FD timestep, and thus reduce execution time. For the low frequencies typically used in geophysical exploration, accuracy is not unduly compromised. Grid boundary reflections are mitigated via convolutional perfectly matched layers (C-PMLs) imposed at the six grid flanks. A shared-memory-parallel code implementation via OpenMP directives enables rapid algorithm execution on a multi-thread computational platform. Good agreement is obtained in comparisons of numerically-generated data with reference solutions. EM wavefields are sourced via point current density and magnetic dipole vectors. Spatially-extended inductive sources (current carrying wire loops) are under development. We are particularly interested in accurate representation of high-conductivity sub-grid-scale features that are common

  11. Implementation of a high-order compact finite-difference lattice Boltzmann method in generalized curvilinear coordinates (United States)

    Hejranfar, Kazem; Ezzatneshan, Eslam


    In this work, the implementation of a high-order compact finite-difference lattice Boltzmann method (CFDLBM) is performed in the generalized curvilinear coordinates to improve the computational efficiency of the solution algorithm to handle curved geometries with non-uniform grids. The incompressible form of the discrete Boltzmann equation with the Bhatnagar-Gross-Krook (BGK) approximation with the pressure as the independent dynamic variable is transformed into the generalized curvilinear coordinates. Herein, the spatial derivatives in the resulting lattice Boltzmann (LB) equation in the computational plane are discretized by using the fourth-order compact finite-difference scheme and the temporal term is discretized with the fourth-order Runge-Kutta scheme to provide an accurate and efficient incompressible flow solver. A high-order spectral-type low-pass compact filter is used to regularize the numerical solution and remove spurious waves generated by boundary conditions, flow non-linearities and grid non-uniformity. All boundary conditions are implemented based on the solution of governing equations in the generalized curvilinear coordinates. The accuracy and efficiency of the solution methodology presented are demonstrated by computing different benchmark steady and unsteady incompressible flow problems. A sensitivity study is also conducted to evaluate the effects of grid size and filtering on the accuracy and convergence rate of the solution. Four test cases considered herein for validating the present computations and demonstrating the accuracy and robustness of the solution algorithm are: unsteady Couette flow and steady flow in a 2-D cavity with non-uniform grid and steady and unsteady flows over a circular cylinder and the NACA0012 hydrofoil at different flow conditions. Results obtained for the above test cases are in good agreement with the existing numerical and experimental results. The study shows the present solution methodology based on the

  12. Analysis of Different Positions of Fiber-Reinforced Composite Retainers versus Multistrand Wire Retainers Using the Finite Element Method

    Directory of Open Access Journals (Sweden)

    Arezoo Jahanbin


    Full Text Available Background. The aim of this study was to evaluate root displacement of the lower incisors fixed with FRC in different positions versus FSW retainers using the finite element method. Materials and Methods. 3D finite element models were designed for a mandibular anterior segment: Model 1: flexible spiral wire bonded to the lingual teeth surfaces, Model 2: FRC bonded to the upper third of lingual teeth surfaces, and Model 3: FRC bonded to the middle third. FE analysis was performed for three models and then tooth displacements were evaluated. Results. In contrast to lateral incisors and canines, the FSW retainer caused the central teeth to move more than the teeth bonded with FRC in both loadings. Comparison between Models 2 and 3 (in vertical loading showed that FRC retainers that bonded at the upper third of lingual teeth surfaces made central and canine teeth move less than FRC retainers bonded at the middle third; however, for lateral teeth it was the opposite. Conclusion. FRC retainers bonded at the upper third of lingual teeth surfaces make central and canine teeth move less than FRC retainers bonded at the middle third in vertical loading; however, for lateral teeth it was the opposite.

  13. Numerical solution of the state-delayed optimal control problems by a fast and accurate finite difference θ-method (United States)

    Hajipour, Mojtaba; Jajarmi, Amin


    Using the Pontryagin's maximum principle for a time-delayed optimal control problem results in a system of coupled two-point boundary-value problems (BVPs) involving both time-advance and time-delay arguments. The analytical solution of this advance-delay two-point BVP is extremely difficult, if not impossible. This paper provides a discrete general form of the numerical solution for the derived advance-delay system by applying a finite difference θ-method. This method is also implemented for the infinite-time horizon time-delayed optimal control problems by using a piecewise version of the θ-method. A matrix formulation and the error analysis of the suggested technique are provided. The new scheme is accurate, fast and very effective for the optimal control of linear and nonlinear time-delay systems. Various types of finite- and infinite-time horizon problems are included to demonstrate the accuracy, validity and applicability of the new technique.

  14. Finite-Difference Time-Domain Analysis of Twist-Defect-Mode Lasing Dynamics in Cholesteric Photonic Liquid Crystal (United States)

    Matsui, Tatsunosuke; Kitaguchi, Masahiro


    We have numerically investigated lasing dynamics from a twist defect in a cholesteric liquid crystal (CLC) by an auxiliary differential equation finite-difference time-domain (ADE-FDTD) method. As ADEs, the equation of motion of polarization described on the basis of the classical electron oscillator (Lorenz) model and the rate equation in a four-level energy structure are incorporated. A lower lasing threshold has been obtained from the twist-defect mode (TDM) than from band-edge lasing. Standing-wave-like electric fields are strongly localized only in the vicinity where a twist defect is introduced into a CLC, which works as a distributed feedback TDM laser source. The oscillation direction of a standing-wave electric field is not parallel or perpendicular to LC molecules, which is quite different from the bulk CLC case. Our results may be useful for creating more efficient TDM-based CLC lasers.

  15. Analysis of third harmonic generation and four wave mixing in gold nanostructures by nonlinear finite difference time domain. (United States)

    Sasanpour, Pezhman; Shahmansouri, Afsaneh; Rashidian, Bizhan


    Third order nonlinear effects and its enhancement in gold nanostructures has been numerically studied. Analysis method is based on computationally solving nonlinear Maxwell's equations, considering dispersion behavior of permittivity described by Drude model and third order nonlinear susceptibility. Simulation is done by method of nonlinear finite difference time domain method, in which nonlinear equations of electric field are solved by Newton-Raphshon method. As the main outcomes of third order nonlinear susceptibility, four wave mixing and third harmonic generation terms are produced around gold nanostructures. Results of analysis on different geometries and structures show that third order nonlinearity products are more enhanced in places where electric field enhancement is occurred due to surface plasmons. Results indicates that enhancement of nonlinearities is strongly occurred in structures whose interface is dielectric. According to analysis results, nonlinear effects are highly concentrated in the vicinity of nanostructures. Hence this approach can be used in applications where localized ultraviolet light is required.

  16. A two-dimensional finite-difference solution for the transient thermal behavior of a tubular solar collector (United States)

    Lansing, F. L.


    A numerical procedure was established using the finite-difference technique in the determination of the time-varying temperature distribution of a tubular solar collector under changing solar radiancy and ambient temperature. Three types of spatial discretization processes were considered and compared for their accuracy of computations and for selection of the shortest computer time and cost. The stability criteria of this technique were analyzed in detail to give the critical time increment to ensure stable computations. The results of the numerical analysis were in good agreement with the analytical solution previously reported. The numerical method proved to be a powerful tool in the investigation of the collector sensitivity to two different flow patterns and several flow control mechanisms.

  17. Discretely Conservative Finite-Difference Formulations for Nonlinear Conservation Laws in Split Form: Theory and Boundary Conditions (United States)

    Fisher, Travis C.; Carpenter, Mark H.; Nordstroem, Jan; Yamaleev, Nail K.; Swanson, R. Charles


    Simulations of nonlinear conservation laws that admit discontinuous solutions are typically restricted to discretizations of equations that are explicitly written in divergence form. This restriction is, however, unnecessary. Herein, linear combinations of divergence and product rule forms that have been discretized using diagonal-norm skew-symmetric summation-by-parts (SBP) operators, are shown to satisfy the sufficient conditions of the Lax-Wendroff theorem and thus are appropriate for simulations of discontinuous physical phenomena. Furthermore, special treatments are not required at the points that are near physical boundaries (i.e., discrete conservation is achieved throughout the entire computational domain, including the boundaries). Examples are presented of a fourth-order, SBP finite-difference operator with second-order boundary closures. Sixth- and eighth-order constructions are derived, and included in E. Narrow-stencil difference operators for linear viscous terms are also derived; these guarantee the conservative form of the combined operator.

  18. A Finite Difference Solution of a Simply Supported Beam of Orthotropic Composite Materials Using Displacement Potential Formulation

    Directory of Open Access Journals (Sweden)

    S. K. Deb Nath


    Full Text Available Here an efficient displacement potential formulation based finite difference technique is used to solve the elastic field of a simply supported beam of orthotropic composite materials. A simply supported beam made of orthotropic composite material under uniformly distributed loading is considered and its elastic behaviors under such loading conditions are analyzed considering plane stress condition. The solutions of the problem satisfy the force equilibrium conditions as well as boundary conditions. For understanding the elastic behavior of a simply supported beam, the displacement and stress components of some important sections of the beam are shown graphically. Effects of different orthotropic composite materials on the solutions are also analyzed. Besides, at a particular section of the beam, the comparative analysis of the elastic field is carried out by using the FDM and FEM methods.

  19. Seismic modeling with radial basis function-generated finite differences (RBF-FD) – a simplified treatment of interfaces

    Energy Technology Data Exchange (ETDEWEB)

    Martin, Bradley, E-mail:; Fornberg, Bengt, E-mail:


    In a previous study of seismic modeling with radial basis function-generated finite differences (RBF-FD), we outlined a numerical method for solving 2-D wave equations in domains with material interfaces between different regions. The method was applicable on a mesh-free set of data nodes. It included all information about interfaces within the weights of the stencils (allowing the use of traditional time integrators), and was shown to solve problems of the 2-D elastic wave equation to 3rd-order accuracy. In the present paper, we discuss a refinement of that method that makes it simpler to implement. It can also improve accuracy for the case of smoothly-variable model parameter values near interfaces. We give several test cases that demonstrate the method solving 2-D elastic wave equation problems to 4th-order accuracy, even in the presence of smoothly-curved interfaces with jump discontinuities in the model parameters.

  20. Seismic modeling with radial basis function-generated finite differences (RBF-FD) - a simplified treatment of interfaces (United States)

    Martin, Bradley; Fornberg, Bengt


    In a previous study of seismic modeling with radial basis function-generated finite differences (RBF-FD), we outlined a numerical method for solving 2-D wave equations in domains with material interfaces between different regions. The method was applicable on a mesh-free set of data nodes. It included all information about interfaces within the weights of the stencils (allowing the use of traditional time integrators), and was shown to solve problems of the 2-D elastic wave equation to 3rd-order accuracy. In the present paper, we discuss a refinement of that method that makes it simpler to implement. It can also improve accuracy for the case of smoothly-variable model parameter values near interfaces. We give several test cases that demonstrate the method solving 2-D elastic wave equation problems to 4th-order accuracy, even in the presence of smoothly-curved interfaces with jump discontinuities in the model parameters.

  1. A Radial Basis Function (RBF)-Finite Difference (FD) Method for Diffusion and Reaction-Diffusion Equations on Surfaces. (United States)

    Shankar, Varun; Wright, Grady B; Kirby, Robert M; Fogelson, Aaron L


    In this paper, we present a method based on Radial Basis Function (RBF)-generated Finite Differences (FD) for numerically solving diffusion and reaction-diffusion equations (PDEs) on closed surfaces embedded in ℝ d . Our method uses a method-of-lines formulation, in which surface derivatives that appear in the PDEs are approximated locally using RBF interpolation. The method requires only scattered nodes representing the surface and normal vectors at those scattered nodes. All computations use only extrinsic coordinates, thereby avoiding coordinate distortions and singularities. We also present an optimization procedure that allows for the stabilization of the discrete differential operators generated by our RBF-FD method by selecting shape parameters for each stencil that correspond to a global target condition number. We show the convergence of our method on two surfaces for different stencil sizes, and present applications to nonlinear PDEs simulated both on implicit/parametric surfaces and more general surfaces represented by point clouds.

  2. On modified finite difference method to obtain the electron energy distribution functions in Langmuir probes (United States)

    Kang, Hyun-Ju; Choi, Hyeok; Kim, Jae-Hyun; Lee, Se-Hun; Yoo, Tae-Ho; Chung, Chin-Wook


    A modified central difference method (MCDM) is proposed to obtain the electron energy distribution functions (EEDFs) in single Langmuir probes. Numerical calculation of the EEDF with MCDM is simple and has less noise. This method provides the second derivatives at a given point as the weighted average of second order central difference derivatives calculated at different voltage intervals, weighting each by the square of the interval. In this paper, the EEDFs obtained from MCDM are compared to those calculated via the averaged central difference method. It is found that MCDM effectively suppresses the noises in the EEDF, while the same number of points are used to calculate of the second derivative.

  3. On modified finite difference method to obtain the electron energy distribution functions in Langmuir probes

    Energy Technology Data Exchange (ETDEWEB)

    Kang, Hyun-Ju; Chung, Chin-Wook, E-mail: [Department of Electrical Engineering, Hanyang University, 222, Wangsimni-ro, Seongdong-gu, Seoul 133-791 (Korea, Republic of); Choi, Hyeok; Kim, Jae-Hyun; Lee, Se-Hun; Yoo, Tae-Ho [Seoul Science High School, 63, Hyehwa-ro, Jongno-gu, Seoul 110-530 (Korea, Republic of)


    A modified central difference method (MCDM) is proposed to obtain the electron energy distribution functions (EEDFs) in single Langmuir probes. Numerical calculation of the EEDF with MCDM is simple and has less noise. This method provides the second derivatives at a given point as the weighted average of second order central difference derivatives calculated at different voltage intervals, weighting each by the square of the interval. In this paper, the EEDFs obtained from MCDM are compared to those calculated via the averaged central difference method. It is found that MCDM effectively suppresses the noises in the EEDF, while the same number of points are used to calculate of the second derivative.

  4. Three-dimensional finite element stress analysis: the technique and methodology of non-linear property simulation and soft tissue loading behavior for different partial denture designs. (United States)

    Kanbara, Ryo; Nakamura, Yoshinori; Ochiai, Kent T; Kawai, Tatsushi; Tanaka, Yoshinobu


    The purpose of this study was to develop and report upon a methodology for a non-linear capacity 3D modeling finite element analysis evaluating the loading behavior of different partial denture designs. A 3D finite element model using human CT data was constructed. An original material constant conversion program was implemented in the data simulation of non-linear tissue behavior. The finite element method material properties of residual ridge mucosa were found to have seven material constants and six conversion points of stress values. Periodontal tissues were found to have three constants, and two conversion points. Three magnetic attachment partial denture designs with different bracing elements were evaluated. Technical procedures for finite element model simulation of nonlinear tissue behavior properties evaluating the oral behavior of prosthetic device designs are reported for prosthodontic testing. The use of horizontal cross-arch bracing positively impacts upon the comparative stability of the partial denture designs tested.

  5. Influence of Regional Difference in Bone Mineral Density on Hip Fracture Site in Elderly Females by Finite Element Analysis. (United States)

    Lin, Z L; Li, P F; Pang, Z H; Zheng, X H; Huang, F; Xu, H H; Li, Q L


    Hip fracture is a kind of osteoporotic fractures in elderly patients. Its important monitoring indicator is to measure bone mineral density (BMD) using DXA. The stress characteristics and material distribution in different parts of the bones can be well simulated by three-dimensional finite element analysis. Our previous studies have demonstrated a linear positive correlation between clinical BMD and the density of three-dimensional finite element model of the femur. However, the correlation between the density variation between intertrochanteric region and collum femoris region of the model and the fracture site has not been studied yet. The present study intends to investigate whether the regional difference in the density of three-dimensional finite element model of the femur can be used to predict hip fracture site in elderly females. The CT data of both hip joints were collected from 16 cases of elderly female patients with hip fractures. Mimics 15.01 software was used to reconstruct the model of proximal femur on the healthy side. Ten kinds of material properties were assigned. In Abaqus 6.12 software, the collum femoris region and intertrochanteric region were, respectively, drawn for calculating the corresponding regional density of the model, followed by prediction of hip fracture site and final comparison with factual fracture site. The intertrochanteric region/collum femoris region density was [(1.20 ± 0.02) × 10(6)] on the fracture site and [(1.22 ± 0.03) × 10(6)] on the non-fracture site, and the difference was statistically significant (P = 0.03). Among 16 established models of proximal femur on the healthy side, 14 models were consistent with the actual fracture sites, one model was inconsistent, and one model was unpredictable, with the coincidence rate of 87.5 %. The intertrochanteric region or collum femoris region with lower BMD is more prone to hip fracture of the type on the corresponding site.

  6. Validation of finite difference core diffusion calculation methods with FEM and NEM for VVER-1000 MWe reactor

    Energy Technology Data Exchange (ETDEWEB)

    Jagannathan, V. [Light Water Reactor Physics Section, Reactor Physics Design Div., Bhabha Atomic Research Centre, Mumbai - 400 085 (India); RPDD, Central Complex, BARC, Mumbai - 400085 (India); Singh, T. [Reactor Physics and Nuclear Engineering Section, Reactor Group, BARC, Mumbai (India); Pal, U.; Karthikeyan, R. [Light Water Reactor Physics Section, Reactor Physics Design Div., Bhabha Atomic Research Centre, Mumbai - 400 085 (India); Sundaram, G. [Nuclear Safety Group, KK-NPC, Mumbai (India)


    India is developing several in-house fuel management codes for the design evaluation of WER-1000 M We reactors, being built at Kudankulam, Tamil Nadu in collaboration with Russian Federation. A lattice burnup code EXCEL provides the few group lattice parameters of various fuel assembly types constituting the core. The core diffusion analyses have been performed by two methods. In the first method the entire fuel assembly is treated as a single homogenized cell. Each fuel assembly cell is divided into 6n{sup 2} triangles, where 'n' is the number of uniform divisions on a side of the hexagon. Regular triangular meshes are used in the active core as well as in surrounding reflector regions. This method is incorporated in the code TRIHEXFA. In the second method a pin by pin description of the core is accomplished by considering the few group lattice parameters generated by EXCEL code for various fuel and non-fuel cells in each fuel assembly. Regular hexagonal cells of one pin pitch are considered in the core and reflector regions. This method is incorporated in HEXPIN code. Both these codes use centre mesh finite difference method (FDM) for regular triangular or hexagonal meshes. It is well known that the large size of the WER fuel assembly, the zigzag structure of the core-baffle zone, the distribution of water tubes of different diameter in this baffle zone and the surrounding steel and water layers of different thickness, all lead to a very complex description of the core-reflector interface. We are analyzing the WER core in fresh state by two other approaches to obtain independent benchmark reference solutions. They are finite element method (FEM) and nodal expansion method (NEM). The few group cross sections of EXCEL are used in the FEM and NEM analyses. The paper would present the comparison of the results of core followup simulations of FD codes with those of FEM and NEM analyses. (authors)

  7. Optimally Accurate Second-Order Time-Domain Finite-Difference Scheme for Acoustic, Electromagnetic, and Elastic Wave Modeling

    Directory of Open Access Journals (Sweden)

    C. Bommaraju


    Full Text Available Numerical methods are extremely useful in solving real-life problems with complex materials and geometries. However, numerical methods in the time domain suffer from artificial numerical dispersion. Standard numerical techniques which are second-order in space and time, like the conventional Finite Difference 3-point (FD3 method, Finite-Difference Time-Domain (FDTD method, and Finite Integration Technique (FIT provide estimates of the error of discretized numerical operators rather than the error of the numerical solutions computed using these operators. Here optimally accurate time-domain FD operators which are second-order in time as well as in space are derived. Optimal accuracy means the greatest attainable accuracy for a particular type of scheme, e.g., second-order FD, for some particular grid spacing. The modified operators lead to an implicit scheme. Using the first order Born approximation, this implicit scheme is transformed into a two step explicit scheme, namely predictor-corrector scheme. The stability condition (maximum time step for a given spatial grid interval for the various modified schemes is roughly equal to that for the corresponding conventional scheme. The modified FD scheme (FDM attains reduction of numerical dispersion almost by a factor of 40 in 1-D case, compared to the FD3, FDTD, and FIT. The CPU time for the FDM scheme is twice of that required by the FD3 method. The simulated synthetic data for a 2-D P-SV (elastodynamics problem computed using the modified scheme are 30 times more accurate than synthetics computed using a conventional scheme, at a cost of only 3.5 times as much CPU time. The FDM is of particular interest in the modeling of large scale (spatial dimension is more or equal to one thousand wave lengths or observation time interval is very high compared to reference time step wave propagation and scattering problems, for instance, in ultrasonic antenna and synthetic scattering data modeling for Non

  8. A note on the leap-frog scheme in two and three dimensions. [finite difference method for partial differential equations (United States)

    Abarbanel, S.; Gottlieb, D.


    The paper considers the leap-frog finite-difference method (Kreiss and Oliger, 1973) for systems of partial differential equations of the form du/dt = dF/dx + dG/dy + dH/dz, where d denotes partial derivative, u is a q-component vector and a function of x, y, z, and t, and the vectors F, G, and H are functions of u only. The original leap-frog algorithm is shown to admit a modification that improves on the stability conditions for two and three dimensions by factors of 2 and 2.8, respectively, thereby permitting larger time steps. The scheme for three dimensions is considered optimal in the sense that it combines simple averaging and large time steps.

  9. Implementation of Unsplit Perfectly Matched Layer Absorbing Boundary Condition in 3 Dimensional Finite Difference Time Domain Method

    Directory of Open Access Journals (Sweden)

    B. U. Musa


    Full Text Available The C++ programming language was used to implement three-dimensional (3-D finite-difference time-domain (FDTD technique to simulate radiation of high frequency electromagnetic waves in free space. To achieve any meaningful results the computational domain of interest should have to be truncated in some way and this is achieved by applying absorbing boundary conditions. A uniaxial perfectly matched layer (UPML absorbing boundary condition is used in this work. The discretised equations of the UPML in FDTD time stepping scheme were derived and has been successfully implemented using the computer program. Simulation results showed that the UPML behaves as an absorber. This was confirmed by comparing the results with another boundary condition, the Mur ABC.

  10. Linear and non-linear stability analysis for finite difference discretizations of high-order Boussinesq equations

    DEFF Research Database (Denmark)

    Fuhrman, David R.; Bingham, Harry B.; Madsen, Per A.


    This paper considers a method of lines stability analysis for finite difference discretizations of a recently published Boussinesq method for the study of highly non-linear and extremely dispersive water waves. The analysis demonstrates the near-equivalence of classical linear Fourier (von Neumann......) techniques with matrix-based methods for formulations in both one and two horizontal dimensions. The matrix-based method is also extended to show the local de-stabilizing effects of the non-linear terms, as well as the stabilizing effects of numerical dissipation. A comparison of the relative stability...... of rotational and irrotational formulations in two horizontal dimensions provides evidence that the irrotational formulation has significantly better stability properties when the deep-water non-linearity is high, particularly on refined grids. Computation of matrix pseudospectra shows that the system is only...

  11. Sparkling feather reflections of a bird-of-paradise explained by finite-difference time-domain modeling (United States)

    Wilts, Bodo D.; Michielsen, Kristel; De Raedt, Hans; Stavenga, Doekele G.


    Birds-of-paradise are nature’s prime examples of the evolution of color by sexual selection. Their brilliant, structurally colored feathers play a principal role in mating displays. The structural coloration of both the occipital and breast feathers of the bird-of-paradise Lawes’ parotia is produced by melanin rodlets arranged in layers, together acting as interference reflectors. Light reflection by the silvery colored occipital feathers is unidirectional as in a classical multilayer, but the reflection by the richly colored breast feathers is three-directional and extraordinarily complex. Here we show that the reflection properties of both feather types can be quantitatively explained by finite-difference time-domain modeling using realistic feather anatomies and experimentally determined refractive index dispersion values of keratin and melanin. The results elucidate the interplay between avian coloration and vision and indicate tuning of the mating displays to the spectral properties of the avian visual system. PMID:24591592

  12. Thermal and structural finite element analysis of water cooled silicon monochromator for synchrotron radiation comparison of two different cooling schemes

    CERN Document Server

    Artemiev, A I; Busetto, E; Hrdy, J; Mrazek, D; Plesek, I; Savoia, A


    The article describes the results of Finite Element Analysis (FEA) of the first Si monochromator crystal distortions due to Synchrotron Radiation (SR) heat load and consequent analysis of the influence of the distortions on a double crystal monochromator performance. Efficiencies of two different cooling schemes are compared. A thin plate of Si crystal is lying on copper cooling support in both cases. There are microchannels inside the cooling support. In the first model the direction of the microchannels is parallel to the diffraction plane. In the second model the direction of the microchannels is perpendicular to the diffraction plane or in other words, it is a conventional cooling scheme. It is shown that the temperature field along the crystal volume is more uniform and more symmetrical in the first model than in the second (conventional) one.

  13. On long-time instabilities in staggered finite difference simulations of the seismic acoustic wave equations on discontinuous grids (United States)

    Gao, Longfei; Ketcheson, David; Keyes, David


    We consider the long-time instability issue associated with finite difference simulation of seismic acoustic wave equations on discontinuous grids. This issue is exhibited by a prototype algebraic problem abstracted from practical application settings. Analysis of this algebraic problem leads to better understanding of the cause of the instability and provides guidance for its treatment. Specifically, we use the concept of discrete energy to derive the proper solution transfer operators and design an effective way to damp the unstable solution modes. Our investigation shows that the interpolation operators need to be matched with their companion restriction operators in order to properly couple the coarse and fine grids. Moreover, to provide effective damping, specially designed diffusive terms are introduced to the equations at designated locations and discretized with specially designed schemes. These techniques are applied to simulations in practical settings and are shown to lead to superior results in terms of both stability and accuracy.

  14. The finite-difference time-domain (FD-TD) method for electromagnetic scattering and interaction problems (United States)

    Taflove, A.; Umashankar, K. R.


    The formulation and recent applications of the finite-difference time-domain (FD-TD) method for the numerical modeling of electromagnetic scattering and interaction problems are considered. It is shown that improvements in FD-TD modeling concepts and software implementation often make it a preferable choice for structures which cannot be easily treated by conventional integral equations and asymptotic approaches. Recent FD-TD modeling validations in research areas including coupling to wires and wire bundles in free space and cavities, scattering from surfaces in relativistic motion, inverse scattering, and radiation condition theory, are reviewed. Finally, the advantages and disadvantages of FD-TD, and guidelines concerning when FD-TD should and should not be used in high-frequency electromagnetic modeling problems, are summarized.

  15. A study of infrasound propagation based on high-order finite difference solutions of the Navier-Stokes equations. (United States)

    Marsden, O; Bogey, C; Bailly, C


    The feasibility of using numerical simulation of fluid dynamics equations for the detailed description of long-range infrasound propagation in the atmosphere is investigated. The two dimensional (2D) Navier Stokes equations are solved via high fidelity spatial finite differences and Runge-Kutta time integration, coupled with a shock-capturing filter procedure allowing large amplitudes to be studied. The accuracy of acoustic prediction over long distances with this approach is first assessed in the linear regime thanks to two test cases featuring an acoustic source placed above a reflective ground in a homogeneous and weakly inhomogeneous medium, solved for a range of grid resolutions. An atmospheric model which can account for realistic features affecting acoustic propagation is then described. A 2D study of the effect of source amplitude on signals recorded at ground level at varying distances from the source is carried out. Modifications both in terms of waveforms and arrival times are described.

  16. A Finite-Time Thermal Cycle Variational Optimization with a Stefan–Boltzmann Law for Three Different Criteria

    Directory of Open Access Journals (Sweden)

    Juan C. Chimal-Eguía


    Full Text Available This work shows the power of the variational approach for studying the efficiency of thermal engines in the context of the Finite Time Thermodynamics (FTT. Using an endoreversible Curzon–Ahlborn (CA heat engine as a model for actual thermal engines, three different criteria for thermal efficiency were analyzed: maximum power output, ecological function, and maximum power density. By means of this procedure, the performance of the CA heat engine with a nonlinear heat transfer law (the Stefan–Boltzmann law was studied to describe the heat exchanges between the working substance and its thermal reservoirs. The specific case of the Müser engine for all the criteria was analyzed. The results confirmed some previous findings using other procedures and additionally new results for the Müser engine performance were obtained.

  17. Sparkling feather reflections of a bird-of-paradise explained by finite-difference time-domain modeling. (United States)

    Wilts, Bodo D; Michielsen, Kristel; De Raedt, Hans; Stavenga, Doekele G


    Birds-of-paradise are nature's prime examples of the evolution of color by sexual selection. Their brilliant, structurally colored feathers play a principal role in mating displays. The structural coloration of both the occipital and breast feathers of the bird-of-paradise Lawes' parotia is produced by melanin rodlets arranged in layers, together acting as interference reflectors. Light reflection by the silvery colored occipital feathers is unidirectional as in a classical multilayer, but the reflection by the richly colored breast feathers is three-directional and extraordinarily complex. Here we show that the reflection properties of both feather types can be quantitatively explained by finite-difference time-domain modeling using realistic feather anatomies and experimentally determined refractive index dispersion values of keratin and melanin. The results elucidate the interplay between avian coloration and vision and indicate tuning of the mating displays to the spectral properties of the avian visual system.

  18. Size validity of plasma-metamaterial cloaking monitored by scattering wave in finite-difference time-domain method (United States)

    Bambina, Alexandre; Yamaguchi, Shuhei; Iwai, Akinori; Miyagi, Shigeyuki; Sakai, Osamu


    Limitation of the cloak-size reduction is investigated numerically by a finite-difference time-domain (FDTD) method. A metallic pole that imitates an antenna is cloaked with an anisotropic and parameter-gradient medium against electromagnetic-wave propagation in microwave range. The cloaking structure is a metamaterial submerged in a plasma confined in a vacuum chamber made of glass. The smooth-permittivity plasma can be compressed in the radial direction, which enables us to decrease the size of the cloak. Theoretical analysis is performed numerically by comparing scattering waves in various cases; there exists a high reduction of the scattering wave when the radius of the cloak is larger than a quarter of one wavelength. This result indicates that the required size of the cloaking layer is more than an object scale in the Rayleigh scattering regime.

  19. Finite difference/spectral approximations for the distributed order time fractional reaction-diffusion equation on an unbounded domain (United States)

    Chen, Hu; Lü, Shujuan; Chen, Wenping


    The numerical approximation of the distributed order time fractional reaction-diffusion equation on a semi-infinite spatial domain is discussed in this paper. A fully discrete scheme based on finite difference method in time and spectral approximation using Laguerre functions in space is proposed. The scheme is unconditionally stable and convergent with order O (τ2 + Δα2 +N (1 - m) / 2), where τ, Δα, N, and m are the time-step size, step size in distributed-order variable, polynomial degree, and regularity in the space variable of the exact solution, respectively. A pseudospectral scheme is also proposed and analyzed. Some numerical examples are presented to demonstrate the efficiency of the proposed scheme.

  20. Staggered-grid finite-difference acoustic modeling with the Time-Domain Atmospheric Acoustic Propagation Suite (TDAAPS).

    Energy Technology Data Exchange (ETDEWEB)

    Aldridge, David Franklin; Collier, Sandra L. (U.S. Army Research Laboratory); Marlin, David H. (U.S. Army Research Laboratory); Ostashev, Vladimir E. (NOAA/Environmental Technology Laboratory); Symons, Neill Phillip; Wilson, D. Keith (U.S. Army Cold Regions Research Engineering Lab.)


    This document is intended to serve as a users guide for the time-domain atmospheric acoustic propagation suite (TDAAPS) program developed as part of the Department of Defense High-Performance Modernization Office (HPCMP) Common High-Performance Computing Scalable Software Initiative (CHSSI). TDAAPS performs staggered-grid finite-difference modeling of the acoustic velocity-pressure system with the incorporation of spatially inhomogeneous winds. Wherever practical the control structure of the codes are written in C++ using an object oriented design. Sections of code where a large number of calculations are required are written in C or F77 in order to enable better compiler optimization of these sections. The TDAAPS program conforms to a UNIX style calling interface. Most of the actions of the codes are controlled by adding flags to the invoking command line. This document presents a large number of examples and provides new users with the necessary background to perform acoustic modeling with TDAAPS.

  1. Solving the nonlinear Schrödinger equation using cubic B-spline interpolation and finite difference methods (United States)

    Ahmad, Azhar; Azmi, Amirah; Majid, Ahmad Abd.; Hamid, Nur Nadiah Abd


    In this paper, Nonlinear Schrödinger (NLS) equation with Neumann boundary conditions is solved using finite difference method (FDM) and cubic B-spline interpolation method (CuBSIM). First, the approach is based on the FDM applied on the time and space discretization with the help of theta-weighted method. However, our main interest is the second approach, whereby FDM is applied on the time discretization and cubic B-spline is utilized as an interpolation function in the space dimension with the same help of theta-weighted method. The CuBSIM is shown to be stable by using von Neumann stability analysis. The proposed method is tested on a test problem with single soliton motion of the NLS equation. The accuracy of the numerical results is measured by the Euclidean-norm and infinity-norm. CuBSIM is found to produce more accurate results than the FDM.

  2. Investigation of mechanical responses to the tactile perception of surfaces with different textures using the finite element method

    Directory of Open Access Journals (Sweden)

    Wei Tang


    Full Text Available Tactile perception is essential for humans to perceive the world, and it usually results in mechanical responses from the finger. In this study, a nonlinear, viscoelastic, and multilayered finite element model of the finger was developed. The relationship between the mechanical responses within the finger and tactile perception while the finger scanned different surface textures was studied. The results showed that the sensitivity of tactile perception is affected by the peak value of von Mises stress, which is itself determined by the shape and density of a given texture. The von Mises stress varies periodically with time, and this variation depends on the periodicity of the texture. Displacement signals around Pacinian corpuscles have periodic variation. The period of displacement decreases as the density of the texture increases. The spectral centroid increases as the spacing of the texture decreases. The related mechanisms are discussed in this article.

  3. Finite-difference algorithms for the time-domain Maxwell's equations - A numerical approach to RCS analysis (United States)

    Vinh, Hoang; Dwyer, Harry A.; Van Dam, C. P.


    The applications of two CFD-based finite-difference methods to computational electromagnetics are investigated. In the first method, the time-domain Maxwell's equations are solved using the explicit Lax-Wendroff scheme and in the second method, the second-order wave equations satisfying the Maxwell's equations are solved using the implicit Crank-Nicolson scheme. The governing equations are transformed to a generalized curvilinear coordinate system and solved on a body-conforming mesh using the scattered-field formulation. The induced surface current and the bistatic radar cross section are computed and the results are validated for several two-dimensional test cases involving perfectly-conducting scatterers submerged in transverse-magnetic plane waves.

  4. Estimation of State of Charge for Lithium-Ion Battery Based on Finite Difference Extended Kalman Filter

    Directory of Open Access Journals (Sweden)

    Ze Cheng


    Full Text Available An accurate estimation of the state of charge (SOC of the battery is of great significance for safe and efficient energy utilization of electric vehicles. Given the nonlinear dynamic system of the lithium-ion battery, the parameters of the second-order RC equivalent circuit model were calibrated and optimized using a nonlinear least squares algorithm in the Simulink parameter estimation toolbox. A comparison was made between this finite difference extended Kalman filter (FDEKF and the standard extended Kalman filter in the SOC estimation. The results show that the model can essentially predict the dynamic voltage behavior of the lithium-ion battery, and the FDEKF algorithm can maintain good accuracy in the estimation process and has strong robustness against modeling error.

  5. On Long-Time Instabilities in Staggered Finite Difference Simulations of the Seismic Acoustic Wave Equations on Discontinuous Grids

    KAUST Repository

    Gao, Longfei


    We consider the long-time instability issue associated with finite difference simulation of seismic acoustic wave equations on discontinuous grids. This issue is exhibited by a prototype algebraic problem abstracted from practical application settings. Analysis of this algebraic problem leads to better understanding of the cause of the instability and provides guidance for its treatment. Specifically, we use the concept of discrete energy to derive the proper solution transfer operators and design an effective way to damp the unstable solution modes. Our investigation shows that the interpolation operators need to be matched with their companion restriction operators in order to properly couple the coarse and fine grids. Moreover, to provide effective damping, specially designed diffusive terms are introduced to the equations at designated locations and discretized with specially designed schemes. These techniques are applied to simulations in practical settings and are shown to lead to superior results in terms of both stability and accuracy.

  6. A Fast O(N log N Finite Difference Method for the One-Dimensional Space-Fractional Diffusion Equation

    Directory of Open Access Journals (Sweden)

    Treena Basu


    Full Text Available This paper proposes an approach for the space-fractional diffusion equation in one dimension. Since fractional differential operators are non-local, two main difficulties arise after discretization and solving using Gaussian elimination: how to handle the memory requirement of O(N2 for storing the dense or even full matrices that arise from application of numerical methods and how to manage the significant computational work count of O(N3 per time step, where N is the number of spatial grid points. In this paper, a fast iterative finite difference method is developed, which has a memory requirement of O(N and a computational cost of O(N logN per iteration. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.

  7. Performance Improvements for Coarse Mesh Finite Difference Acceleration L3:RTM.PRT.P13.02

    Energy Technology Data Exchange (ETDEWEB)

    Collins, Benjamin S. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Hamilton, Steven P. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Stimpson, Shane [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Yee, Ben [Univ. of Michigan, Ann Arbor, MI (United States); Larsen, Edward W. [Univ. of Michigan, Ann Arbor, MI (United States); Kochunas, Brendan [Univ. of Michigan, Ann Arbor, MI (United States)


    The development of VERA-CS in recent years has focused on developing the capability to simulate multiple cycles of operating commercial nuclear power plants. Now that these capabilities have advanced to the point where it is being deployed to users, the focus is on improving the computational performance of various components in VERA-CS. In this work, the focus is on the Coarse Mesh Finite Difference (CMFD) solution in MPACT. CMFD serves multiple purposes in the 2D/1D solution methodology. First, it is a natural mechanism to tie together the radial MOC transport and the axial SP3 solution. Because the CMFD system solves the multigroup three-dimensional core in one system, it pulls together the global response of the system. In addition, the CMFD solution provides a framework to accelerate the convergence of the eigenvalue problem.

  8. Finite-Difference Time-Domain Simulation of Light Propagation in 2D Periodic and Quasi-Periodic Photonic Structures

    Directory of Open Access Journals (Sweden)

    N. Dadashzadeh


    Full Text Available Ultra-short pulse is a promising technology for achieving ultra-high data rate transmission which is required to follow the increased demand of data transport over an optical communication system. Therefore, the propagation of such type of pulses and the effects that it may suffer during its transmission through an optical waveguide has received a great deal of attention in the recent years. We provide an overview of recent theoretical developments in a numerical modeling of Maxwell's equations to analyze the propagation of short laser pulses in photonic structures. The process of short light pulse propagation through 2D periodic and quasi-periodic photonic structures is simulated based on Finite-Difference Time-Domain calculations of Maxwell’s equations.

  9. Tomographic reconstruction of melanin structures of optical coherence tomography via the finite-difference time-domain simulation (United States)

    Huang, Shi-Hao; Wang, Shiang-Jiu; Tseng, Snow H.


    Optical coherence tomography (OCT) provides high resolution, cross-sectional image of internal microstructure of biological tissue. We use the Finite-Difference Time-Domain method (FDTD) to analyze the data acquired by OCT, which can help us reconstruct the refractive index of the biological tissue. We calculate the refractive index tomography and try to match the simulation with the data acquired by OCT. Specifically, we try to reconstruct the structure of melanin, which has complex refractive indices and is the key component of human pigment system. The results indicate that better reconstruction can be achieved for homogenous sample, whereas the reconstruction is degraded for samples with fine structure or with complex interface. Simulation reconstruction shows structures of the Melanin that may be useful for biomedical optics applications.

  10. Full-Wave Analysis of Traveling-Wave Field-Effect Transistors Using Finite-Difference Time-Domain Method

    Directory of Open Access Journals (Sweden)

    Koichi Narahara


    Full Text Available Nonlinear transmission lines, which define transmission lines periodically loaded with nonlinear devices such as varactors, diodes, and transistors, are modeled in the framework of finite-difference time-domain (FDTD method. Originally, some root-finding routine is needed to evaluate the contributions of nonlinear device currents appropriately to the temporally advanced electrical fields. Arbitrary nonlinear transmission lines contain large amount of nonlinear devices; therefore, it costs too much time to complete calculations. To reduce the calculation time, we recently developed a simple model of diodes to eliminate root-finding routines in an FDTD solver. Approximating the diode current-voltage relation by a piecewise-linear function, an extended Ampere's law is solved in a closed form for the time-advanced electrical fields. In this paper, we newly develop an FDTD model of field-effect transistors (FETs, together with several numerical examples that demonstrate pulse-shortening phenomena in a traveling-wave FET.

  11. An efficient finite differences method for the computation of compressible, subsonic, unsteady flows past airfoils and panels (United States)

    Colera, Manuel; Pérez-Saborid, Miguel


    A finite differences scheme is proposed in this work to compute in the time domain the compressible, subsonic, unsteady flow past an aerodynamic airfoil using the linearized potential theory. It improves and extends the original method proposed in this journal by Hariharan, Ping and Scott [1] by considering: (i) a non-uniform mesh, (ii) an implicit time integration algorithm, (iii) a vectorized implementation and (iv) the coupled airfoil dynamics and fluid dynamic loads. First, we have formulated the method for cases in which the airfoil motion is given. The scheme has been tested on well known problems in unsteady aerodynamics -such as the response to a sudden change of the angle of attack and to a harmonic motion of the airfoil- and has been proved to be more accurate and efficient than other finite differences and vortex-lattice methods found in the literature. Secondly, we have coupled our method to the equations governing the airfoil dynamics in order to numerically solve problems where the airfoil motion is unknown a priori as happens, for example, in the cases of the flutter and the divergence of a typical section of a wing or of a flexible panel. Apparently, this is the first self-consistent and easy-to-implement numerical analysis in the time domain of the compressible, linearized coupled dynamics of the (generally flexible) airfoil-fluid system carried out in the literature. The results for the particular case of a rigid airfoil show excellent agreement with those reported by other authors, whereas those obtained for the case of a cantilevered flexible airfoil in compressible flow seem to be original or, at least, not well-known.

  12. A Matlab-based finite-difference solver for the Poisson problem with mixed Dirichlet-Neumann boundary conditions (United States)

    Reimer, Ashton S.; Cheviakov, Alexei F.


    A Matlab-based finite-difference numerical solver for the Poisson equation for a rectangle and a disk in two dimensions, and a spherical domain in three dimensions, is presented. The solver is optimized for handling an arbitrary combination of Dirichlet and Neumann boundary conditions, and allows for full user control of mesh refinement. The solver routines utilize effective and parallelized sparse vector and matrix operations. Computations exhibit high speeds, numerical stability with respect to mesh size and mesh refinement, and acceptable error values even on desktop computers. Catalogue identifier: AENQ_v1_0 Program summary URL: Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License v3.0 No. of lines in distributed program, including test data, etc.: 102793 No. of bytes in distributed program, including test data, etc.: 369378 Distribution format: tar.gz Programming language: Matlab 2010a. Computer: PC, Macintosh. Operating system: Windows, OSX, Linux. RAM: 8 GB (8, 589, 934, 592 bytes) Classification: 4.3. Nature of problem: To solve the Poisson problem in a standard domain with “patchy surface”-type (strongly heterogeneous) Neumann/Dirichlet boundary conditions. Solution method: Finite difference with mesh refinement. Restrictions: Spherical domain in 3D; rectangular domain or a disk in 2D. Unusual features: Choice between mldivide/iterative solver for the solution of large system of linear algebraic equations that arise. Full user control of Neumann/Dirichlet boundary conditions and mesh refinement. Running time: Depending on the number of points taken and the geometry of the domain, the routine may take from less than a second to several hours to execute.

  13. High Order Finite Difference Methods with Subcell Resolution for 2D Detonation Waves (United States)

    Wang, W.; Shu, C. W.; Yee, H. C.; Sjogreen, B.


    In simulating hyperbolic conservation laws in conjunction with an inhomogeneous stiff source term, if the solution is discontinuous, spurious numerical results may be produced due to different time scales of the transport part and the source term. This numerical issue often arises in combustion and high speed chemical reacting flows.

  14. Electronic transport through nanowires: a real-space finite-difference approach

    NARCIS (Netherlands)

    Khomyakov, Petr


    Nanoelectronics is a fast developing ¯eld. Therefore understanding of the electronic transport at the nanoscale is currently of great interest. This thesis "Electronic transport through nanowires: a real-space ¯nite-difference approach" aims at a general theoretical treatment of coherent electronic

  15. Distribution of micromotion in implants and alveolar bone with different thread profiles in immediate loading: a finite element study. (United States)

    Chang, Pei-Kun; Chen, Yung-Chuan; Huang, Ching-Chieh; Lu, Wei-Hua; Chen, Yi-Chun; Tsai, Hsun-Heng


    To detect the differences in the distribution of micromotion within implants and alveolar bone with different implant thread designs during immediate loading. A three-dimensional finite element model with contact elements was used to simulate the contact behavior between the implant and alveolar bone. Implants with four different thread designs were created: Acme (trapezoidal) thread (AT), buttress thread (BT), square thread (ST), and a standard V-thread (VT). To simulate immediate loading, the model was designed without osseointegration between the implant and alveolar bone. A load of 300 N was applied axially to the model, and the micromovements were measured. The maximum micromotion values of the ST, AT, VT, and BT models were 8.53, 9.57, 11.00, and 15.00 µm, respectively. All micromotion was located near the interface of cortical and cancellous bone. Different thread designs showed different distribution of micromotion during loading. This indicates that initial stability in immediate loading may be affected by thread design. The ST profile showed the most favorable result in the study. An implant with an ST profile might provide the best primary stability in an immediate loading situation.

  16. Stress analysis in bone tissue around single implants with different diameters and veneering materials: a 3-D finite element study. (United States)

    Santiago Junior, Joel Ferreira; Pellizzer, Eduardo Piza; Verri, Fellippo Ramos; de Carvalho, Paulo Sérgio Perri


    The aim of this study was to evaluate the stress distribution on bone tissue with a single prosthesis supported by implants of large and conventional diameter and presenting different veneering materials using the 3-D finite element method. Sixteen models were fabricated to reproduce a bone block with implants, using two diameters (3.75×10 mm and 5.00×10 mm), four different veneering materials (composite resin, acrylic resin, porcelain, and NiCr crown), and two loads (axial (200 N) and oblique (100 N)). For data analysis, the maximum principal stress and von Mises criterion were used. For the axial load, the cortical bone in all models did not exhibit significant differences, and the trabecular bone presented higher tensile stress with reduced implant diameter. For the oblique load, the cortical bone presented a significant increase in tensile stress on the same side as the loading for smaller implant diameters. The trabecular bone showed a similar but more discreet trend. There was no difference in bone tissue with different veneering materials. The veneering material did not influence the stress distribution in the supporting tissues of single implant-supported prostheses. The large-diameter implants improved the transference of occlusal loads to bone tissue and decreased stress mainly under oblique loads. Oblique loading was more detrimental to distribution stresses than axial loading. © 2013.

  17. Influence of Different Modeling Strategies for CFRP on Finite Element Simulation Results


    Liu Xueshu; Huang Li; Xu Maoqing; Zhang Zhipeng


    Numerical simulation is used to predict the behavior and response of carbon fiber reinforced plastic (CFRP). Sometimes zero thickness of interface layer is introduced into the numerical model to investigate the inter-layer behavior like delamination. To investigate the influence of critical volume-type defect like void, usually appeared in matrix rich region at the interface between layers, on mechanical properties of CFRP, numerical models with different interface thickness were created and ...

  18. Time-accurate finite difference solutions to the incompressible Navier-Stokes/energy equations (United States)

    Mirfakhraee, Ali; Davis, Sanford


    Two new algorithms for solving coupled Navier-Stokes and energy equations are presented. The algorithms are compared with available Navier-Stokes solutions for the model problem of a driven-cavity-flow over a range of Reynolds numbers. It is noted that the algorithms represent two different implementations of the fractional step approach to the solution of the coupled Navier-Stokes and energy equations using the Boussinesq approximation.

  19. Modeling of Nanophotonic Resonators with the Finite-Difference Frequency-Domain Method

    DEFF Research Database (Denmark)

    Ivinskaya, Aliaksandra; Lavrinenko, Andrei; Shyroki, Dzmitry


    lattice constant in the region of high field intensity, we are able to find the eigenwavelength $lambda $ with a half-percent precision and the $Q$-factor with an order-of-magnitude accuracy. We also suggest the $lambda /n$ rule (where $n$ is the cavity refractive index) for the optimal cavity...... easily to better resolve mode features. We explore the convergence of the eigenmode wavelength $lambda $ and quality factor $Q$ of an open dielectric sphere and of a very-high- $Q$ photonic crystal cavity calculated with different mesh density distributions. On a grid having, for example, 10 nodes per...



    B. Hamilton; S. Bilbao


    In this paper, we investigate finite difference schemes forthe 3-D wave equation using 27-point stencils on the cubiclattice, a 13-point stencil on the face-centered cubic (FCC)lattice, and a 9-point stencil on the body-centered cubic(BCC) lattice. The tiling of the wavenumber space for nonCartesian grids is considered in order to analyse numericaldispersion. Schemes are compared for computational effi-ciency in terms of minimising numerical wave speed error.It is shown that the 13-point scheme...

  1. Ambient Vibration Tests of an Arch Dam with Different Reservoir Water Levels: Experimental Results and Comparison with Finite Element Modelling

    Directory of Open Access Journals (Sweden)

    Sergio Vincenzo Calcina


    Full Text Available This paper deals with the ambient vibration tests performed in an arch dam in two different working conditions in order to assess the effect produced by two different reservoir water levels on the structural vibration properties. The study consists of an experimental part and a numerical part. The experimental tests were carried out in two different periods of the year, at the beginning of autumn (October 2012 and at the end of winter (March 2013, respectively. The measurements were performed using a fast technique based on asynchronous records of microtremor time-series. In-contact single-station measurements were done by means of one single high resolution triaxial tromometer and two low-frequency seismometers, placed in different points of the structure. The Standard Spectral Ratio method has been used to evaluate the natural frequencies of vibration of the structure. A 3D finite element model of the arch dam-reservoir-foundation system has been developed to verify analytically determined vibration properties, such as natural frequencies and mode shapes, and their changes linked to water level with the experimental results.

  2. Evaluation of different screw fixation techniques and screw diameters in sagittal split ramus osteotomy: finite element analysis method. (United States)

    Sindel, A; Demiralp, S; Colok, G


    Sagittal split ramus osteotomy (SSRO) is used for correction of numerous congenital or acquired deformities in facial region. Several techniques have been developed and used to maintain fixation and stabilisation following SSRO application. In this study, the effects of the insertion formations of the bicortical different sized screws to the stresses generated by forces were studied. Three-dimensional finite elements analysis (FEA) and static linear analysis methods were used to investigate difference which would occur in terms of forces effecting onto the screws and transmitted to bone between different application areas. No significant difference was found between 1·5- and 2-mm screws used in SSRO fixation. Besides, it was found that 'inverted L' application was more successful compared to the others and that was followed by 'L' and 'linear' formations which showed close rates to each other. Few studies have investigated the effect of thickness and application areas of bicortical screws. This study was performed on both advanced and regressed jaws positions. © 2014 John Wiley & Sons Ltd.

  3. Influence of Different Modeling Strategies for CFRP on Finite Element Simulation Results

    Directory of Open Access Journals (Sweden)

    Liu Xueshu


    Full Text Available Numerical simulation is used to predict the behavior and response of carbon fiber reinforced plastic (CFRP. Sometimes zero thickness of interface layer is introduced into the numerical model to investigate the inter-layer behavior like delamination. To investigate the influence of critical volume-type defect like void, usually appeared in matrix rich region at the interface between layers, on mechanical properties of CFRP, numerical models with different interface thickness were created and tensile property and three-point bending simulation results were compared to experimental ones. It is found that accurate result is obtained with increasing of the interface thickness and up to 20% that of layer thickness is recommended to model the matrix rich region.

  4. Finite difference solution for a generalized Reynolds equation with homogeneous two-phase flow (United States)

    Braun, M. J.; Wheeler, R. L., III; Hendricks, R. C.; Mullen, R. L.

    An attempt is made to relate elements of two-phase flow and kinetic theory to the modified generalized Reynolds equation and to the energy equation, in order to arrive at a unified model simulating the pressure and flows in journal bearings, hydrostatic journal bearings, or squeeze film dampers when a two-phase situation occurs due to sudden fluid depressurization and heat generation. The numerical examples presented furnish a test of the algorithm for constant properties, and give insight into the effect of the shaft fluid heat transfer coefficient on the temperature profiles. The different level of pressures achievable for a given angular velocity depends on whether the bearing is thermal or nonisothermal; upwind differencing is noted to be essential for the derivation of a realistic profile.

  5. Seismic wavefield simulation in 2D elastic and viscoelastic tilted transversely isotropic media: comparisons between four different kinds of finite-difference grid schemes (United States)

    Li, Zhong-sheng; Bai, Chao-ying; Sun, Yao-chong


    In this paper, we use the staggered grid, the auxiliary grid, the rotated staggered grid and the non-staggered grid finite-difference methods to simulate the wavefield propagation in 2D elastic tilted transversely isotropic (TTI) and viscoelastic TTI media, respectively. Under the stability conditions, we choose different spatial and temporal intervals to get wavefront snapshots and synthetic seismograms to compare the four algorithms in terms of computational accuracy, CPU time, phase shift, frequency dispersion and amplitude preservation. The numerical results show that: (1) the rotated staggered grid scheme has the least memory cost and the fastest running speed; (2) the non-staggered grid scheme has the highest computational accuracy and least phase shift; (3) the staggered grid has less frequency dispersion even when the spatial interval becomes larger.

  6. Finite element analysis of the stability of transverse acetabular fractures in standing and sitting positions by different fixation options. (United States)

    Yildirim, Ahmet Ozgur; Alemdaroglu, Kadir Bahadir; Yuksel, Halil Yalcin; Öken, Özdamar Fuad; Ucaner, Ahmet


    Treatment of a transverse acetabular fracture type is possible from an anterior approach, a posterior approach or both. Different fixation methods have been described but whether one is superior to the other is still under debate. The aim of the current study was to test the different fixation alternatives of stabilization of transverse acetabular fractures under two basic physiological loading conditions: standing and sitting utilizing a finite element model. A transtectal transverse fracture model was fixed in five different alternatives: an anterior column plate; a posterior column plate; an anterior column plate combined with a posterior column screw; a posterior column plate combined with an anterior column screw; and a posterior column plate and an anterior column plate. In these models, a load of 400N was applied at standing and sitting positions and the displacements were analyzed by using three-dimensional finite element stress analysis method. In the model simulating standing human position, overall motion at the posterior column was minimum when two columns were plated (0.071mm). The second best fixation was posterior column plate with an anterior column screw (0.077mm). Overall motion at the anterior column was minimum by posterior column plate with an anterior column screw (0.0326mm). The plating of two columns was associated with motion of (0.0333mm). In the model that simulates sitting position, the motion at the posterior column was minimum when two columns were plated (0.0478mm), and (0.0517mm) when a posterior column plate with an anterior column screw was used. Overall motion in the anterior column was minimum when posterior column plate with an anterior column screw (0.0198mm) was used, whereas the motion was (0.0203mm) when plating of both columns was examined. Posterior column plating combined with an anterior column screw has quite comparable results to a both column plating in transverse fractures, suggesting that two column fixations might

  7. A fourth order accuracy summation-by-parts finite difference scheme for acoustic reverse time migration in boundary-conforming grids (United States)

    Wang, Ying; Zhou, Hui; Yuan, Sanyi; Ye, Yameng


    The fourth order accuracy finite difference scheme is known advantageous in reducing memory and improving efficiency. Summation-by-parts finite difference operator is a natural way for wavefield simulation in complicated domains containing surface topography and irregular interfaces. The application of summation-by-parts method guarantees the stability of numerical approximation for heterogeneous media on curvilinear grids. This paper extends the second order summation-by-parts finite difference method to the fourth order case for the discretization of acoustic wave equation and perfect matched layer in boundary-conforming grids. In particular, the implementation of the fourth order method for wavefield simulation and reverse time migration in complicated domains can significantly improve the efficiency and decrease the storage. The elliptic method is applied for boundary-conforming grid generation in complicated domains. Under such grids, the two-dimensional acoustic wave equation in second order displacement formulation is compactly reformulated for forward modeling and reverse time migration, and the symmetric and compact form of perfectly matched layers expressed in a curvilinear coordinate system are applied to suppress artificial reflections. The discretizations of the acoustic wave equation and perfectly matched layer formula are fourth and second order accuracy in space and time respectively, where the spatial discretization satisfies the principle of summation-by-parts and is stable. Numerical experiments are presented to compare the accuracy of the second with fourth order summation-by-parts finite difference methods and to evaluate the efficiency of reverse time migration by using these two methods. As well, comparisons are performed between the fourth order accuracy summation-by-parts finite difference method and central finite difference method to illustrate the stability superiority of summation-by-parts operators.


    A three-point backward finite-difference method has been derived for a system of mixed hyperbolic¯¯parabolic (convection¯¯diffusion) partial differential equations (mixed PDEs). The method resorts to the three-point backward differenci...

  9. A multiscale mortar multipoint flux mixed finite element method

    KAUST Repository

    Wheeler, Mary Fanett


    In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite element method that reduces to cell-centered finite differences on irregular grids. The subdomain grids do not have to match across the interfaces. Continuity of flux between coarse elements is imposed via a mortar finite element space on a coarse grid scale. With an appropriate choice of polynomial degree of the mortar space, we derive optimal order convergence on the fine scale for both the multiscale pressure and velocity, as well as the coarse scale mortar pressure. Some superconvergence results are also derived. The algebraic system is reduced via a non-overlapping domain decomposition to a coarse scale mortar interface problem that is solved using a multiscale flux basis. Numerical experiments are presented to confirm the theory and illustrate the efficiency and flexibility of the method. © EDP Sciences, SMAI, 2012.

  10. Investigation of graphene-on-metal substrates for SPR-based sensor using finite-difference time domain. (United States)

    Said, Fairus Atida; Menon, Pulliyaseri Susthitha; Rajendran, Venkatachalam; Shaari, Sahbudin; Majlis, Burhanuddin Y


    In this study, the authors investigated the effects of a single layer graphene as a coating layer on top of metal thin films such as silver, gold, aluminum and copper using finite-difference time domain method. To enhance the resolution of surface plasmon resonance (SPR) sensor, it is necessary to increase the SPR reflectivity and decrease the full-width-half maximum (FWHM) of the SPR curve so that there is minimum uncertainty in the determination of the resonance dip. Numerical data was verified with analytical and experimental data where all the data were in good agreement with resonance angle differing in <10% due to noise present in components such as humidity and temperature. In further analysis, reflectivity and FWHM were compared among four types of metal with various thin film thicknesses where graphene was applied on top of the metal layers, and data was compared against pure conventional metal thin films. A 60 nm-thick Au thin film results in higher performance with reflectivity of 92.4% and FWHM of 0.88° whereas single layer graphene-on-60 nm-thick Au gave reflectivity of 91.7% and FWHM of 1.32°. However, a graphene-on-40 nm-thick Ag also gave good performance with narrower FWHM of 0.88° and reflection spectra of 89.2%.

  11. A generalized volumetric dispersion model for a class of two-phase separation/reaction: finite difference solutions (United States)

    Siripatana, Chairat; Thongpan, Hathaikarn; Promraksa, Arwut


    This article explores a volumetric approach in formulating differential equations for a class of engineering flow problems involving component transfer within or between two phases. In contrast to conventional formulation which is based on linear velocities, this work proposed a slightly different approach based on volumetric flow-rate which is essentially constant in many industrial processes. In effect, many multi-dimensional flow problems found industrially can be simplified into multi-component or multi-phase but one-dimensional flow problems. The formulation is largely generic, covering counter-current, concurrent or batch, fixed and fluidized bed arrangement. It was also intended to use for start-up, shut-down, control and steady state simulation. Since many realistic and industrial operation are dynamic with variable velocity and porosity in relation to position, analytical solutions are rare and limited to only very simple cases. Thus we also provide a numerical solution using Crank-Nicolson finite difference scheme. This solution is inherently stable as tested against a few cases published in the literature. However, it is anticipated that, for unconfined flow or non-constant flow-rate, traditional formulation should be applied.

  12. Parallel adaptive mesh refinement method based on WENO finite difference scheme for the simulation of multi-dimensional detonation (United States)

    Wang, Cheng; Dong, XinZhuang; Shu, Chi-Wang


    For numerical simulation of detonation, computational cost using uniform meshes is large due to the vast separation in both time and space scales. Adaptive mesh refinement (AMR) is advantageous for problems with vastly different scales. This paper aims to propose an AMR method with high order accuracy for numerical investigation of multi-dimensional detonation. A well-designed AMR method based on finite difference weighted essentially non-oscillatory (WENO) scheme, named as AMR&WENO is proposed. A new cell-based data structure is used to organize the adaptive meshes. The new data structure makes it possible for cells to communicate with each other quickly and easily. In order to develop an AMR method with high order accuracy, high order prolongations in both space and time are utilized in the data prolongation procedure. Based on the message passing interface (MPI) platform, we have developed a workload balancing parallel AMR&WENO code using the Hilbert space-filling curve algorithm. Our numerical experiments with detonation simulations indicate that the AMR&WENO is accurate and has a high resolution. Moreover, we evaluate and compare the performance of the uniform mesh WENO scheme and the parallel AMR&WENO method. The comparison results provide us further insight into the high performance of the parallel AMR&WENO method.

  13. A time domain finite-difference technique for oblique incidence of antiplane waves in heterogeneous dissipative media

    Directory of Open Access Journals (Sweden)

    A. Caserta


    Full Text Available This paper deals with the antiplane wave propagation in a 2D heterogeneous dissipative medium with complex layer interfaces and irregular topography. The initial boundary value problem which represents the viscoelastic dynamics driving 2D antiplane wave propagation is formulated. The discretization scheme is based on the finite-difference technique. Our approach presents some innovative features. First, the introduction of the forcing term into the equation of motion offers the advantage of an easier handling of different inputs such as general functions of spatial coordinates and time. Second, in the case of a straight-line source, the symmetry of the incident plane wave allows us to solve the problem of oblique incidence simply by rotating the 2D model. This artifice reduces the oblique incidence to the vertical one. Third, the conventional rheological model of the generalized Maxwell body has been extended to include the stress-free boundary condition. For this reason we solve explicitly the stress-free boundary condition, not following the most popular technique called vacuum formalism. Finally, our numerical code has been constructed to model the seismic response of complex geological structures: real geological interfaces are automatically digitized and easily introduced in the input model. Three numerical applications are discussed. To validate our numerical model, the first test compares the results of our code with others shown in the literature. The second application rotates the input model to simulate the oblique incidence. The third one deals with a real high-complexity 2D geological structure.

  14. Finite Divergence

    DEFF Research Database (Denmark)

    Hansen, Michael Edberg; Pandya, P. K.; Chaochen, Zhou


    Real-time and hybrid systems have been studied so far under the assumption of finite variability. In this paper, we consider models in which systems exhibiting finite divergence can also be analysed. In such systems, the state of the system can change infinitely often in a finite time. This kind...... of behaviour arises in many representations of hybrid systems, and also in theories of nonlinear systems. The aim is to provide a theory where pathological behaviour such as finite divergence can be analysed-if only to prove that it does not occur in systems of interest. Finite divergence is studied using...


    Directory of Open Access Journals (Sweden)

    Richasanty Septima S


    Full Text Available The research in this thesis was done to examine the model of traffic flow of volcanic disaster evacuation path for uphill and downhill roads. The assessment was focused on the area of disaster evacuation path from the Pante Raya Bener Meriah intersection to Takengon. This model is assessed for two different types of time when which a disaster occurs; the disaster occurred at night and the disaster occurred during the day, especially during peak hours (working hours. The model was developed with attention to the exixtence of inflow and outflow along the evacuation route. Furthermore, the model obtained is solved numerically by using finite difference method. The chosen approach of this method is upwind scheme with time and space steps using forward difference and backward difference. The solution of this model in the form of simulated vehicle density along evacuation pathways. The research conducted is in the form of a model of traffic flow on evacuation paths and restricted to the inflow and outflow without alternative path as well as the conditions of the road which are uphill and downhill, showed a high density of vehicles either at night or during the day. Uphill road conditions resulted in decreased vehicle speed and vehicle density will increase, while downhill road conditions resulted in increased vehicle speed and vehicle density will decrease, meaning that the road conditions which are uphill and downhill will greatly affect the process of evacuation. Degree vehicles of evacuation efficiency occuring at night without an alternative pathway produces a high efficiency so that it can be interpreted that the evacuation process in the evening was successful and runs better than the evacuation process during the day, and this is caused by the existence of vehicles on the road evacuation process started thus affecting the efficiency levels.

  16. Analysis of pelvic strain in different gait configurations in a validated cohort of computed tomography based finite element models. (United States)

    Salo, Zoryana; Beek, Maarten; Wright, David; Maloul, Asmaa; Whyne, Cari Marisa


    The pelvis functions to transmit upper body loads to the lower limbs and is critical in human locomotion. Semi-automated, landmark-based finite element (FE) morphing and mapping techniques eliminate the need for segmentation and have shown to accelerate the generation of multiple specimen-specific pelvic FE models to enable the study of pelvic mechanical behaviour. The purpose of this research was to produce an experimentally validated cohort of specimen-specific FE models of the human pelvis and to use this cohort to analyze pelvic strain patterns during gait. Using an initially segmented specimen-specific pelvic FE model asa source model, four more specimen-specific pelvic FE models were generated from target clinical CT scans using landmark-based morphing and mapping techniques. FE strains from the five models were compared to the experimental strains obtained from cadaveric testing via linear regression analysis, (R(2) values ranging from 0.70 to 0.93). Inter-specimen variability in FE strain distributions was seen among the five specimen-specific pelvic FE models. The validated cohort of specimen-specific pelvic FE models was utilized to examine pelvic strains at different phases of the gait cycle. Each validated specimen-specific FE model was reconfigured into gait cycle phases representing heel-strike/heel-off and midstance/midswing. No significant difference was found in the double-leg stance and heel-strike/heel-off models (p=0.40). A trend was observed between double-leg stance and midstance/midswing models (p=0.07), and a significant difference was found between heel-strike/heel-off models and midstance/midswing models (p=0.02). Significant differences were also found in comparing right vs. left models (heel-strike/heel-off p=0.14, midstance/midswing p=0.04). Copyright © 2017 Elsevier Ltd. All rights reserved.

  17. Influence of three different implant thread designs on stress distribution: A three-dimensional finite element analysis

    Directory of Open Access Journals (Sweden)

    Mansi Manish Oswal


    Full Text Available Purpose: Clinical success of implant prosthodontics is dependent in part upon the type of implant thread design. The selection of implant thread design plays an important role in the outcome of the treatment. This study was undertaken to evaluate the pattern of stress distribution using a finite element analysis; hence, the area which would be bearing maximum load for a given design would be arrived. Materials and Methods: Three implants with different thread designs, namely V-thread, buttress, and reverse buttress thread designs were considered and dimensions were standardized. The site considered was the mandibular molar region with cortical and trabecular bone assuming to be isotropic and homogeneous. The implant modeling was done with the CATIA software. Vertical loads of 100N were applied. The stresses were calculated as Von Mises stress criterion. Results: Maximum stresses were seen at the cortical bone and were transferred to the implant. Minimum Von Mises stresses were seen with reverse buttress thread design at the cortical bone. The stresses were observed least at the cancellous bone and maximum at the implant. Conclusion: Hence, within the limitations of this study the results obtained can be applied clinically for appropriate selection of implant thread design for a predictable success of implant therapy.

  18. Numerical solver for first-principles transport calculation based on real-space finite-difference method (United States)

    Iwase, Shigeru; Hoshi, Takeo; Ono, Tomoya


    We propose an efficient procedure to obtain Green's functions by combining the shifted conjugate orthogonal conjugate gradient (shifted COCG) method with the nonequilibrium Green's function (NEGF) method based on a real-space finite-difference (RSFD) approach. The bottleneck of the computation in the NEGF scheme is matrix inversion of the Hamiltonian including the self-energy terms of electrodes to obtain the perturbed Green's function in the transition region. This procedure first computes unperturbed Green's functions and calculates perturbed Green's functions from the unperturbed ones using a mathematically strict relation. Since the matrices to be inverted to obtain the unperturbed Green's functions are sparse, complex-symmetric, and shifted for a given set of sampling energy points, we can use the shifted COCG method, in which once the Green's function for a reference energy point has been calculated the Green's functions for the other energy points can be obtained with a moderate computational cost. We calculate the transport properties of a C60@(10,10) carbon nanotube (CNT) peapod suspended by (10,10)CNTs as an example of a large-scale transport calculation. The proposed scheme opens the possibility of performing large-scale RSFD-NEGF transport calculations using massively parallel computers without the loss of accuracy originating from the incompleteness of the localized basis set.

  19. A two dimensional finite difference time domain analysis of the quiet zone fields of an anechoic chamber (United States)

    Ryan, Deirdre A.; Luebbers, Raymond J.; Nguyen, Truong X.; Kunz, Karl S.; Steich, David J.


    Prediction of anechoic chamber performance is a difficult problem. Electromagnetic anechoic chambers exist for a wide range of frequencies but are typically very large when measured in wavelengths. Three dimensional finite difference time domain (FDTD) modeling of anechoic chambers is possible with current computers but at frequencies lower than most chamber design frequencies. However, two dimensional FDTD (2D-FTD) modeling enables much greater detail at higher frequencies and offers significant insight into compact anechoic chamber design and performance. A major subsystem of an anechoic chamber for which computational electromagnetic analyses exist is the reflector. First, an analysis of the quiet zone fields of a low frequency anechoic chamber produced by a uniform source and a reflector in two dimensions using the FDTD method is presented. The 2D-FDTD results are compared with results from a three dimensional corrected physical optics calculation and show good agreement. Next, a directional source is substituted for the uniform radiator. Finally, a two dimensional anechoic chamber geometry, including absorbing materials, is considered, and the 2D-FDTD results for these geometries appear reasonable.

  20. Finite-difference analysis of plasmon-induced forces of metal nano-clusters by the Lorentz force formulation. (United States)

    Fujii, Masafumi


    We analyze light-induced forces on metal nano-spheres by using the three-dimensional finite-difference time-domain method with the Lorentz force formulation. Convergent analysis of the force on metal nano-particle clusters has been achieved by integrating the Lorentz and the Coulomb forces over the volume of the metal particles. Comparison to the Mie theory of radiation pressure on metal spheres under a plane wave illumination has verified rigorously the accuracy of the numerical method. We also analyze separate two metal spheres in close proximity and the results of the induced forces are compared to those in previous publications. The present method allows analysis of forces on various irregular structures; we apply the method to touching metal spheres, forming a simple cluster with a slight deformation at the contact point, to analyze the forces induced by the plasmonic resonance of the clusters. We show that the fundamental resonance modes, which newly appear in an infrared range when spheres are touching, exhibit strong binding forces within the clusters. Based on the numerical analyses we identify the resonance modes and evaluate quantitatively the infrared-induced forces on metal nano-sphere clusters.

  1. A GPGPU based program to solve the TDSE in intense laser fields through the finite difference approach

    CERN Document Server

    Broin, Cathal Ó


    We present a General-purpose computing on graphics processing units (GPGPU) based computational program and framework for the electronic dynamics of atomic systems under intense laser fields. We present our results using the case of hydrogen, however the code is trivially extensible to tackle problems within the single-active electron (SAE) approximation. Building on our previous work, we introduce the first available GPGPU based implementation of the Taylor, Runge-Kutta and Lanczos based methods created with strong field ab-initio simulations specifically in mind; CLTDSE. The code makes use of finite difference methods and the OpenCL framework for GPU acceleration. The specific example system used is the classic test system; Hydrogen. After introducing the standard theory, and specific quantities which are calculated, the code, including installation and usage, is discussed in-depth. This is followed by some examples and a short benchmark between an 8 hardware thread (i.e logical core) Intel Xeon CPU and an ...

  2. Computable error estimates of a finite difference scheme for option pricing in exponential Lévy models

    KAUST Repository

    Kiessling, Jonas


    Option prices in exponential Lévy models solve certain partial integro-differential equations. This work focuses on developing novel, computable error approximations for a finite difference scheme that is suitable for solving such PIDEs. The scheme was introduced in (Cont and Voltchkova, SIAM J. Numer. Anal. 43(4):1596-1626, 2005). The main results of this work are new estimates of the dominating error terms, namely the time and space discretisation errors. In addition, the leading order terms of the error estimates are determined in a form that is more amenable to computations. The payoff is only assumed to satisfy an exponential growth condition, it is not assumed to be Lipschitz continuous as in previous works. If the underlying Lévy process has infinite jump activity, then the jumps smaller than some (Formula presented.) are approximated by diffusion. The resulting diffusion approximation error is also estimated, with leading order term in computable form, as well as the dependence of the time and space discretisation errors on this approximation. Consequently, it is possible to determine how to jointly choose the space and time grid sizes and the cut off parameter (Formula presented.). © 2014 Springer Science+Business Media Dordrecht.

  3. Experimental validation of a finite-difference model for the prediction of transcranial ultrasound fields based on CT images (United States)

    Bouchoux, Guillaume; Bader, Kenneth B.; Korfhagen, Joseph J.; Raymond, Jason L.; Shivashankar, Ravishankar; Abruzzo, Todd A.; Holland, Christy K.


    The prevalence of stroke worldwide and the paucity of effective therapies have triggered interest in the use of transcranial ultrasound as an adjuvant to thrombolytic therapy. Previous studies have shown that 120 kHz ultrasound enhanced thrombolysis and allowed efficient penetration through the temporal bone. The objective of our study was to develop an accurate finite-difference model of acoustic propagation through the skull based on computed tomography (CT) images. The computational approach, which neglected shear waves, was compared with a simple analytical model including shear waves. Acoustic pressure fields from a two-element annular array (120 and 60 kHz) were acquired in vitro in four human skulls. Simulations were performed using registered CT scans and a source term determined by acoustic holography. Mean errors below 14% were found between simulated pressure fields and corresponding measurements. Intracranial peak pressures were systematically underestimated and reflections from the contralateral bone were overestimated. Determination of the acoustic impedance of the bone from the CT images was the likely source of error. High correlation between predictions and measurements (R2 = 0.93 and R2 = 0.88 for transmitted and reflected waves amplitude, respectively) demonstrated that this model is suitable for a quantitative estimation of acoustic fields generated during 40-200 kHz ultrasound-enhanced ischemic stroke treatment.

  4. Finite-Difference Modeling of Acoustic and Gravity Wave Propagation in Mars Atmosphere: Application to Infrasounds Emitted by Meteor Impacts (United States)

    Garcia, Raphael F.; Brissaud, Quentin; Rolland, Lucie; Martin, Roland; Komatitsch, Dimitri; Spiga, Aymeric; Lognonné, Philippe; Banerdt, Bruce


    The propagation of acoustic and gravity waves in planetary atmospheres is strongly dependent on both wind conditions and attenuation properties. This study presents a finite-difference modeling tool tailored for acoustic-gravity wave applications that takes into account the effect of background winds, attenuation phenomena (including relaxation effects specific to carbon dioxide atmospheres) and wave amplification by exponential density decrease with height. The simulation tool is implemented in 2D Cartesian coordinates and first validated by comparison with analytical solutions for benchmark problems. It is then applied to surface explosions simulating meteor impacts on Mars in various Martian atmospheric conditions inferred from global climate models. The acoustic wave travel times are validated by comparison with 2D ray tracing in a windy atmosphere. Our simulations predict that acoustic waves generated by impacts can refract back to the surface on wind ducts at high altitude. In addition, due to the strong nighttime near-surface temperature gradient on Mars, the acoustic waves are trapped in a waveguide close to the surface, which allows a night-side detection of impacts at large distances in Mars plains. Such theoretical predictions are directly applicable to future measurements by the INSIGHT NASA Discovery mission.

  5. An efficient hybrid pseudospectral/finite-difference scheme for solving the TTI pure P-wave equation

    KAUST Repository

    Zhan, Ge


    The pure P-wave equation for modelling and migration in tilted transversely isotropic (TTI) media has attracted more and more attention in imaging seismic data with anisotropy. The desirable feature is that it is absolutely free of shear-wave artefacts and the consequent alleviation of numerical instabilities generally suffered by some systems of coupled equations. However, due to several forward-backward Fourier transforms in wavefield updating at each time step, the computational cost is significant, and thereby hampers its prevalence. We propose to use a hybrid pseudospectral (PS) and finite-difference (FD) scheme to solve the pure P-wave equation. In the hybrid solution, most of the cost-consuming wavenumber terms in the equation are replaced by inexpensive FD operators, which in turn accelerates the computation and reduces the computational cost. To demonstrate the benefit in cost saving of the new scheme, 2D and 3D reverse-time migration (RTM) examples using the hybrid solution to the pure P-wave equation are carried out, and respective runtimes are listed and compared. Numerical results show that the hybrid strategy demands less computation time and is faster than using the PS method alone. Furthermore, this new TTI RTM algorithm with the hybrid method is computationally less expensive than that with the FD solution to conventional TTI coupled equations. © 2013 Sinopec Geophysical Research Institute.

  6. Finite Difference Energy Method for nonlinear numerical analysis of reinforced concrete slab using simplified isotropic damage model

    Directory of Open Access Journals (Sweden)

    M. V. A. Lima

    Full Text Available This work presents a model to predict the flexural behavior of reinforced concrete slabs, combining the Mazars damage model for simulation of the loss of stiffness of the concrete during the cracking process and the Classical Theory of Laminates, to govern the bending of the structural element. A variational formulation based on the principle of virtual work was developed for the model, and then treated numerically according to the Finite Difference Energy Method, with the end result a program developed in Fortran. To validate the model thus proposed have been simulated with the program, some cases of slabs in flexure in the literature. The evaluation of the results obtained in this study demonstrated the capability of the model, in view of the good predictability of the behavior of slabs in flexure, sweeping the path of equilibrium to the rupture of the structural element. Besides the satisfactory prediction of the behavior observed as positive aspects of the model to its relative simplicity and reduced number of experimental parameters necessary for modeling.

  7. Evaluation of Forces Generated on Three Different Rotary File Systems in Apical Third of Root Canal using Finite Element Analysis. (United States)

    Medha, Ashish; Patil, Suvarna; Hoshing, Upendra; Bandekar, Siddhesh


    AIM of the study is to evaluate the distribution of forces on the instrument in the apical 3rd of curved canal with three Nickel Titanium rotary systems. Three brands of instruments (ProTaper Universal; DENTSPLY Maillefer, RevoS; MicroMega and Hyflex; Coltene-Whaledent, Allstetten, Switzerland) were scanned with the Laser assisted computerized scanner to produce a real-size, 3-dimensional (3-D) model for each. The stresses on the instrument during simulated shaping of a root canal were analyzed numerically by using a 3-D finite element package, taking into account the nonlinear mechanical behavior of the nickel-titanium material. RevoS shows lowest values for force generation in the apical 3rd of canal as compared to Protaper which shows highest values, while Hyflex shows intermediate values for forces. With FE simulation of root canal shaping by 3 files, it was observed that different instrument designs would experience unequal degree of force generation in canal, as well as reaction torque from the root canal wall.

  8. Convergence and precision characteristics of finite difference time domain method for the analysis of spectroscopic ellipsometry data at oblique incidence (United States)

    Foo, Yishu; Zapien, Juan Antonio


    The finite difference time domain (FDTD) method presents attractive advantages for analysis of the spectroscopic ellipsometry (SE) response of complex, non-planar samples including generality and suitability to address complex structures as well as non-linear effects and/or non-periodic morphologies. However, it is imperative to advance our understanding, and more importantly, to design strategies to improve the computational time of FDTD method calculations. In a previous report we show the ability to simulate the SE response of prototypical samples based on far-field projections of near-field simulation based on the FDTD method with accuracy equivalent to ∼0.5 monolayer precision in film thickness up to 70° angle of incidence (AoI). In this contribution, we provide a refined strategy that results in ∼3 orders of magnitude improvement in the determination of the SE data as estimated by the χ2 figure of merit for modeling of SE data at angles as large as 80° AoI with respect to the standard solution. Significantly the proposed strategy also provides improvement in the computation time that speeds up by a factor ∼4× at 70° AoI but that can be as large as ∼20× for 40° AoI.

  9. Three-dimensional finite element analysis of zirconia all-ceramic cantilevered fixed partial dentures with different framework designs. (United States)

    Miura, Shoko; Kasahara, Shin; Yamauchi, Shinobu; Egusa, Hiroshi


    The purpose of this study were: to perform stress analyses using three-dimensional finite element analysis methods; to analyze the mechanical stress of different framework designs; and to investigate framework designs that will provide for the long-term stability of both cantilevered fixed partial dentures (FPDs) and abutment teeth. An analysis model was prepared for three units of cantilevered FPDs that assume a missing mandibular first molar. Four types of framework design (Design 1, basic type; Design 2, framework width expanded buccolingually by 2 mm; Design 3, framework height expanded by 0.5 mm to the occlusal surface side from the end abutment to the connector area; and Design 4, a combination of Designs 2 and 3) were created. Two types of framework material (yttrium-oxide partially stabilized zirconia and a high precious noble metal gold alloy) and two types of abutment material (dentin and brass) were used. In the framework designs, Design 1 exhibited the highest maximum principal stress value for both zirconia and gold alloy. In the abutment tooth, Design 3 exhibited the highest maximum principal stress value for all abutment teeth. In the present study, Design 4 (the design with expanded framework height and framework width) could contribute to preventing the concentration of stress and protecting abutment teeth. © 2017 Eur J Oral Sci.

  10. A multithreaded and GPU-optimized compact finite difference algorithm for turbulent mixing at high Schmidt number using petascale computing (United States)

    Clay, M. P.; Yeung, P. K.; Buaria, D.; Gotoh, T.


    Turbulent mixing at high Schmidt number is a multiscale problem which places demanding requirements on direct numerical simulations to resolve fluctuations down the to Batchelor scale. We use a dual-grid, dual-scheme and dual-communicator approach where velocity and scalar fields are computed by separate groups of parallel processes, the latter using a combined compact finite difference (CCD) scheme on finer grid with a static 3-D domain decomposition free of the communication overhead of memory transposes. A high degree of scalability is achieved for a 81923 scalar field at Schmidt number 512 in turbulence with a modest inertial range, by overlapping communication with computation whenever possible. On the Cray XE6 partition of Blue Waters, use of a dedicated thread for communication combined with OpenMP locks and nested parallelism reduces CCD timings by 34% compared to an MPI baseline. The code has been further optimized for the 27-petaflops Cray XK7 machine Titan using GPUs as accelerators with the latest OpenMP 4.5 directives, giving 2.7X speedup compared to CPU-only execution at the largest problem size. Supported by NSF Grant ACI-1036170, the NCSA Blue Waters Project with subaward via UIUC, and a DOE INCITE allocation at ORNL.

  11. Wave-vector and polarization dependent impedance model for a hexagonal periodic metasurface exemplified through finite-difference time-domain simulations. (United States)

    Ding, Yi S; He, Yang


    An isotropic impedance sheet model is proposed for a loop-type hexagonal periodic metasurface. Both frequency and wave-vector dispersion are considered near the resonance frequency. Therefore both the angle and polarization dependences of the metasurface impedance can be properly and simultaneously described in our model. The constitutive relation of this model is transformed into auxiliary differential equations which are integrated into the finite-difference time-domain algorithm. Finally, a finite large metasurface sample under oblique illumination is used to test the model and the algorithm. Our model and algorithm can significantly increase the accuracy of the homogenization methods for modeling periodic metasurfaces.

  12. Low-Frequency Loudspeaker-Room Simulation Using Finite Differences in the Time Domain-Part 1: Analysis

    DEFF Research Database (Denmark)

    Celestinos, Adrian; Nielsen, Sofus Birkedal


    Small- and medium-size rectangular rooms have a strong influence on the low-frequency performance of loudspeakers. A simulation program based on the finite-difference time-domain (FDTD) method is introduced to analyze the sound field produced by loudspeakers in rectangular rooms at low frequencies...

  13. Neurite, a finite difference large scale parallel program for the simulation of electrical signal propagation in neurites under mechanical loading.

    Directory of Open Access Journals (Sweden)

    Julián A García-Grajales

    Full Text Available With the growing body of research on traumatic brain injury and spinal cord injury, computational neuroscience has recently focused its modeling efforts on neuronal functional deficits following mechanical loading. However, in most of these efforts, cell damage is generally only characterized by purely mechanistic criteria, functions of quantities such as stress, strain or their corresponding rates. The modeling of functional deficits in neurites as a consequence of macroscopic mechanical insults has been rarely explored. In particular, a quantitative mechanically based model of electrophysiological impairment in neuronal cells, Neurite, has only very recently been proposed. In this paper, we present the implementation details of this model: a finite difference parallel program for simulating electrical signal propagation along neurites under mechanical loading. Following the application of a macroscopic strain at a given strain rate produced by a mechanical insult, Neurite is able to simulate the resulting neuronal electrical signal propagation, and thus the corresponding functional deficits. The simulation of the coupled mechanical and electrophysiological behaviors requires computational expensive calculations that increase in complexity as the network of the simulated cells grows. The solvers implemented in Neurite--explicit and implicit--were therefore parallelized using graphics processing units in order to reduce the burden of the simulation costs of large scale scenarios. Cable Theory and Hodgkin-Huxley models were implemented to account for the electrophysiological passive and active regions of a neurite, respectively, whereas a coupled mechanical model accounting for the neurite mechanical behavior within its surrounding medium was adopted as a link between electrophysiology and mechanics. This paper provides the details of the parallel implementation of Neurite, along with three different application examples: a long myelinated axon

  14. Influence of different post design and composition on stress distribution in maxillary central incisor: Finite element analysis

    Directory of Open Access Journals (Sweden)

    Silva Natercia


    Full Text Available Background: Post design and material has very important effects on dentinal stress distribution since the post placement can create stresses that lead to root fracture. Materials and Methods: In this study we use finite element analysis (FEA to evaluate stress distribution on endodontically treated maxillary central incisors that have been restored with different prefabricated posts. Six models were generated from the image of anatomical plate: Four metallic posts (ParaPost XH, ParaPost XT, ParaPost XP, and Flexi-Flange and one fiberglass post (ParaPost Fiber Lux. The sixth model was a control-a sound maxillary central incisor. We used CAD software and exported the models to ANSYS 9.0. All the materials and structures were considered elastic, isotropic, homogeneous, and linear except the fiberglass post which was considered orthotropic. The values for the mechanical properties were obtained by a review of the literature and the model was meshed with 8-node tetrahedral elements. A load of 2N was applied to the lingual surface at an angle of 135°. Results: The stress results were recorded by shear stress and von Mises criteria; it was observed that there was no difference for stress distribution among the titanium posts in the radicular portions and into posts. There was higher stress concentration on the coronary portion with the titanium posts than with the glass fiber post. It seems that the metallic posts′ external configuration does not influence the stress distribution. Conclusion: Fiber posts show more homogeneous stress distribution than metallic posts. The post material seems to be more relevant for the stress distribution in endodontically treated teeth than the posts′ external configuration.

  15. Finite Boltzmann schemes

    NARCIS (Netherlands)

    Sman, van der R.G.M.


    In the special case of relaxation parameter = 1 lattice Boltzmann schemes for (convection) diffusion and fluid flow are equivalent to finite difference/volume (FD) schemes, and are thus coined finite Boltzmann (FB) schemes. We show that the equivalence is inherent to the homology of the

  16. A New Accurate Finite-Difference Scheme Based on the Optimally Accurate Operators and Boundary-Condition Consistent Material Parameterization (United States)

    Kristek, J.; Moczo, P.; Galis, M.


    Geller and Takeuchi (1995) developed optimally accurate finite-difference (FD) operators. The operators minimize the error of the numerical solution of the discretized equation of motion. The criterion for obtaining the optimally accurate operators requires that the leading term of the truncation error of the discretized homogeneous (without body-force term) equation of motion (that is if operand is an eigenfunction and frequency is equal to eigenfrequency) is zero. Consequently, the optimally accurate operators satisfy (up to the leading term of the truncation error) homogeneous equation of motion. The grid dispersion of an optimally accurate FD scheme is significantly smaller than that of a standard FD scheme. A heterogeneous FD scheme cannot be anything else than a FD approximation to the heterogeneous formulation of the equation of motion (the same form of the equation for a point away from a material discontinuity and a point at the material discontinuity). If an optimally accurate FD scheme for heterogeneous media is to be obtained, the optimally accurate operators have to be applied to the heterogeneous formulation of the equation of motion. Moczo et al. (2002) found a heterogeneous formulation and developed a FD scheme based on standard staggered-grid 4th-order operators. The scheme is capable to sense both smooth material heterogeneity and material discontinuity at any position in a spatial grid. We present a new FD scheme that combines optimally accurate operators of Geller and Takeuchi (1995) with a material parameterization of Moczo et al. (2002). Models of a single material discontinuity, interior constant-velocity layer, and interior layer with the velocity gradient were calculated with the new scheme, conventional-operator scheme and analytically. Numerical results clearly isolate and demonstrate effects of the boundary and grid dispersion. The results demonstrate significant accuracy improvement compared to previous FD schemes.

  17. Three Dimensional Finite Element Analysis of Distal Abutment Stresses of Removable Partial Dentures with Different Retainer Designs

    Directory of Open Access Journals (Sweden)

    Simindokht Zarrati


    Full Text Available Objectives: This finite element method study aimed to compare the amount of stress on an isolated mandibular second premolar in two conventional reciprocal parallel interface designs of removable partial dentures (RPDs and the same RPD abutment tooth (not isolated.Materials and Methods: A Kennedy Class 1, modification 1 RPD framework was simulated on a 3D model of mandible with three different designs: an isolated tooth with a mesial rest, an isolated tooth with mesial and distal rests and an abutment with a mesial rest (which was not isolated; 26 N occlusal forces were exerted bilaterally on the first molar sites. Stress on the abutment teeth was analyzed using Cosmos Works 2009 Software.Results: In all designs, the abutment tooth stress concentration was located in the buccal alveolar crest. In the first model, the von Mises stress distribution in the contact area of I-bar clasp and cervical portion of the tooth was 19 MPa and the maximum stress was 30 MPa. In the second model, the maximum von Mises stress distribution was 15 MPa in the cervical of the tooth. In the third model, the maximum von Mises stress was located in the cervical of the tooth and the distal proximal plate.Conclusion: We recommend using both mesial and distal rests on the distal abutment teeth of distal extension RPDs. The abutment of an extension base RPD, which is not isolated in presence of its neighboring more anterior tooth, may have a better biomechanical prognosis.      

  18. Stress distribution in delayed replanted teeth splinted with different orthodontic wires: a three-dimensional finite element analysis. (United States)

    de Souza, Fernando Isquierdo; Poi, Wilson Roberto; da Silva, Vanessa Ferreira; Martini, Ana Paula; Melo, Regis Alexandre da Cunha; Panzarini, Sonia Regina; Rocha, Eduardo Passos


    The aim was to evaluate the biomechanical behavior of the supporting bony structures of replanted teeth and the periodontal ligament (PDL) of adjacent teeth when orthodontic wires with different mechanical properties are applied, with three-dimensional finite element analysis. Based on tomographic and microtomographic data, a three-dimensional model of the anterior maxilla with the corresponding teeth (tooth 13-tooth 23) was generated to simulate avulsion and replantation of the tooth 21. The teeth were splinted with orthodontic wire (Ø 0.8 mm) and composite resin. The elastic modulus of the three orthodontic wires used, that is, steel wire (FA), titanium-molybdenum wire (FTM), and nitinol wire (FN) were 200 GPa, 84 GPa, and 52 GPa, respectively. An oblique load (100 N) was applied at an angle of 45° on the incisal edge of the replanted tooth and was analyzed using Ansys Workbench software. The maximum (σmax) and minimum (σmin) principal stresses generated in the PDL, cortical and alveolar bones, and the modified von Mises (σvM) values for the orthodontic wires were obtained. With regard to the cortical bone and PDL, the highest σmin and σmax values for FTM, FN, and FA were checked. With regard to the alveolar bone, σmax and σmin values were highest for FA, followed by FTM and FN. The σvM values of the orthodontic wires followed the order of rigidity of the alloys, that is, FA > FTM > FN. The biomechanical behavior of the analyzed structures with regard to all the three patterns of flexibility was similar. © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

  19. Finite Element Analysis of Implant-Assisted Removable Partial Denture Attachment with Different Matrix Designs During Bilateral Loading. (United States)

    Shahmiri, Reza; Das, Raj


    The aim of this study was to investigate the effect of different matrix designs on resilient attachment on an implant-assisted removable partial denture (IARPD) using finite element analysis (FEA). A laser scanner was used to extract the geometrical data of a human partially edentulous mandible. A 12-mm-long and 4.8-mm-diameter-wide implant was modeled, and two types of intradental attachment of snap fastener principle (elliptical) and resilient attachment (titanium) matrices were modeled along with tooth roots and periodontal ligaments. The modeling was performed with a combination of reverse engineering and solid modeling. The model incorporated a removable partial denture and was loaded with realistic bilateral forces. The FEA was used to analyze the stress and strain distributions in the IARPD and in the metal framework. Stresses and deformations in the metal framework and resin denture base surfaces were analyzed for the elliptical and titanium matrix designs. The maximum von Mises stresses were 605.85 and 614.96 MPa in the metal framework surface and 10.35 and 10.63 MPa in the resin denture base surface, respectively, for the elliptical and titanium matrix designs. The maximum deformations (displacements) were 418.5 and 428.3 μm in the metal framework surface for the elliptical and titanium matrix designs, respectively. The corresponding values of displacements for the resin denture base surface were 325.52 and 249.22 μm for the elliptical and titanium matrix designs, respectively. The maximum displacements in the matrixes were, however, nearly the same (229.51 and 229.47 μm) for both the elliptical and titanium matrixes. The titanium matrix design was a more favorable design compared with the elliptical design, because it had lower lateral deformation as indicated by the maximum displacement.

  20. Extracting Transient Strain from GPS: A Novel Application of the Radial Basis Function-Finite Difference Method (United States)

    Hines, T.; Hetland, E.


    We present a novel, statistically rigorous method for smoothing and differentiating GPS data in both space and time. This method illuminates spatial and temporal variations of fundamentally important quantities such as strain rate, and results in high fidelity images of both tectonic and non-tectonic signals in GPS data. The main difficulty in spatially smoothing GPS data is that the data is not observed on a regular grid, which prevents the use of most of the well known filtering techniques. Our method is based on the recently developed radial basis function-finite difference (RBF-FD) method, which is designed for differentiating data at scattered observation points. We demonstrate that the RBF-FD method can also be effectively used to smooth scattered data, including data from both dense continuous GPS networks and sparser, semi-continuous networks. Existing methods which have been used to smooth GPS data involve least squares fitting of an interpolant to the observed displacement field. Our method has three distinguishing features which set it apart from previous strategies. 1) We use a prior assumption that the deformation is locally smooth, and so we can still smooth a displacement field containing known discontinuities from, for example, a creeping fault. 2) Our method is mathematically equivalent to a low-pass filter which has a well defined, user specified cutoff frequency. 3) The system of equations being solved in our method is sparse and well conditioned, making it possible to spatially and temporally smooth decades of GPS data from hundreds of stations. We present the results of our method for several real world cases, which include an unprecedented view of transient deformation in the Cascadia subduction zone.

  1. Understanding anisotropic mechanical properties of shales at different length scales: In situ micropillar compression combined with finite element calculations (United States)

    Keller, Lukas M.; Schwiedrzik, Jakob J.; Gasser, Philippe; Michler, Johann


    From microstructural observations and experimental work it is known that shales consist of a mechanically weak porous fine-grained clay matrix with embedded and mechanically strong silt/sand grains. Thereby, the respective contents of weak and strong constituents control bulk mechanical properties. In addition, the clay matrix is characterized by a preferred orientation of clay platelets, which are a major control on the bulk anisotropy of shales. To date, little is known about the micromechanical properties of the fine-grained porous clay matrix, which is particularly true in case of its micromechanical anisotropy. Such information can, however, only be assessed on the microscale. Therefore, the drained micromechanical properties parallel and perpendicular to bedding were investigated by means of compressing micropillars with a flat punch indenter in a scanning electron microscope. Microscopic failure mechanism was found to be anisotropic: (i) in case loading was parallel to bedding it occurred by a combination of localized shearing, kinking/buckling of elongated clay aggregates, and bedding parallel splitting and (ii) for loading perpendicular to bedding failure occurred mainly by localized shearing. The measured stiffness of the drained porous clay matrix perpendicular (Ev) and parallel (Eh) to bedding was about 8 GPa and 30 GPa, respectively. Using these stiffness values as input in voxel-based finite element modeling and in combination with realistic microstructures, which are characterized with different contents of "soft" and "hard" constituents, revealed that the measured high microscale anisotropy Eh/Ev = 3.75 is crucial in understanding the bulk anisotropy of clay rocks.

  2. Perfectly matched layer method in the finite-difference time-domain and frequency-domain calculations

    DEFF Research Database (Denmark)

    Shyroki, Dzmitry; Lavrinenko, Andrei


    A complex-coordinate method known under the guise of the perfectly matched layer (PML) method for treating unbounded domains in computational electrodynamics is related to similar techniques in fluid dynamics and classical quantum theory. It may also find use in electronic-structure finite...... within thin layers of space adjacent to the computational domain boundaries, i.e., the PMLs....

  3. Finite element analysis of sagittal balance in different morphotype: Forces and resulting strain in pelvis and spine. (United States)

    Filardi, Vincenzo; Simona, Portaro; Cacciola, Giorgio; Bertino, Salvatore; Soliera, Luigi; Barbanera, Andrea; Pisani, Alessandro; Milardi, Demetrio; Alessia, Bramanti


    In humans, vertical posture acquisition caused several changes in bones and muscles which can be assumed as verticalization. Pelvis, femur, and vertebral column gain an extension position which decreases muscular work by paravertebral muscles in the latter. It's widely known that six different morphological categories exist; each category differs from the others by pelvic parameters and vertebral column curvatures. Both values depend on the Pelvic Incidence, calculated as the angle between the axes passing through the rotation centre of the two femur heads and the vertical axis passing through the superior plate of the sacrum. The aim of this study is to evaluate the distribution of stress and the resulting strain along the axial skeleton using finite element analysis. The use of this computational method allows performing different analyses investigating how different bony geometries and skeletal structures can behavior under specific loading conditions. A computerized tomography (CT) of artificial bones, carried on at 1.5 mm of distance along sagittal, coronal and axial planes with the knee at 0° flexion (accuracy 0.5 mm), was used to obtain geometrical data of the model developed. Lines were imported into a commercial code (Hypermesh by Altair(®)) in order to interpolate main surfaces and create the solid version of the model. In particular six different models were created according Roussoly's classification, by arranging geometrical position of the skeletal components. Loading conditions were obtained by applying muscular forces components to T1 till to L5, according to a reference model (Daniel M. 2011), and a fixed constrain was imposed on the lower part of the femurs. Materials were assumed as elastic with an Elastic modulus of 15 GPa, a Shear Modulus of 7 GPa for bony parts, and an Elastic modulus of 6 MPa, a Shear Modulus of 3 MPa for cartilaginous parts. Six different simulations have been carried out in order to evaluate the mechanical behavior

  4. Explicit Finite-Difference Scheme for the Numerical Solution of the Model Equation of Nonlinear Hereditary Oscillator with Variable-Order Fractional Derivatives

    Directory of Open Access Journals (Sweden)

    Parovik Roman I.


    Full Text Available The paper deals with the model of variable-order nonlinear hereditary oscillator based on a numerical finite-difference scheme. Numerical experiments have been carried out to evaluate the stability and convergence of the difference scheme. It is argued that the approximation, stability and convergence are of the first order, while the scheme is stable and converges to the exact solution.

  5. A new time–space domain high-order finite-difference method for the acoustic wave equation

    KAUST Repository

    Liu, Yang


    A new unified methodology was proposed in Finkelstein and Kastner (2007) [39] to derive spatial finite-difference (FD) coefficients in the joint time-space domain to reduce numerical dispersion. The key idea of this method is that the dispersion relation is completely satisfied at several designated frequencies. We develop this new time-space domain FD method further for 1D, 2D and 3D acoustic wave modeling using a plane wave theory and the Taylor series expansion. New spatial FD coefficients are frequency independent though they lead to a frequency dependent numerical solution. We prove that the modeling accuracy is 2nd-order when the conventional (2 M)th-order space domain FD and the 2nd-order time domain FD stencils are directly used to solve the acoustic wave equation. However, under the same discretization, the new 1D method can reach (2 M)th-order accuracy and is always stable. The 2D method can reach (2 M)th-order accuracy along eight directions and has better stability. Similarly, the 3D method can reach (2 M)th-order accuracy along 48 directions and also has better stability than the conventional FD method. The advantages of the new method are also demonstrated by the results of dispersion analysis and numerical modeling of acoustic wave equation for homogeneous and inhomogeneous acoustic models. In addition, we study the influence of the FD stencil length on numerical modeling for 1D inhomogeneous media, and derive an optimal FD stencil length required to balance the accuracy and efficiency of modeling. A new time-space domain high-order staggered-grid FD method for the 1D acoustic wave equation with variable densities is also developed, which has similar advantages demonstrated by dispersion analysis, stability analysis and modeling experiments. The methodology presented in this paper can be easily extended to solve similar partial difference equations arising in other fields of science and engineering. © 2009 Elsevier Inc.

  6. Biomechanical investigation of thoracolumbar spine in different postures during ejection using a combined finite element and multi-body approach. (United States)

    Du, Chengfei; Mo, Zhongjun; Tian, Shan; Wang, Lizhen; Fan, Jie; Liu, Songyang; Fan, Yubo


    The aim of this study is to investigate the dynamic response of a multi-segment model of the thoracolumbar spine and determine how the sitting posture affects the response under the impact of ejection. A nonlinear finite element model of the thoracolumbar-pelvis complex (T9-S1) was developed and validated. A multi-body dynamic model of a pilot was also constructed so an ejection seat restraint system could be incorporated into the finite element model. The distribution of trunk mass on each vertebra was also considered in the model. Dynamics analysis showed that ejection impact induced obvious axial compression and anterior flexion of the spine, which may contribute to spinal injuries. Compared with a normal posture, the relaxed posture led to an increase in stress on the cortical wall, endplate, and intradiscal pressure of 43%, 10%, 13%, respectively, and accordingly increased the risk of inducing spinal injuries. Copyright © 2014 John Wiley & Sons, Ltd.

  7. Effect of Augmentation Material Stiffness on Adjacent Vertebrae after Osteoporotic Vertebroplasty Using Finite Element Analysis with Different Loading Methods. (United States)

    Cho, Ah-Reum; Cho, Sang-Bong; Lee, Jae-Ho; Kim, Kyung-Hoon


    Vertebroplasty is an effective treatment for osteoporotic vertebral fractures, which are one of the most common fractures associated with osteoporosis. However, clinical observation has shown that the risk of adjacent vertebral body fractures may increase after vertebroplasty. The mechanism underlying adjacent vertebral body fracture after vertebroplasty is not clear; excessive stiffness resulting from polymethyl methacrylate has been suspected as an important mechanism. The aim of our study was to compare the effects of bone cement stiffness on adjacent vertebrae after osteoporotic vertebroplasty under load-controlled versus displacement-controlled conditions. An experimental computer study using a finite element analysis. Medical research institute, university hospital, Korean. A three-dimensional digital anatomic model of L1/2 bone structure was reconstructed from human computed tomographic images. The reconstructed three-dimensional geometry was processed for finite element analysis such as meshing elements and applying material properties. Two boundary conditions, load-controlled and displacement-controlled methods, were applied to each of 5 deformation modes: compression, flexion, extension, lateral bending, and torsion. The adjacent L1 vertebra, irrespective of augmentation, revealed nearly similar maximum von Mises stresses under the load-controlled condition. However, for the displacement-controlled condition, the maximum von Mises stresses in the cortical bone and inferior endplate of the adjacent L1 vertebra increased significantly after cement augmentation. This increase was more significant than that with stiffer bone cement under all modes, except the torsion mode. The finite element model was simplified, excluding muscular forces and incorporating a large volume of bone cement, to more clearly demonstrate effects of bone cement stiffness on adjacent vertebrae after vertebroplasty. Excessive stiffness of augmented bone cement increases the risk of

  8. Different Modelling Approaches to Coupling Wall and Floor Panels within a Dynamic Finite Element Model of a Lightweight Building

    DEFF Research Database (Denmark)

    Kiel, Nikolaj; Andersen, Lars Vabbersgaard; Niu, Bin


    As a result of the increasing interest of constructing environmentally friendly lightweight buildings, analyses of vibrational and acoustical transmission in these buildings have become increasingly important. Structures where vibrational transmission may result in undesirable vibrations with pos......As a result of the increasing interest of constructing environmentally friendly lightweight buildings, analyses of vibrational and acoustical transmission in these buildings have become increasingly important. Structures where vibrational transmission may result in undesirable vibrations...... with possible sound emission as a consequence, must be avoided. A parametric modular finite element model has been developed for this purpose as described in a companion paper presented at this conference. In [1]. This model is intended as a basis for vibro-acoustic analysis of lightweight buildings......, with as many applications as possible, for the least possible computational cost. The coupling method of the structural panels in the above mentioned modular finite element model is in this paper discussed and evaluated. The coupling of the panels are performed using the commercial finite element program...

  9. Energies and wave functions of an off-centre donor in hemispherical quantum dot: Two-dimensional finite difference approach and ritz variational principle

    Energy Technology Data Exchange (ETDEWEB)

    Nakra Mohajer, Soukaina; El Harouny, El Hassan [Laboratoire de Physique de la Matière Condensée, Département de Physique, Faculté des Sciences, Université Abdelmalek Essaadi, B.P. 2121 M’Hannech II, 93030 Tétouan (Morocco); Ibral, Asmaa [Equipe d’Optique et Electronique du Solide, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida Principale, El Jadida (Morocco); Laboratoire d’Instrumentation, Mesure et Contrôle, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida Principale, El Jadida (Morocco); El Khamkhami, Jamal [Laboratoire de Physique de la Matière Condensée, Département de Physique, Faculté des Sciences, Université Abdelmalek Essaadi, B.P. 2121 M’Hannech II, 93030 Tétouan (Morocco); and others


    Eigenvalues equation solutions of a hydrogen-like donor impurity, confined in a hemispherical quantum dot deposited on a wetting layer and capped by an insulating matrix, are determined in the framework of the effective mass approximation. Conduction band alignments at interfaces between quantum dot and surrounding materials are described by infinite height barriers. Ground and excited states energies and wave functions are determined analytically and via one-dimensional finite difference approach in case of an on-center donor. Donor impurity is then moved from center to pole of hemispherical quantum dot and eigenvalues equation is solved via Ritz variational principle, using a trial wave function where Coulomb attraction between electron and ionized donor is taken into account, and by two-dimensional finite difference approach. Numerical codes developed enable access to variations of donor total energy, binding energy, Coulomb correlation parameter, spatial extension and radial probability density with respect to hemisphere radius and impurity position inside the quantum dot.

  10. A Finite Difference Scheme for Double-Diffusive Unsteady Free Convection from a Curved Surface to a Saturated Porous Medium with a Non-Newtonian Fluid

    KAUST Repository

    El-Amin, Mohamed


    In this paper, a finite difference scheme is developed to solve the unsteady problem of combined heat and mass transfer from an isothermal curved surface to a porous medium saturated by a non-Newtonian fluid. The curved surface is kept at constant temperature and the power-law model is used to model the non-Newtonian fluid. The explicit finite difference method is used to solve simultaneously the equations of momentum, energy and concentration. The consistency of the explicit scheme is examined and the stability conditions are determined for each equation. Boundary layer and Boussinesq approximations have been incorporated. Numerical calculations are carried out for the various parameters entering into the problem. Velocity, temperature and concentration profiles are shown graphically. It is found that as time approaches infinity, the values of wall shear, heat transfer coefficient and concentration gradient at the wall, which are entered in tables, approach the steady state values.

  11. Finite-difference time-domain modeling of infrasound from pulsating auroras and comparison with recent experiments (United States)

    de Larquier, S.; Pasko, V. P.; Stenbaek-Nielsen, H. C.; Wilson, C. R.; Olson, J. V.


    Atmospheric infrasonic waves are acoustic waves with frequencies ranging from 0.02 to 10 Hz, slightly higher than the acoustic cut-off frequency (approximately 0.032 Hz), but lower than the audible frequencies (typically 20 Hz-15 kHz) [e.g., Blanc, Ann. Geophys., 3, 673, 1985]. A number of natural events have been identified as generating atmospheric infrasound, such as volcanoes, tornadoes, avalanches, earthquakes [e.g., Bedard and Georges, Physics Today, S3, 32, 2000], ocean surfaces [e.g., Gossard and Hooke, Waves in the Atmosphere, Elsevier, 1975, Ch. 9], lightning [e.g., Assink et al., GRL, 35, L15802, 2008; Pasko, JGR, 114, D08205, 2009], or transient luminous events in the middle atmosphere termed sprites [e.g., Farges, Lightning: Principles, Instruments and Applications, H.D. Betz et al. (eds), Springer, 2009, Ch. 18]. The importance of infrasound studies has been emphasized in the past ten years from the Comprehensive Nuclear-Test-Ban Treaty verification perspective [e.g., Le Pichon et al., JGR, 114, D08112, 2009]. A proper understanding of infrasound propagation in the atmosphere is required for identification and classification of different infrasonic waves and their sources [Drob et al., JGR, 108, D21, 4680, 2003]. The goal of the present work is to provide a quantitative interpretation and explanation of infrasonic signatures from pulsating auroras reported recently by Wilson et al. [GRL, 32, L14810, 2005]. The infrasound signals observed with an infrasonic array at Fairbanks, Alaska had a mean amplitude of 0.05 Pa, a delay of about 5 minutes from the pulsating aurora, and an almost normal incidence on the ground plane [Wilson et al., 2005]. We employ a finite-difference time-domain (FDTD) model of infrasound propagation in a realistic atmosphere. We use the absorption model of infrasound introduced by Sutherland and Bass [J. Acoust. Soc. Am., 115, 1012, 2004]. Classical absorption mechanisms as well as molecular relaxation mechanisms are taken into

  12. Three-dimensional modeling in the electromagnetic/magnetotelluric methods. Accuracy of various finite-element and finite difference methods; Denjiho MT ho ni okeru sanjigen modeling. Shushu no yugen yosoho to sabunho no seido

    Energy Technology Data Exchange (ETDEWEB)

    Sasaki, Y. [Kyushu University, Fukuoka (Japan). Faculty of Engineering


    To enhance the reliability of electromagnetic/magnetotelluric (MT) survey, calculation results of finite-element methods (FEMs) and finite difference methods (FDMs) were compared. Accuracy of individual methods and convergence of repitition solution were examined. As a result of the investigation, it was found that appropriate accuracy can be obtained from the edge FEM and FDM for the example of vertical magnetic dipole, and that the best accuracy can be obtained from the FDM among four methods for the example of MT survey. It was revealed that the ICBCG (incomplete Cholesky bi-conjugate gradient) method is an excellent method as a solution method of simultaneous equations from the viewpoint of accuracy and calculation time. For the joint FEM, solutions of SOR method converged for both the examples. It was concluded that the cause of error is not due to the error of numerical calculation, but due to the consideration without discontinuity of electric field. The conditions of coefficient matrix increased with decreasing the frequency, which resulted in the unstable numerical calculation. It would be required to incorporate the constraint in a certain form. 4 refs., 12 figs.

  13. Mass conservative and energy stable finite difference methods for the quasi-incompressible Navier-Stokes-Cahn-Hilliard system: Primitive variable and projection-type schemes (United States)

    Guo, Z.; Lin, P.; Lowengrub, J.; Wise, S. M.


    In this paper we describe two fully mass conservative, energy stable, finite difference methods on a staggered grid for the quasi-incompressible Navier-Stokes-Cahn-Hilliard (q-NSCH) system governing a binary incompressible fluid flow with variable density and viscosity. Both methods, namely the primitive method (finite difference method in the primitive variable formulation) and the projection method (finite difference method in a projection-type formulation), are so designed that the mass of the binary fluid is preserved, and the energy of the system equations is always non-increasing in time at the fully discrete level. We also present an efficient, practical nonlinear multigrid method - comprised of a standard FAS method for the Cahn-Hilliard equation, and a method based on the Vanka-type smoothing strategy for the Navier-Stokes equation - for solving these equations. We test the scheme in the context of Capillary Waves, rising droplets and Rayleigh-Taylor instability. Quantitative comparisons are made with existing analytical solutions or previous numerical results that validate the accuracy of our numerical schemes. Moreover, in all cases, mass of the single component and the binary fluid was conserved up to 10 to -8 and energy decreases in time.

  14. Finite elements and approximation

    CERN Document Server

    Zienkiewicz, O C


    A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o

  15. Hybrid LBM-MRT model coupled with finite difference method for double-diffusive mixed convection in rectangular enclosure with insulated moving lid (United States)

    Bettaibi, Soufiene; Kuznik, Frédéric; Sediki, Ezeddine


    This paper presents a numerical study of thermosolutal mixed convection in rectangular enclosure with sliding top lid. The fluid flow is solved by the multiple relaxation time (MRT) lattice Boltzmann method (LBM), whereas the temperature and concentration fields are computed by finite difference method (FDM). The main objective of this study is to investigate the accuracy and the effectiveness of such model to predict thermodynamics for heat and mass transfer in a driven cavity. This model is validated with different numerical methods in the current literature. A good agreement is obtained between our results and previous works. The different comparisons demonstrate the robustness and the accuracy of the proposed approach.

  16. Comparative study on triangular and quadrilateral meshes by a finite-volume method with a central difference scheme

    KAUST Repository

    Yu, Guojun


    In this article, comparative studies on computational accuracies and convergence rates of triangular and quadrilateral meshes are carried out in the frame work of the finite-volume method. By theoretical analysis, we conclude that the number of triangular cells needs to be 4/3 times that of quadrilateral cells to obtain similar accuracy. The conclusion is verified by a number of numerical examples. In addition, the convergence rates of the triangular meshes are found to be slower than those of the quadrilateral meshes when the same accuracy is obtained with these two mesh types. © 2012 Taylor and Francis Group, LLC.

  17. Aspects of numerical and representational methods related to the finite-difference simulation of advective and dispersive transport of freshwater in a thin brackish aquifer (United States)

    Merritt, M.L.


    The simulation of the transport of injected freshwater in a thin brackish aquifer, overlain and underlain by confining layers containing more saline water, is shown to be influenced by the choice of the finite-difference approximation method, the algorithm for representing vertical advective and dispersive fluxes, and the values assigned to parametric coefficients that specify the degree of vertical dispersion and molecular diffusion that occurs. Computed potable water recovery efficiencies will differ depending upon the choice of algorithm and approximation method, as will dispersion coefficients estimated based on the calibration of simulations to match measured data. A comparison of centered and backward finite-difference approximation methods shows that substantially different transition zones between injected and native waters are depicted by the different methods, and computed recovery efficiencies vary greatly. Standard and experimental algorithms and a variety of values for molecular diffusivity, transverse dispersivity, and vertical scaling factor were compared in simulations of freshwater storage in a thin brackish aquifer. Computed recovery efficiencies vary considerably, and appreciable differences are observed in the distribution of injected freshwater in the various cases tested. The results demonstrate both a qualitatively different description of transport using the experimental algorithms and the interrelated influences of molecular diffusion and transverse dispersion on simulated recovery efficiency. When simulating natural aquifer flow in cross-section, flushing of the aquifer occurred for all tested coefficient choices using both standard and experimental algorithms. ?? 1993.

  18. A Cell-Centered Multiphase ALE Scheme With Structural Coupling

    Energy Technology Data Exchange (ETDEWEB)

    Dunn, Timothy Alan [Univ. of California, Davis, CA (United States)


    A novel computational scheme has been developed for simulating compressible multiphase flows interacting with solid structures. The multiphase fluid is computed using a Godunov-type finite-volume method. This has been extended to allow computations on moving meshes using a direct arbitrary-Eulerian- Lagrangian (ALE) scheme. The method has been implemented within a Lagrangian hydrocode, which allows modeling the interaction with Lagrangian structural regions. Although the above scheme is general enough for use on many applications, the ultimate goal of the research is the simulation of heterogeneous energetic material, such as explosives or propellants. The method is powerful enough for application to all stages of the problem, including the initial burning of the material, the propagation of blast waves, and interaction with surrounding structures. The method has been tested on a number of canonical multiphase tests as well as fluid-structure interaction problems.

  19. Finite superstrings

    CERN Document Server

    Restuccia, A; Taylor, J G


    This is the first complete account of the construction and finiteness analysis of multi-loop scattering amplitudes for superstrings, and of the guarantee that for certain superstrings (in particular the heterotic one), the symmetries of the theory in the embedding space-time are those of the super-poincaré group SP10 and that the multi-loop amplitudes are each finite. The book attempts to be self-contained in its analysis, although it draws on the works of many researchers. It also presents the first complete field theory for such superstrings. As such it demonstrates that gravity can be quant

  20. Do High Consumers of Sugar-Sweetened Beverages Respond Differently to Price Changes? A Finite Mixture IV-Tobit Approach. (United States)

    Etilé, Fabrice; Sharma, Anurag


    This study compares the impact of sugar-sweetened beverages (SSBs) tax between moderate and high consumers in Australia. The key methodological contribution is that price response heterogeneity is identified while controlling for censoring of consumption at zero and endogeneity of expenditure by using a finite mixture instrumental variable Tobit model. The SSB price elasticity estimates show a decreasing trend across increasing consumption quantiles, from -2.3 at the median to -0.2 at the 95th quantile. Although high consumers of SSBs have a less elastic demand for SSBs, their very high consumption levels imply that a tax would achieve higher reduction in consumption and higher health gains. Our results also suggest that an SSB tax would represent a small fiscal burden for consumers whatever their pre-policy level of consumption, and that an excise tax should be preferred to an ad valorem tax. Copyright © 2015 John Wiley & Sons, Ltd.

  1. A finite element analysis of two different dental implants: stress distribution in the prosthesis, abutment, implant, and supporting bone. (United States)

    Quaresma, Sergio E T; Cury, Patricia R; Sendyk, Wilson R; Sendyk, Claudio


    This study evaluates the influence of 2 commercially available dental implant systems on stress distribution in the prosthesis, abutment, implant, and supporting alveolar bone under simulated occlusal forces, employing a finite element analysis. The implants and abutments evaluated consisted of a stepped cylinder implant connected to a screw-retained, internal, hexagonal abutment (system 1) and a conical implant connected to a solid, internal, conical abutment (system 2). A porcelain-covered, silver-palladium alloy was used as a crown. In each case, a simulated, 100-N vertical load was applied to the buccal cusp. A finite element model was created based on the physical properties of each component, and the values of the von Mises stresses generated in the prosthesis, abutment, implant, and supporting alveolar bone were calculated. In the prostheses, the maximum von Mises stresses were concentrated at the points of load application in both systems, and they were greater in system 1 (148 N/mm2) than in system 2 (55 N/mm2). Stress was greater on the abutment of system 2 than of system 1 on both the buccal (342 N/mm2 x 294 N/mm2) and lingual (294 N/mm2 x 148 N/ mm2) faces. Stress in the cortical, alveolar bone crest was greater in system 1 than in system 2 (buccal: 99.5 N/mm2 x 55 N/mm2, lingual: 55 N/mm2 x 24.5 N/mm2, respectively). Within the limits of this investigation, the stepped cylinder implant connected to a screw-retained, internal hexagonal abutment produces greater stresses on the alveolar bone and prosthesis and lower stresses on the abutment complex. In contrast, the conical implant connected to a solid, internal, conical abutment furnishes lower stresses on the alveolar bone and prosthesis and greater stresses on the abutment.

  2. Determination of excited states of quantum systems by finite difference time domain method (FDTD) with supersymmetric quantum mechanics (SUSY-QM)

    Energy Technology Data Exchange (ETDEWEB)

    Sudiarta, I. Wayan; Angraini, Lily Maysari, E-mail: [Physics Study Program, University of Mataram, Jln. Majapahit 62 Mataram, NTB (Indonesia)


    We have applied the finite difference time domain (FDTD) method with the supersymmetric quantum mechanics (SUSY-QM) procedure to determine excited energies of one dimensional quantum systems. The theoretical basis of FDTD, SUSY-QM, a numerical algorithm and an illustrative example for a particle in a one dimensional square-well potential were given in this paper. It was shown that the numerical results were in excellent agreement with theoretical results. Numerical errors produced by the SUSY-QM procedure was due to errors in estimations of superpotentials and supersymmetric partner potentials.

  3. Evaluation and Modeling of the Variation of Electromagnetic Field on the Cross Section of a Transmission Line Using Finite Difference Method

    Directory of Open Access Journals (Sweden)

    Jorge I. Silva O.


    Full Text Available This paper present a purpose to characterize power lines in order to identify level of operation since the power grid planning. In order to model a power line was required the use of computational tools to generate a mathematical model in MATLAB, which was based on the finite difference method and represent the electromagnetic field (EMF contribution. The results were contrasted with real and measured values taken from a cross section of a power line that was previously modeled. Statistical analysis showed an accurate estimation of the electric and magnetic field emitted by the line identifying the same shape of the plotted curve and values in an acceptable range.


    Directory of Open Access Journals (Sweden)



    Full Text Available Nonlinear finite element (FE models are prepared to investigate the behaviour of concrete-filled steel tube (CFST beams strengthened by carbon fibre reinforced polymer (CFRP sheets. The beams are strengthened from the bottom side only by varied sheet lengths (full and partial beam lengths and then subjected to ultimate flexural loads. Three surface interaction techniques are used to implement the bonding behaviour between the steel tube and the CFRP sheet, namely, full tie interaction (TI, cohesive element (CE and cohesive behaviour (CB techniques using ABAQUS software. Results of the comparison between the FE analysis and existing experimental study confirm that the FE models with the TI technique could be applicable for beams strengthened by CFRP sheets with a full wrapping length; the technique could not accurately implement the CFRP delamination failure, which occurred for beams with a partial wrapping length. Meanwhile, the FE models with the CE and CB techniques are applicable in the implementation of both CFRP failures (rapture and delamination for both full and partial wrapping lengths, respectively. Where, the ultimate loads' ratios achieved by the FE models using TI, CE and CB techniques about 1.122, 1.047 and 1.045, respectively, comparing to the results of existing experimental tests.

  5. Continuous Modeling Technique of Fiber Pullout from a Cement Matrix with Different Interface Mechanical Properties Using Finite Element Program

    Directory of Open Access Journals (Sweden)

    Leandro Ferreira Friedrich

    Full Text Available Abstract Fiber-matrix interface performance has a great influence on the mechanical properties of fiber reinforced composite. This influence is mainly presented during fiber pullout from the matrix. As fiber pullout process consists of fiber debonding stage and pullout stage which involve complex contact problem, numerical modeling is a best way to investigate the interface influence. Although many numerical research works have been conducted, practical and effective technique suitable for continuous modeling of fiber pullout process is still scarce. The reason is in that numerical divergence frequently happens, leading to the modeling interruption. By interacting the popular finite element program ANSYS with the MATLAB, we proposed continuous modeling technique and realized modeling of fiber pullout from cement matrix with desired interface mechanical performance. For debonding process, we used interface elements with cohesive surface traction and exponential failure behavior. For pullout process, we switched interface elements to spring elements with variable stiffness, which is related to the interface shear stress as a function of the interface slip displacement. For both processes, the results obtained are very good in comparison with other numerical or analytical models and experimental tests. We suggest using the present technique to model toughening achieved by randomly distributed fibers.

  6. The overlapped radial basis function-finite difference (RBF-FD) method: A generalization of RBF-FD (United States)

    Shankar, Varun


    We present a generalization of the RBF-FD method that computes RBF-FD weights in finite-sized neighborhoods around the centers of RBF-FD stencils by introducing an overlap parameter δ ∈ (0 , 1 ] such that δ = 1 recovers the standard RBF-FD method and δ = 0 results in a full decoupling of stencils. We provide experimental evidence to support this generalization, and develop an automatic stabilization procedure based on local Lebesgue functions for the stable selection of stencil weights over a wide range of δ values. We provide an a priori estimate for the speedup of our method over RBF-FD that serves as a good predictor for the true speedup. We apply our method to parabolic partial differential equations with time-dependent inhomogeneous boundary conditions - Neumann in 2D, and Dirichlet in 3D. Our results show that our method can achieve as high as a 60× speedup in 3D over existing RBF-FD methods in the task of forming differentiation matrices.

  7. Two-Dimensional Finite-Difference Modeling of Broadband Regional Wave Propagation Phenomena: Validation of Regional Three-Dimensional Earth Models and Prediction of Anomalous Regional Phases

    Energy Technology Data Exchange (ETDEWEB)

    Goldstein, P; Ryall, F D; Pasyanos, M E; Schultz, C A; Walter, W R


    An important challenge for seismic monitoring of nuclear explosions at low magnitude to verify a nuclear-test-ban treaty is the development of techniques that use regional phases for detection, location, and identification. In order to use such phases, region-specific earth models and tools are needed that accurately predict features such as travel times, amplitudes, and spectral characteristics. In this paper, we present our efforts to use two-dimensional finite-difference modeling to help develop and validate regional earth models for the Middle East and North Africa and to develop predictive algorithms for identifying anomalous regional phases. To help develop and validate a model for the Middle East and North Africa, we compare data and finite-difference simulations for selected regions. We show that the proposed three-dimensional regional model is a significant improvement over standard one-dimensional models by comparing features of broadband data and simulations and differences between observed and predicted features such as narrow-band group velocities. We show how a potential trade-off between source and structure can be avoided by constraining source parameters such as depth, mechanism, and moment/source-time function with independent data. We also present numerous observations of anomalous timing and amplitude of regional phases and show how incorporation of two-dimensional structure can explain many of these observations. Based on these observations, and the predictive capability of our simulations, we develop a simple model that can accurately predict the timing of such phases.

  8. Biomechanics of cervical tooth region and noncarious cervical lesions of different morphology; three-dimensional finite element analysis. (United States)

    Jakupović, Selma; Anić, Ivica; Ajanović, Muhamed; Korać, Samra; Konjhodžić, Alma; Džanković, Aida; Vuković, Amra


    The present study aims to investigate the influence of presence and shape of cervical lesions on biomechanical behavior of mandibular first premolar, subjected to two types of occlusal loading using three-dimensional (3D) finite element method (FEM). 3D models of the mandibular premolar are created from a micro computed tomography X-ray image: model of sound mandibular premolar, model with the wedge-shaped cervical lesion (V lesion), and model with saucer-shaped cervical lesion (U lesion). By FEM, straining of the tooth tissues under functional and nonfunctional occlusal loading of 200 (N) is analyzed. For the analysis, the following software was used: CTAn program 1.10 and ANSYS Workbench (version 14.0). The results are presented in von Mises stress. Values of calculated stress in all tooth structures are higher under nonfunctional occlusal loading, while the functional loading is resulted in homogeneous stress distribution. Nonfunctional load in the cervical area of sound tooth model as well as in the sub-superficial layer of the enamel resulted with a significant stress (over 50 [MPa]). The highest stress concentration on models with lesions is noticed on the apex of the V-shaped lesion, while stress in saucer U lesion is significantly lower and distributed over wider area. The type of the occlusal teeth loading has the biggest influence on cervical stress intensity. Geometric shape of the existing lesion is very important in the distribution of internal stress. Compared to the U-shaped lesions, V-shaped lesions show significantly higher stress concentrations under load. Exposure to stress would lead to its progression.

  9. Application of the finite difference method to model pH and substrate concentration in a double-chamber microbial fuel cell. (United States)

    Zhang, Liwei; Deshusses, Marc


    The purpose of this study was to develop a mathematical model that can describe glucose degradation in a microbial fuel cell (MFC) with the use of finite difference approach. The dynamic model can describe both substrate and pH changes in the anode chamber of a double-chamber MFC. It was developed using finite differences and incorporates basic mass transfer concepts. Model simulation results could fit the experimental data for substrate consumption well, while there was a moderate discrepancy (maximum 0.11 pH unit) between the simulated pH and the experimental data. A parametric sensitivity analysis showed that increases in acetate and propionate consumption rates can cause great decrease in chemical oxygen demand (COD) in the anode chamber, while an increase in glucose consumption rate does not result in significant changes of COD reduction. Therefore, the rate limitation steps of glucose degradation are the oxidations of secondary degradation products of glucose (acetate and propionate). Due to the buffering effect of the nutrient solution, the increases in glucose, acetate and propionate consumption rates did not result in much change on pH of the anode chamber.

  10. On the Derivation of Highest-Order Compact Finite Difference Schemes for the One- and Two-Dimensional Poisson Equation with Dirichlet Boundary Conditions

    KAUST Repository

    Settle, Sean O.


    The primary aim of this paper is to answer the question, What are the highest-order five- or nine-point compact finite difference schemes? To answer this question, we present several simple derivations of finite difference schemes for the one- and two-dimensional Poisson equation on uniform, quasi-uniform, and nonuniform face-to-face hyperrectangular grids and directly prove the existence or nonexistence of their highest-order local accuracies. Our derivations are unique in that we do not make any initial assumptions on stencil symmetries or weights. For the one-dimensional problem, the derivation using the three-point stencil on both uniform and nonuniform grids yields a scheme with arbitrarily high-order local accuracy. However, for the two-dimensional problem, the derivation using the corresponding five-point stencil on uniform and quasi-uniform grids yields a scheme with at most second-order local accuracy, and on nonuniform grids yields at most first-order local accuracy. When expanding the five-point stencil to the nine-point stencil, the derivation using the nine-point stencil on uniform grids yields at most sixth-order local accuracy, but on quasi- and nonuniform grids yields at most fourth- and third-order local accuracy, respectively. © 2013 Society for Industrial and Applied Mathematics.

  11. A finite volume method for fluctuating hydrodynamics of simple fluids (United States)

    Narayanan, Kiran; Samtaney, Ravi; Moran, Brian


    Fluctuating hydrodynamics accounts for stochastic effects that arise at mesoscopic and macroscopic scales. We present a finite volume method for numerical solutions of the fluctuating compressible Navier Stokes equations. Case studies for simple fluids are demonstrated via the use of two different equations of state (EOS) : a perfect gas EOS, and a Lennard-Jones EOS for liquid argon developed by Johnson et al. (Mol. Phys. 1993). We extend the fourth order conservative finite volume scheme originally developed by McCorquodale and Colella (Comm. in App. Math. & Comput. Sci. 2011), to evaluate the deterministic and stochastic fluxes. The expressions for the cell-centered discretizations of the stochastic shear stress and stochastic heat flux are adopted from Espanol, P (Physica A. 1998), where the discretizations were shown to satisfy the fluctuation-dissipation theorem. A third order Runge-Kutta scheme with weights proposed by Delong et al. (Phy. Rev. E. 2013) is used for the numerical time integration. Accuracy of the proposed scheme will be demonstrated. Comparisons of the numerical solution against theory for a perfect gas as well as liquid argon will be presented. Regularizations of the stochastic fluxes in the limit of zero mesh sizes will be discussed. Supported by KAUST Baseline Research Funds.

  12. Stress Distribution on Short Implants at Maxillary Posterior Alveolar Bone Model With Different Bone-to-Implant Contact Ratio: Finite Element Analysis. (United States)

    Yazicioglu, Duygu; Bayram, Burak; Oguz, Yener; Cinar, Duygu; Uckan, Sina


    The aim of this study was to evaluate the stress distribution of the short dental implants and bone-to-implant contact ratios in the posterior maxilla using 3-dimensional (3D) finite element models. Two different 3D maxillary posterior bone segments were modeled. Group 1 was composed of a bone segment consisting of cortical bone and type IV cancellous bone with 100% bone-to-implant contact. Group 2 was composed of a bone segment consisting of cortical bone and type IV cancellous bone including spherical bone design and homogenous tubular hollow spaced structures with 30% spherical porosities and 70% bone-to-implant contact ratio. Four-millimeter-diameter and 5-mm-height dental implants were assumed to be osseointegrated and placed at the center of the segments. Lateral occlusal bite force (300 N) was applied at a 25° inclination to the implants long axis. The maximum von Mises stresses in cortical and cancellous bones and implant-abutment complex were calculated. The von Mises stress values on the implants and the cancellous bone around the implants of the 70% bone-to-implant contact group were almost 3 times higher compared with the values of the 100% bone-to-implant contact group. For clinical reality, use of the 70% model for finite element analysis simulation of the posterior maxilla region better represents real alveolar bone and the increased stress and strain distributions evaluated on the cortical and cancellous bone around the dental implants.

  13. Simulation of airbag impact on eyes with different axial lengths after transsclerally fixated posterior chamber intraocular lens by using finite element analysis

    Directory of Open Access Journals (Sweden)

    Huang J


    Full Text Available Jane Huang,1 Eiichi Uchio,1 Satoru Goto2 1Department of Ophthalmology, Fukuoka University School of Medicine, Fukuoka, 2Nihon ESI KK Technical Division, Tokyo, Japan Purpose: To determine the biomechanical response of an impacting airbag on eyes with different axial lengths with transsclerally fixated posterior chamber intraocular lens (PC IOL.Materials and methods: Simulations in a model human eye were performed with a computer using a finite element analysis program created by Nihon, ESI Group. The airbag was set to be deployed at five different velocities and to impact on eyes with three different axial lengths. These eyes were set to have transsclerally fixated PC IOL by a 10-0 polypropylene possessing a tensile force limit of 0.16 N according to the United States Pharmacopeia XXII.Results: The corneoscleral opening was observed at a speed of 40 m/second or more in all model eyes. Eyes with the longest axial length of 25.85 mm had the greatest extent of deformity at any given impact velocity. The impact force exceeded the tensile force of 10-0 polypropylene at an impact velocity of 60 m/second in all eyes, causing breakage of the suture. Conclusion: Eyes with transsclerally fixated PC IOL could rupture from airbag impact at high velocities. Eyes with long axial lengths experienced a greater deformity upon airbag impact due to a thinner eye wall. Further basic research on the biomechanical response for assessing eye injuries could help in developing a better airbag and in the further understanding of ocular traumas. Keywords: airbag, ocular trauma, computer simulation, transsclerally fixated posterior chamber intraocular lens, finite element analysis

  14. Prediction of low-frequency structure-borne sound in concrete structures using the finite-difference time-domain method. (United States)

    Asakura, T; Ishizuka, T; Miyajima, T; Toyoda, M; Sakamoto, S


    Due to limitations of computers, prediction of structure-borne sound remains difficult for large-scale problems. Herein a prediction method for low-frequency structure-borne sound transmissions on concrete structures using the finite-difference time-domain scheme is proposed. The target structure is modeled as a composition of multiple plate elements to reduce the dimensions of the simulated vibration field from three-dimensional discretization by solid elements to two-dimensional discretization. This scheme reduces both the calculation time and the amount of required memory. To validate the proposed method, the vibration characteristics using the numerical results of the proposed scheme are compared to those measured for a two-level concrete structure. Comparison of the measured and simulated results suggests that the proposed method can be used to simulate real-scale structures.

  15. GPR data modeling by using the Finite Difference Time Domain (FDTD) methods; Modelagem de dados de GPR atraves do metodo FDTD

    Energy Technology Data Exchange (ETDEWEB)

    Dias, Gleide A.N.; Silva, Jadir C.; Rocha, Paula F.; Costa, Jorge L. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Dept. de Geologia]. E-mail:;;;


    Presently the oil industry has shown the importance of defining the structural framework of reservoirs. This study intends to contribute for the solution of this problem, using synthetic models in order to evaluate the electromagnetic signal due to a certain target. Use was made of an algorithm, which is based in the Finite Difference Time Domain Methods (FDTD). The simulated results of this survey found the best parameters for the chosen frequencies. In the present study there were simulated polarization, geometry and constitutive parameters (dielectric permittivity and electric conductivity). The results, using frequencies of 50 and 100 MHz, show clearly the effects of the electromagnetic waves attenuation and their problems related with signal resolution of targets in depth. (author)

  16. Finite-difference time-domain (FDTD) analysis on the interaction between a metal block and a radially polarized focused beam. (United States)

    Kitamura, Kyoko; Sakai, Kyosuke; Noda, Susumu


    Radially polarized focused beams have attracted a great deal of attention because of their unique properties characterized by the longitudinal field. Although this longitudinal field is strongly confined to the beam axis, the energy flow, i.e., the Poynting vector, has null intensity on the axis. Hence, the interaction of the focused beam and matter has thus far been unclear. We analyzed the interactions between the focused beam and a subwavelength metal block placed at the center of the focus using three-dimensional finite-difference time-domain (FDTD) calculation. We found that most of the Poynting energy propagates through to the far-field, and that a strong enhancement of the electric field appeared on the metal surface. This enhancement is attributed to the constructive interference of the symmetric electric field and the coupling to the surface plasmon mode.

  17. COSIM: A Finite-Difference Computer Model to Predict Ternary Concentration Profiles Associated With Oxidation and Interdiffusion of Overlay-Coated Substrates (United States)

    Nesbitt, James A.


    A finite-difference computer program (COSIM) has been written which models the one-dimensional, diffusional transport associated with high-temperature oxidation and interdiffusion of overlay-coated substrates. The program predicts concentration profiles for up to three elements in the coating and substrate after various oxidation exposures. Surface recession due to solute loss is also predicted. Ternary cross terms and concentration-dependent diffusion coefficients are taken into account. The program also incorporates a previously-developed oxide growth and spalling model to simulate either isothermal or cyclic oxidation exposures. In addition to predicting concentration profiles after various oxidation exposures, the program can also be used to predict coating life based on a concentration dependent failure criterion (e.g., surface solute content drops to 2%). The computer code is written in FORTRAN and employs numerous subroutines to make the program flexible and easily modifiable to other coating oxidation problems.

  18. Solving the nonlinear Schrödinger equation using cubic B-spline interpolation and finite difference methods on dual solitons (United States)

    Ahmad, Azhar; Azmi, Amirah; Majid, Ahmad Abd.; Hamid, Nur Nadiah Abd


    In this paper, Nonlinear Schrödinger (NLS) equation with Neumann boundary conditions is solved using cubic B-spline interpolation method (CuBSIM) and finite difference method (FDM). Firstly, FDM is applied on the time discretization and cubic B-spline is utilized as an interpolation function in the space dimension with the help of theta-weighted method. The second approach is based on the FDM applied on the time and space discretization with the help of theta-weighted method. The CuBSIM is shown to be stable by using von Neumann stability analysis. The proposed method is tested on the interaction of the dual solitons of the NLS equation. The accuracy of the numerical results is measured by the Euclidean-norm and infinity-norm. CuBSIM is found to produce more accurate results than the FDM.

  19. Simulation of cylindrical flow to a well using the U.S. Geological Survey Modular Finite-Difference Ground-Water Flow Model (United States)

    Reilly, Thomas E.; Harbaugh, Arlen W.


    Cylindrical (axisymmetric) flow to a well is an important specialized topic of ground-water hydraulics and has been applied by many investigators to determine aquifer properties and determine heads and flows in the vicinity of the well. A recent modification to the U.S. Geological Survey Modular Three-Dimensional Finite-Difference Ground-Water Flow Model provides the opportunity to simulate axisymmetric flow to a well. The theory involves the conceptualization of a system of concentric shells that are capable of reproducing the large variations in gradient in the vicinity of the well by decreasing their area in the direction of the well. The computer program presented serves as a preprocessor to the U.S. Geological Survey model by creating the input data file needed to implement the axisymmetric conceptualization. Data input requirements to this preprocessor are described, and a comparison with a known analytical solution indicates that the model functions appropriately.

  20. Ab initio calculation of the deformation potential and photoelastic coefficients of silicon with a non-uniform finite-difference solver based on the local density approximation (United States)

    Witzens, Jeremy


    The band diagram, deformation potential and photoelastic tensor of silicon are calculated self-consistently under uniaxial and shear strain by solving for the electronic wavefunctions with a finite-difference method. Many-body effects are accounted for by the local density approximation. In order to accommodate the large number of grid points required due to the diverging electrostatic potential near the atomic nuclei in an all-electron calculation, a non-uniform meshing is adopted. Internal displacements are taken into account by adding an additional coordinate transform to the method of Bir and Pikus. Good consistency of the calculated deformation potential and photoelastic coefficients is obtained with prior experimental and theoretical results, validating the numerical methods. Furthermore, it is shown that a slight correction of the multiplicative coefficient of the Xα approximation for conduction bands results in good agreement with experiment for both the direct and indirect bandgaps.

  1. Fatigue surviving, fracture resistance, shear stress and finite element analysis of glass fiber posts with different diameters. (United States)

    Wandscher, Vinícius Felipe; Bergoli, César Dalmolin; de Oliveira, Ariele Freitas; Kaizer, Osvaldo Bazzan; Souto Borges, Alexandre Luiz; Limberguer, Inácio da Fontoura; Valandro, Luiz Felipe


    This study evaluated the shear stress presented in glass fiber posts with parallel fiber (0°) and different coronal diameters under fatigue, fracture resistance and FEA. 160 glass-fiber posts (N=160) with eight different coronal diameters were used (DT=double tapered, number of the post=coronal diameter and W=Wider - fiber post with coronal diameter wider than the conventional): DT1.4; DT1.8W; DT1.6; DT2W; DT1.8; DT2.2W; DT2; DT2.2. Eighty posts were submitted to mechanical cycling (3×10(6) cycles; inclination: 45°; load: 50N; frequency: 4Hz; temperature: 37°C) to assess the surviving under intermittent loading and other eighty posts were submitted to fracture resistance testing (resistance [N] and shear-stress [MPa] values were obtained). The eight posts types were 3D modeled (Rhinoceros 4.0) and the shear-stress (MPa) evaluated using FEA (Ansys 13.0). One-way ANOVA showed statistically differences to fracture resistance (DT2.2W and DT2.2 showed higher values) and shear stress values (DT1.4 showed lower values). Only the DT1.4 fiber posts failed after mechanical cycling. FEA showed similar values of shear stress between the groups and these values were similar to those obtained by shear stress testing. The failure analysis showed that 95% of specimens failed by shear. Posts with parallel fiber (0°) may suffer fractures when an oblique shear load is applied on the structure; except the thinner group, greater coronal diameters promoted the same shear stresses. Copyright © 2014 Elsevier Ltd. All rights reserved.

  2. Finite Element Simulation of NiTi Umbrella-Shaped Implant Used on Femoral Head under Different Loadings

    Directory of Open Access Journals (Sweden)

    Reza Mehrabi


    Full Text Available In this study, an umbrella-shaped device that is used for osteonecrosis treatment is simulated. The femoral head is subjected to various complex loadings as a result of a person’s daily movements. Implant devices used in the body are made of shape memory alloy materials because of their remarkable resistance to wear and corrosion, good biocompatibility, and variable mechanical properties. Since this NiTi umbrella-shaped implant is simultaneously under several loadings, a 3-D model of shape memory alloy is utilized to investigate the behavior of the implant under different conditions. Shape memory and pseudo-elasticity behavior of NiTi is analyzed using a numerical model. The simulation is performed within different temperatures and in an isothermal condition with varied and complex loadings. The objective of this study is to evaluate the performance of the device under thermal and multi-axial forces via numerically study. Under tensile loading, the most critical points are on the top part of the implant. It is also shown that changes in temperature have a minor effect on the Von Mises stress. Applied forces and torques have significant influence on the femoral head. Simulations results indicate that the top portion of the umbrella is under the most stress when embedded in the body. Consequently, the middle, curved portion of the umbrella is under the least amount of stress.

  3. Stress distribution in fixed-partial prosthesis and peri-implant bone tissue with different framework materials and vertical misfit levels: a three-dimensional finite element analysis. (United States)

    Bacchi, Ataís; Consani, Rafael L X; Mesquita, Marcelo F; dos Santos, Mateus B F


    The purpose of this study was to evaluate the influence of superstructure material and vertical misfits on the stresses created in an implant-supported partial prosthesis. A three-dimensional (3-D) finite element model was prepared based on common clinical data. The posterior part of a severely resorbed jaw with two osseointegrated implants at the second premolar and second molar regions was modeled using specific modeling software (SolidWorks 2010). Finite element models were created by importing the solid model into mechanical simulation software (ANSYS Workbench 11). The models were divided into groups according to the prosthesis framework material (type IV gold alloy, silver-palladium alloy, commercially pure titanium, cobalt-chromium alloy, or zirconia) and vertical misfit level (10 µm, 50 µm, and 100 µm) created at one implant-prosthesis interface. The gap of the vertical misfit was set to be closed and the stress values were measured in the framework, porcelain veneer, retention screw, and bone tissue. Stiffer materials led to higher stress concentration in the framework and increased stress values in the retention screw, while in the same circumstances, the porcelain veneer showed lower stress values, and there was no significant difference in stress in the peri-implant bone tissue. A considerable increase in stress concentration was observed in all the structures evaluated within the misfit amplification. The framework material influenced the stress concentration in the prosthetic structures and retention screw, but not that in bone tissue. All the structures were significantly influenced by the increase in the misfit levels.

  4. Three dimensional finite element analysis of mandibular premolar restored with fiber post and resin composite with different cavity designs

    Directory of Open Access Journals (Sweden)

    Daraporn Sae-Lee


    Full Text Available The investigation of the stress distribution and fatigue lifetime of endodontically treated mandibular premolar with various cavity designs for access opening, restored by resin composite with or without a fiber post was performed. A 3D model of a mandibular premolar with one root canal was selected. The 11 study models of tooth structure including enamel, dentine and pulp tissue were generated with different cavity designs, i.e., Class I, Class II OM, Class II MOD, Class V, Class V pulp exposure, cortical and cancellous bone, root canal configuration, as well as fiber post. A load of 150 Newtons was applied on the lingual incline plane of the buccal cusp at an angle of 45 degrees to the long axis of the tooth. The results show that the stress distributions in all models were similar, i.e., the maximum von Mises stresses were observed at the level of the cement-enamel junction (CEJ, and the stress decreased abruptly from the outer to the inner part of the tooth. The maximum von Mises stress along the tooth axis was concentrated at the load-bearing areas, and decreased gradually from the coronal region to the apex of the root. The fatigue lifetimes of the models restored with a fiber post were greater than those without a fiber post.

  5. Simulation of airbag impact on eyes with different axial lengths after transsclerally fixated posterior chamber intraocular lens by using finite element analysis (United States)

    Huang, Jane; Uchio, Eiichi; Goto, Satoru


    Purpose To determine the biomechanical response of an impacting airbag on eyes with different axial lengths with transsclerally fixated posterior chamber intraocular lens (PC IOL). Materials and methods Simulations in a model human eye were performed with a computer using a finite element analysis program created by Nihon, ESI Group. The airbag was set to be deployed at five different velocities and to impact on eyes with three different axial lengths. These eyes were set to have transsclerally fixated PC IOL by a 10-0 polypropylene possessing a tensile force limit of 0.16 N according to the United States Pharmacopeia XXII. Results The corneoscleral opening was observed at a speed of 40 m/second or more in all model eyes. Eyes with the longest axial length of 25.85 mm had the greatest extent of deformity at any given impact velocity. The impact force exceeded the tensile force of 10-0 polypropylene at an impact velocity of 60 m/second in all eyes, causing breakage of the suture. Conclusion Eyes with transsclerally fixated PC IOL could rupture from airbag impact at high velocities. Eyes with long axial lengths experienced a greater deformity upon airbag impact due to a thinner eye wall. Further basic research on the biomechanical response for assessing eye injuries could help in developing a better airbag and in the further understanding of ocular traumas. PMID:25709387

  6. Effect of conduction band non-parabolicity on the optical gain of quantum cascade lasers based on the effective two-band finite difference method (United States)

    Cho, Gookbin; Kim, Jungho


    We theoretically investigate the effect of conduction band non-parabolicity (NPB) on the optical gain spectrum of quantum cascade lasers (QCLs) using the effective two-band finite difference method. Based on the effective two-band model to consider the NPB effect in the multiple quantum wells (QWs), the wave functions and confined energies of electron states are calculated in two different active-region structures, which correspond to three-QW single-phonon and four-QW double-phonon resonance designs. In addition, intersubband optical dipole moments and polar-optical-phonon scattering times are calculated and compared without and with the conduction band NPB effect. Finally, the calculation results of optical gain spectra are compared in the two QCL structures having the same peak gain wavelength of 8.55 μm. The gain peaks are greatly shifted to longer wavelengths and the overall gain magnitudes are slightly reduced when the NPB effect is considered. Compared with the three-QW active-region design, the redshift of the peak gain is more prominent in the four-QW active-region design, which makes use of higher electronic states for the lasing transition.

  7. [Three dimensional finite element analysis on stress distribution in dentin of the maxillary central incisor restored with different shapes and materials of post]. (United States)

    Zhang, Xuying; Sun, Jing; Lu, Jun


    To investigate the stress distribution in dentin of the maxillary central incisor restored with post-core which is related to different shapes and materials. CT scan, digital-image processing and Unigraphics (UG) software were applied to construct the three-dimensional finite element models of maxillary central incisor restored with cone or column post-core. Based on this model, stress distribution of Von Mises in dentin with three different materials(polyethylene fiber resin, carbon fiber and zirconia) were analyzed respectively. Static loading(100N) was used on the lingual boundary line between upper-one-third and middle-one-third of maxillary central incisor, the direction of the loading was 45 degrees to the tooth long axis. In posts made of zirconia and restored with column post, the stress distribution in dentin was higher than with cone post (P0.05). The elastic modulus of post-core materials affected the stress distribution, and the higher the elastic modulus was, the higher the stress concentrated. Cone post excels column post in higher elastic modulus materials. Using the lower elastic modulus materials possibly can avail to the stress distribution and prevent the root breakage. During the root canal preparation, the dentin around the root neck should be conserved as more as possible, especially the dentin in the labial side.

  8. HYDRA-I: a three-dimensional finite difference code for calculating the thermohydraulic performance of a fuel assembly contained within a canister

    Energy Technology Data Exchange (ETDEWEB)

    McCann, R.A.


    A finite difference computer code, named HYDRA-I, has been developed to simulate the three-dimensional performance of a spent fuel assembly contained within a cylindrical canister. The code accounts for the coupled heat transfer modes of conduction, convection, and radiation and permits spatially varying boundary conditions, thermophysical properties, and power generation rates. This document is intended as a manual for potential users of HYDRA-I. A brief discussion of the governing equations, the solution technique, and a detailed description of how to set up and execute a problem are presented. HYDRA-I is designed for operation on a CDC 7600 computer. An appendix is included that summarizes approximately two dozen different cases that have been examined. The cases encompass variations in fuel assembly and canister configurations, power generation rates, filler materials, and gases. The results presented show maximum and various local temperatures and heat fluxes illustrating the changing importance of the three heat transfer modes. Finally, the need for comparison with experimental data is emphasized as an aid in code verification although the limited data available indicate excellent agreement.

  9. Implementation and testing of stable, fast implicit solvation in molecular dynamics using the smooth-permittivity finite difference Poisson-Boltzmann method. (United States)

    Prabhu, Ninad V; Zhu, Peijuan; Sharp, Kim A


    A fast stable finite difference Poisson-Boltzmann (FDPB) model for implicit solvation in molecular dynamics simulations was developed using the smooth permittivity FDPB method implemented in the OpenEye ZAP libraries. This was interfaced with two widely used molecular dynamics packages, AMBER and CHARMM. Using the CHARMM-ZAP software combination, the implicit solvent model was tested on eight proteins differing in size, structure, and cofactors: calmodulin, horseradish peroxidase (with and without substrate analogue bound), lipid carrier protein, flavodoxin, ubiquitin, cytochrome c, and a de novo designed 3-helix bundle. The stability and accuracy of the implicit solvent simulations was assessed by examining root-mean-squared deviations from crystal structure. This measure was compared with that of a standard explicit water solvent model. In addition we compared experimental and calculated NMR order parameters to obtain a residue level assessment of the accuracy of MD-ZAP for simulating dynamic quantities. Overall, the agreement of the implicit solvent model with experiment was as good as that of explicit water simulations. The implicit solvent method was up to eight times faster than the explicit water simulations, and approximately four times slower than a vacuum simulation (i.e., with no solvent treatment). (c) 2004 Wiley Periodicals, Inc.

  10. Data Modeling Using Finite Differences (United States)

    Rhoads, Kathryn; Mendoza Epperson, James A.


    The Common Core State Standards for Mathematics (CCSSM) states that high school students should be able to recognize patterns of growth in linear, quadratic, and exponential functions and construct such functions from tables of data (CCSSI 2010). In their work with practicing secondary teachers, the authors found that teachers may make some tacit…

  11. Stable, high-order SBP-SAT finite difference operators to enable accurate simulation of compressible turbulent flows on curvilinear grids, with application to predicting turbulent jet noise (United States)

    Byun, Jaeseung; Bodony, Daniel; Pantano, Carlos


    Improved order-of-accuracy discretizations often require careful consideration of their numerical stability. We report on new high-order finite difference schemes using Summation-By-Parts (SBP) operators along with the Simultaneous-Approximation-Terms (SAT) boundary condition treatment for first and second-order spatial derivatives with variable coefficients. In particular, we present a highly accurate operator for SBP-SAT-based approximations of second-order derivatives with variable coefficients for Dirichlet and Neumann boundary conditions. These terms are responsible for approximating the physical dissipation of kinetic and thermal energy in a simulation, and contain grid metrics when the grid is curvilinear. Analysis using the Laplace transform method shows that strong stability is ensured with Dirichlet boundary conditions while weaker stability is obtained for Neumann boundary conditions. Furthermore, the benefits of the scheme is shown in the direct numerical simulation (DNS) of a Mach 1.5 compressible turbulent supersonic jet using curvilinear grids and skew-symmetric discretization. Particularly, we show that the improved methods allow minimization of the numerical filter often employed in these simulations and we discuss the qualities of the simulation.

  12. Modeling arbitrarily directed slots that are narrow both in width and depth with regard to the FDTD spatial cell. [Finite Difference-Time Domain (TDTD)

    Energy Technology Data Exchange (ETDEWEB)

    Riley, D.J.; Turner, C.D.


    The Hybrid Thin-Slot Algorithm (HTSA) integrates a transient integral-equation solution for an aperture in an infinite plane into a finite-difference time-domain (FDTD) code. The technique was introduced for linear apertures and was extended to include wall loss and lossy internal gaskets. A general implementation for arbitrary thin slots is briefly described here. The 3-D FDTD-code TSAR was selected for the implementation. The HTSA does not provide universal solutions to the narrow slot problem, but has merits appropriate for particular applications. The HTSA is restricted to planar slots, but can solve the important case that both the width and depth of the slot are narrow compared to the FDTD spatial cell. IN addition, the HTSA is not bound to the FDTD discrete spatial and time increments, and therefore, high-resolution solutions for the slot physics are possible. The implementation of the HTSA into TSAR is based upon a slot data file'' that includes the cell indices where the desired slots are exist within the FDTD mesh. For an HTSA-defined slot, the wall region local to the slot is shorted, and therefore, to change the slot's topology simply requires altering the file to include the desired cells. 7 refs.

  13. A finite difference thermal model of a cylindrical microwave heating applicator using locally conformal overlapping grids: part I--theoretical formulation. (United States)

    Al-Rizzo, Hussain M; Tranquilla, Jim M; Feng, Ma


    In this paper, we present a versatile mathematical formulation of a newly developed 3-D locally conformal Finite Difference (FD) thermal algorithm developed specificallyfor coupled electromagnetic (EM) and heat diffusion simulations utilizing Overlapping Grids (OGFD) in the Cartesian and cylindrical coordinate systems. The motivation for this research arises from an attempt to characterize the dominant thermal transport phenomena typically encountered during the process cycle of a high-power, microwave-assisted material processing system employing a geometrically composite cylindrical multimode heating furnace. The cylindrical FD scheme is only applied to the outer shell of the housing cavity whereas the Cartesian FD scheme is used to advance the temperature elsewhere including top and bottom walls, and most of the inner region of the cavity volume. The temperature dependency of the EM constitutive and thermo-physical parameters of the material being processed is readily accommodated into the OGFD update equations. The time increment, which satisfies the stability constraint of the explicit OGFD time-marching scheme, is derived. In a departure from prior work, the salient features of the proposed algorithm are first, the locally conformal discretization scheme accurately describes the diffusion of heat and second, significant heat-loss mechanisms usually encountered in microwave heating problems at the interfacial boundary temperature nodes have been considered. These include convection and radiation between the surface of the workload and air inside the cavity, heat convection and radiation between the inner cavity walls and interior cavity volume, and free cooling of the outermost cavity walls.

  14. Computational fluid dynamics and frequency-dependent finite-difference time-domain method coupling for the interaction between microwaves and plasma in rocket plumes

    Energy Technology Data Exchange (ETDEWEB)

    Kinefuchi, K. [Department of Aeronautics and Astronautics, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-8656 (Japan); Funaki, I.; Shimada, T.; Abe, T. [Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1, Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210 (Japan)


    Under certain conditions during rocket flights, ionized exhaust plumes from solid rocket motors may interfere with radio frequency transmissions. To understand the relevant physical processes involved in this phenomenon and establish a prediction process for in-flight attenuation levels, we attempted to measure microwave attenuation caused by rocket exhaust plumes in a sea-level static firing test for a full-scale solid propellant rocket motor. The microwave attenuation level was calculated by a coupling simulation of the inviscid-frozen-flow computational fluid dynamics of an exhaust plume and detailed analysis of microwave transmissions by applying a frequency-dependent finite-difference time-domain method with the Drude dispersion model. The calculated microwave attenuation level agreed well with the experimental results, except in the case of interference downstream the Mach disk in the exhaust plume. It was concluded that the coupling estimation method based on the physics of the frozen plasma flow with Drude dispersion would be suitable for actual flight conditions, although the mixing and afterburning in the plume should be considered depending on the flow condition.

  15. Study on Scattering and Absorption Properties of Quantum-Dot-Converted Elements for Light-Emitting Diodes Using Finite-Difference Time-Domain Method. (United States)

    Li, Jiasheng; Tang, Yong; Li, Zongtao; Ding, Xinrui; Yuan, Dong; Yu, Binhai


    CdSe/ZnS quantum-dot-converted elements (QDCEs) are good candidates for substituting rare-earth phosphor-converted elements (PCEs) in white light-emitting diodes (LEDs); however, studies on their scattering and absorption properties are scarce, suppressing further increment in the optical and thermal performance of quantum-dot-converted LEDs. Therefore, we introduce the finite-difference time-domain (FDTD) method to achieve the critical optical parameters of QDCEs when used in white LEDs; their scattering cross-section (coefficient), absorption cross-section (coefficient), and scattering phase distributions are presented and compared with those of traditional YAG phosphor-converted elements (PCEs) at varying particle size and concentration. At a commonly used concentration ( < 50 mg / cm 3 ), QDCEs exhibit stronger absorption (tens of millimeters, even for green-to-red-wavelength light) and weaker scattering ( < 1 mm - 1 ) compared to PCEs; the reabsorption, total internal reflection, angular uniformity, and thermal quenching would be more significant concerns for QDCEs. Therefore, the unique scattering and absorption properties of QDCEs should be considered when used in white LEDs. Furthermore, knowledge of these important optical parameters is helpful for beginning a theoretical study on quantum-dot-converted LEDs according to the ray tracing method.

  16. Study on Scattering and Absorption Properties of Quantum-Dot-Converted Elements for Light-Emitting Diodes Using Finite-Difference Time-Domain Method

    Directory of Open Access Journals (Sweden)

    Jiasheng Li


    Full Text Available CdSe/ZnS quantum-dot-converted elements (QDCEs are good candidates for substituting rare-earth phosphor-converted elements (PCEs in white light-emitting diodes (LEDs; however, studies on their scattering and absorption properties are scarce, suppressing further increment in the optical and thermal performance of quantum-dot-converted LEDs. Therefore, we introduce the finite-difference time-domain (FDTD method to achieve the critical optical parameters of QDCEs when used in white LEDs; their scattering cross-section (coefficient, absorption cross-section (coefficient, and scattering phase distributions are presented and compared with those of traditional YAG phosphor-converted elements (PCEs at varying particle size and concentration. At a commonly used concentration ( < 50 mg / cm 3 , QDCEs exhibit stronger absorption (tens of millimeters, even for green-to-red-wavelength light and weaker scattering ( < 1 mm − 1 compared to PCEs; the reabsorption, total internal reflection, angular uniformity, and thermal quenching would be more significant concerns for QDCEs. Therefore, the unique scattering and absorption properties of QDCEs should be considered when used in white LEDs. Furthermore, knowledge of these important optical parameters is helpful for beginning a theoretical study on quantum-dot-converted LEDs according to the ray tracing method.

  17. Stress distribution of endodontically treated teeth with titanium alloy post and carbon fiber post with different alveolar bone height: A three-dimensional finite element analysis. (United States)

    Singh, S Vijay; Bhat, Manohar; Gupta, Saurabh; Sharma, Deepak; Satija, Harsha; Sharma, Sumeet


    A three-dimensional (3D) finite element analysis (FEA) on the stress distribution of endodontically treated teeth with titanium alloy post and carbon fiber post with different alveolar bone height. The 3D model was fabricated using software to represent an endodontically treated mandibular second premolar with post and restored with a full ceramic crown restoration, which was then analyzed using FEA using FEA ANSYS Workbench V13.0 (ANSYS Inc., Canonsburg, Pennsylvania, U.S.A) software. The FEA showed the maximum stresses of 137.43 Mpa in dentin with alveolar bone height of 4 mm when the titanium post was used, 138.48 Mpa when carbon fiber post was used as compared to 105.91 Mpa in the model with alveolar bone height of 2 mm from the cement enamel junction (CEJ) when the titanium post was used and 107.37 Mpa when the carbon fiber post was used. Stress was observed more in alveolar bone height level of 4 mm from CEJ than 2 mm from CEJ. Stresses in the dentin were almost similar when the carbon fiber post was compared to titanium post. However, stresses in the post and the cement were much higher when titanium post was used as compared to carbon fiber post.

  18. Numerical Simulation of Flows about a Stationary and a Free-Falling Cylinder Using Immersed Boundary-Finite Difference Lattice Boltzmann Method

    Directory of Open Access Journals (Sweden)

    Roberto Rojas


    Full Text Available The applicability of the immersed boundary-finite difference lattice Boltzmann method (IB-FDLBM to high Reynolds number flows about a circular cylinder is examined. Two-dimensional simulations of flows past a stationary circular cylinder are carried out for a wide range of the Reynolds number, Re, i.e., 1 ≤ Re ≤ 1×105. An immersed boundary-lattice Boltzmann method (IB-LBM is also used for comparison. Then free-falling circular cylinders are simulated to demonstrate the feasibility of predicting moving particles at high Reynolds numbers. The main conclusions obtained are as follows: (1 steady and unsteady flows about a stationary cylinder are well predicted with IB-LBM and IB-FDLBM, provided that the spatial resolution is high enough to satisfy the conditions of numerical stability, (2 high spatial resolution is required for stable IB-LBM simulation of high Reynolds number flows, (3 IB-FDLBM can stably simulate flows at very high Reynolds numbers without increasing the spatial resolution, (4 IB-FDLBM gives reasonable predictions of the drag coefficient for 1 ≤ Re ≤ 1×105, and (5 IB-FDLBM gives accurate predictions for the motion of free-falling cylinders at intermediate Reynolds numbers.

  19. Three-Dimensional Sound Field Analysis Using Compact Explicit-Finite Difference Time Domain Method with Graphics Processing Unit Cluster System (United States)

    Ishii, Takuto; Tsuchiya, Takao; Okubo, Kan


    In this study, the compact explicit-finite difference time domain (CE-FDTD) method is applied to the three-dimensional sound field analysis to reduce computer resources. There are various derivative schemes in the CE-FDTD method. They are first examined theoretically to evaluate the numerical accuracy. As a theoretical result, it is found that the interpolated wide band (IWB) scheme has the widest bandwidth in which the cut-off frequency is in agreement with the Nyquist frequency. The calculation performance is theoretically estimated, then experimentally evaluated with the graphics processing unit cluster system. As a result, it is found that the memory usage of the IWB scheme is less than one-third of that of the standard leapfrog (SLF) scheme to achieve the same cut-off frequency. It is also found that the calculation time of the IWB scheme with the shared memory is about 19% compared with that of the SLF scheme with the graphics processing unit (GPU) cluster system. The impulse response is calculated for a large room with a volume capacity of about 4500 m3 in which the sampling rate was 40 kHz. It is confirmed that the three-dimensional sound field with the natural reverberation can be calculated by the IWB scheme.

  20. Two-dimensional finite difference model to study temperature distribution in SST regions of human limbs immediately after physical exercise in cold climate (United States)

    Kumari, Babita; Adlakha, Neeru


    Thermoregulation is a complex mechanism regulating heat production within the body (chemical thermoregulation) and heat exchange between the body and the environment (physical thermoregulation) in such a way that the heat exchange is balanced and deep body temperatures are relatively stable. The external heat transfer mechanisms are radiation, conduction, convection and evaporation. The physical activity causes thermal stress and poses challenges for this thermoregulation. In this paper, a model has been developed to study temperature distribution in SST regions of human limbs immediately after physical exercise under cold climate. It is assumed that the subject is doing exercise initially and comes to rest at time t = 0. The human limb is assumed to be of cylindrical shape. The peripheral region of limb is divided into three natural components namely epidermis, dermis and subdermal tissues (SST). Appropriate boundary conditions have been framed based on the physical conditions of the problem. Finite difference has been employed for time, radial and angular variables. The numerical results have been used to obtain temperature profiles in the SST region immediately after continuous exercise for a two-dimensional unsteady state case. The results have been used to analyze the thermal stress in relation to light, moderate and vigorous intensity exercise.

  1. Depropagation and propagation simulation of the acoustic waves by using finite differences operators; Simulacao da propagacao e depropagacao de ondas acusticas usando operadores de diferencas finitas

    Energy Technology Data Exchange (ETDEWEB)

    Botelho, Marco A.B.; Santos, Roberto H.M. dos; Silva, Marcelo S. [Universidade Federal da Bahia (UFBA), Salvador, BA (Brazil). Centro de Pesquisa em Geofisica e Geologia


    The numerical simulation of shot gathers over a (2D) velocity field, which corresponds to a model of Atlantic continental shelf, at the continental break area, using a typical model of the Brazilian Atlantic coast, suggested by PETROBRAS. The finite difference technique (FD) is used to solve the second derivatives in time and space of the acoustic wave equation, using fourth order operators to solve the spatial derivatives and second order operators to solve the time derivative. It is applied an explicitly scheme to calculate the pressure field values at a future instant. The use of rectangular mesh helps to generate data less noisy, since we can control better the numerical dispersion. The source functions (wavelets), as the first and the second derivatives of the gaussian function, are proper to generate synthetic seismograms with the FD method, because they allow an easy discretization. On the forward modeling, which is the simulation of wave fields, allows to control the stability limit of the method, wherever be the given velocity field, just employing compatible small values of the sample rate. The algorithm developed here, which uses only the FD technique, is able to perform the forward modeling, saving the image times, which can be used latter to perform the retropropagation of the wave field and thus migrate the source-gathers the reverse time extrapolation is able to test the used velocity model, and detect determine errors up to 5% on the used velocity model. (author)

  2. quadratic spline finite element method

    Directory of Open Access Journals (Sweden)

    A. R. Bahadir


    Full Text Available The problem of heat transfer in a Positive Temperature Coefficient (PTC thermistor, which may form one element of an electric circuit, is solved numerically by a finite element method. The approach used is based on Galerkin finite element using quadratic splines as shape functions. The resulting system of ordinary differential equations is solved by the finite difference method. Comparison is made with numerical and analytical solutions and the accuracy of the computed solutions indicates that the method is well suited for the solution of the PTC thermistor problem.

  3. Stress and strain distribution in three different mini dental implant designs using in implant retained overdenture: a finite element analysis study. (United States)

    Aunmeungtong, W; Khongkhunthian, P; Rungsiyakull, P


    Finite Element Analysis (FEA) has been used for prediction of stress and strain between dental implant components and bone in the implant design process. Purpose of this study was to characterize and analyze stress and strain distribution occurring in bone and implants and to compare stress and strain of three different implant designs. Three different mini dental implant designs were included in this study: 1. a mini dental implant with an internal implant-abutment connection (MDIi); 2. a mini dental implant with an external implant-abutment connection (MDIe); 3. a single piece mini dental implant (MDIs). All implant designs were scanned using micro-CT scans. The imaging details of the implants were used to simulate models for FEA. An artificial bone volume of 9×9 mm in size was constructed and each implant was placed separately at the center of each bone model. All bone-implant models were simulatively loaded under an axial compressive force of 100 N and a 45-degree force of 100 N loading at the top of the implants using computer software to evaluate stress and strain distribution. There was no difference in stress or strain between the three implant designs. The stress and strain occurring in all three mini dental implant designs were mainly localized at the cortical bone around the bone-implant interface. Oblique 45° loading caused increased deformation, magnitude and distribution of stress and strain in all implant models. Within the limits of this study, the average stress and strain in bone and implant models with MDIi were similar to those with MDIe and MDIs. The oblique 45° load played an important role in dramatically increased average stress and strain in all bone-implant models. Mini dental implants with external or internal connections have similar stress distribution to single piece mini dental implants. In clinical situations, the three types of mini dental implant should exhibit the same behavior to chewing force.

  4. Numerical stability of finite difference algorithms for electrochemical kinetic simulations. Matrix stability analysis of the classic explicit, fully implicit and Crank-Nicolson methods, extended to the 3- and 4-point gradient approximation at the electrodes

    DEFF Research Database (Denmark)

    Bieniasz, Leslaw K.; Østerby, Ole; Britz, Dieter


    We extend the analysis of the stepwise numerical stability of the classic explicit, fully implicit and Crank-Nicolson finite difference algorithms for electrochemical kinetic simulations, to the multipoint gradient approximations at the electrode. The discussion is based on the matrix method...


    Directory of Open Access Journals (Sweden)

    Sebastián Otero G


    representa su capacidad de incorporar en el análisis el valor de la flexibilidad operativa del proyecto.In the past few years, real options, an extension of financial derivatives, have arisen as an alternative to traditional valuation methods, such as net present value (NPV. The key attribute of real options is that they take into consideration the uncertainty and flexibility involved in investment valuation. This article provides an overview of the finite difference method, by presenting an application to the real options valuation. The empirical section of the article, which makes use of the implicit finite difference method (IFD, analyzes the options of waiting, abandoning, contracting, expanding and switching, by valuing all the options involved and their possible combinations. The results are compared with those of the NPV method and the binomial tree with a logarithmic transformation (BTLT. Both methods (IFD and BTLT yield similar results, being both greater than those provided by the NPV. This difference comes to no surprise as it represents the value of the flexibility associated to an investment opportunity.

  6. Differences in Trabecular Microarchitecture and Simplified Boundary Conditions Limit the Accuracy of QCT-based Finite Element Models of Vertebral Failure. (United States)

    Hussein, Amira I; Louzeiro, Daniel; Unnikrishnan, Ginu U; Morgan, Elise F


    Vertebral fractures are common in the elderly, but efforts to reduce their incidence have been hampered by incomplete understanding of the failure processes that are involved. This study's goal was to elucidate failure processes in the lumbar vertebra and to assess the accuracy of quantitative computed tomography (QCT)-based finite element (FE) simulations of these processes. Following QCT scanning, spine segments (n=27) consisting of L1 with adjacent intervertebral discs and neighboring endplates of T12 and L2 were compressed axially in a stepwise manner. A micro-computed tomography scan was performed at each loading step. The resulting time-lapse series of images was analyzed using digital volume correlation (DVC) to quantify deformations throughout the vertebral body. While some diversity among vertebrae was observed in how these deformations progressed, common features were large strains that developed progressively in the superior third and, concomitantly, in the mid-transverse plane, in a manner that was associated with spatial variations in microstructural parameters such as connectivity density. Results of FE simulations corresponded qualitatively to the measured failure patterns when boundary conditions were derived from DVC displacements at the endplate. However, quantitative correspondence was often poor, particularly when boundary conditions were simplified to uniform compressive loading. These findings suggest that variations in trabecular microstructure are one cause of the differences in failure patterns among vertebrae and that both lack of incorporation of these variations into QCT-based FE models and oversimplification of boundary conditions limit the accuracy of these models in simulating vertebral failure.

  7. Finite-Difference Modeling of Seismic Wave Scattering in 3D Heterogeneous Media: Generation of Tangential Motion from an Explosion Source (United States)

    Hirakawa, E. T.; Pitarka, A.; Mellors, R. J.


    Evan Hirakawa, Arben Pitarka, and Robert Mellors One challenging task in explosion seismology is development of physical models for explaining the generation of S-waves during underground explosions. Pitarka et al. (2015) used finite difference simulations of SPE-3 (part of Source Physics Experiment, SPE, an ongoing series of underground chemical explosions at the Nevada National Security Site) and found that while a large component of shear motion was generated directly at the source, additional scattering from heterogeneous velocity structure and topography are necessary to better match the data. Large-scale features in the velocity model used in the SPE simulations are well constrained, however, small-scale heterogeneity is poorly constrained. In our study we used a stochastic representation of small-scale variability in order to produce additional high-frequency scattering. Two methods for generating the distributions of random scatterers are tested. The first is done in the spatial domain by essentially smoothing a set of random numbers over an ellipsoidal volume using a Gaussian weighting function. The second method consists of filtering a set of random numbers in the wavenumber domain to obtain a set of heterogeneities with a desired statistical distribution (Frankel and Clayton, 1986). This method is capable of generating distributions with either Gaussian or von Karman autocorrelation functions. The key parameters that affect scattering are the correlation length, the standard deviation of velocity for the heterogeneities, and the Hurst exponent, which is only present in the von Karman media. Overall, we find that shorter correlation lengths as well as higher standard deviations result in increased tangential motion in the frequency band of interest (0 - 10 Hz). This occurs partially through S-wave refraction, but mostly by P-S and Rg-S waves conversions. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore

  8. MODFLOW–USG version 1: An unstructured grid version of MODFLOW for simulating groundwater flow and tightly coupled processes using a control volume finite-difference formulation (United States)

    Panday, Sorab; Langevin, Christian D.; Niswonger, Richard G.; Ibaraki, Motomu; Hughes, Joseph D.


    A new version of MODFLOW, called MODFLOW–USG (for UnStructured Grid), was developed to support a wide variety of structured and unstructured grid types, including nested grids and grids based on prismatic triangles, rectangles, hexagons, and other cell shapes. Flexibility in grid design can be used to focus resolution along rivers and around wells, for example, or to subdiscretize individual layers to better represent hydrostratigraphic units. MODFLOW–USG is based on an underlying control volume finite difference (CVFD) formulation in which a cell can be connected to an arbitrary number of adjacent cells. To improve accuracy of the CVFD formulation for irregular grid-cell geometries or nested grids, a generalized Ghost Node Correction (GNC) Package was developed, which uses interpolated heads in the flow calculation between adjacent connected cells. MODFLOW–USG includes a Groundwater Flow (GWF) Process, based on the GWF Process in MODFLOW–2005, as well as a new Connected Linear Network (CLN) Process to simulate the effects of multi-node wells, karst conduits, and tile drains, for example. The CLN Process is tightly coupled with the GWF Process in that the equations from both processes are formulated into one matrix equation and solved simultaneously. This robustness results from using an unstructured grid with unstructured matrix storage and solution schemes. MODFLOW–USG also contains an optional Newton-Raphson formulation, based on the formulation in MODFLOW–NWT, for improving solution convergence and avoiding problems with the drying and rewetting of cells. Because the existing MODFLOW solvers were developed for structured and symmetric matrices, they were replaced with a new Sparse Matrix Solver (SMS) Package developed specifically for MODFLOW–USG. The SMS Package provides several methods for resolving nonlinearities and multiple symmetric and asymmetric linear solution schemes to solve the matrix arising from the flow equations and the Newton

  9. Effect of different restorative crown and customized abutment materials on stress distribution in single implants and peripheral bone: A three-dimensional finite element analysis study. (United States)

    Kaleli, Necati; Sarac, Duygu; Külünk, Safak; Öztürk, Özgür


    In recent years, the use of resin-matrix ceramics and polyetheretherketone (PEEK) abutments has been suggested to absorb excessive stresses on dental implants. However, only a few studies have evaluated the effect of these materials on stress distribution in implants and peripheral bone structure. The purpose of this finite element analysis was to evaluate the biomechanical behaviors of resin-matrix ceramics and PEEK customized abutments in terms of stress distribution in implants and peripheral bone. Three-dimensional (3D) models of a bone-level implant system and a titanium base abutment were created by using the standard tessellation language (STL) data of original implant components. An anatomic customized abutment and a maxillary right second premolar crown were then modeled over the titanium base abutment. A bone block representing the maxillary right premolar area was created, and the implant was placed in the bone block with 100% osseointegration. Six different models were created according to combinations of restoration materials (translucent zirconia [TZI], lithium disilicate glass ceramic [IPS], polymer-infiltrated hybrid ceramic [VTE]), and customized abutment materials (PEEK and zirconia). In each model, the implants were loaded vertically (200 N) and obliquely (100 N). The stress distribution in the crown, implant, and abutments was evaluated through the von Mises stress analysis, and the stress distribution in the peripheral bone was examined through the maximum and minimum principal stress analyses. The oblique load resulted in high stress values in the implant components, restorative crown, and cortical bone. Low stress values were observed in the VTE crowns. Zirconia customized abutments exhibited higher stress values than PEEK customized abutments. The stress distributions in the implant and peripheral bone were similar in all models. Changes in restoration and customized abutment material did not affect stress distribution in the implant and

  10. Comparison of frictional resistance among conventional, active and passive selfligating brackets with different combinations of arch wires: a finite elements study. (United States)

    Gómez, Sandra L; Montoya, Yesid; Garcia, Nora L; Virgen, Ana L; Botero, Javier E


    The aim of this study was to compare frictional resistance among conventional, passive and active selfligating brackets using Finite Elements Analysis (FEA). Seventynine (79) slide tests were performed by combining an upper first bicuspid conventional bracket, 0.018" stainless steel wires and 0.010" ligature by means of an INSTRON 3345 load system to obtain average maximum static frictional resistance (MSFR). This value was compared to the FR (frictional resistance) obtained by simulation of a slide of the same combination by FEA following conventional bracket modeling by means of Computer Aided Design (CAD). Once the FEA was validated, bracket CADs were designed (upper right first bicuspid conventional, active and passive selfligating bracket) and bracket properties calculated. MSFR was compared among conventional, active and passive selfligating brackets with different alloys and archwire cross sections such as 0.018", 0.019" x 0.025"and 0.020" x 0.020". Passive selfligating brackets had the lowest MSFR, followed by conventional brackets and active selfligating brackets. In conventional brackets, a 0.018" archwire produced a linear pattern of stress with maximum concentration at the center. Conversely, stress in 0.020 x 0.020" and 0.019 x 0.025" archwires was distributed across the width of the slot. The highest normal forces were 1.53 N for the 0.018" archwire, 4.85 N for the 0.020 x 0.020" archwire and 8.18 N for the 0.019 x 0.025" archwire. Passive selfligating brackets presented less frictional resistance than conventional and active selfligating brackets. Regardless of bracket type, greater contact area between the slot and the archwire and the spring clip increased frictional resistance. Sociedad Argentina de Pediatría.

  11. A Finite Difference, Semi-implicit, Equation-of-State Efficient Algorithm for the Compositional Flow Modeling in the Subsurface: Numerical Examples

    KAUST Repository

    Saavedra, Sebastian


    The mathematical model that has been recognized to have the more accurate approximation to the physical laws govern subsurface hydrocarbon flow in reservoirs is the Compositional Model. The features of this model are adequate to describe not only the performance of a multiphase system but also to represent the transport of chemical species in a porous medium. Its importance relies not only on its current relevance to simulate petroleum extraction processes, such as, Primary, Secondary, and Enhanced Oil Recovery Process (EOR) processes but also, in the recent years, carbon dioxide (CO2) sequestration. The purpose of this study is to investigate the subsurface compositional flow under isothermal conditions for several oil well cases. While simultaneously addressing computational implementation finesses to contribute to the efficiency of the algorithm. This study provides the theoretical framework and computational implementation subtleties of an IMplicit Pressure Explicit Composition (IMPEC)-Volume-balance (VB), two-phase, equation-of-state, approach to model isothermal compositional flow based on the finite difference scheme. The developed model neglects capillary effects and diffusion. From the phase equilibrium premise, the model accounts for volumetric performances of the phases, compressibility of the phases, and composition-dependent viscosities. The Equation of State (EoS) employed to approximate the hydrocarbons behaviour is the Peng Robinson Equation of State (PR-EOS). Various numerical examples were simulated. The numerical results captured the complex physics involved, i.e., compositional, gravitational, phase-splitting, viscosity and relative permeability effects. Regarding the numerical scheme, a phase-volumetric-flux estimation eases the calculation of phase velocities by naturally fitting to phase-upstream-upwinding. And contributes to a faster computation and an efficient programming development.

  12. 3-D Waveguide Effects of Topographical Structural Variation on Full Waveform Propagation: 3-D Finite Difference Modeling Comparisons with Field Data From Yuma Proving Ground, Arizona (United States)

    Anderson, T. S.; Miller, R.; Greenfield, R.; Fisk, D.


    The propagation of seismic waves through regions of complex topography is not thoroughly understood. Surface waves, are of particular interest, as they are large in amplitude and can characterize the source depth, magnitude, and frequency content. The amplitude and frequency content of seismic waves that propagate in regions with large topographical variations are affected by both the scattering and blockage of the wave energy. The ability to predict the 3-d scattering due to topography will improve the understanding of both regional scale surface wave magnitudes, and refine surface wave discriminants as well as at the local scale (Smart Weapons Test Range, Yuma Proving Ground, Arizona. The result of the KGS characterization study is a high-resolution 3-d model that is used in our seismic simulations. The velocities Vs, Vp are calculated by tomography and refraction, attenuation coefficients estimated from the surface wave and from p-waves and are provided in a model with attributes resolved in 3-d to 0.5 meters. In the present work, we present comparisons of synthetic data with seismic data collected at the Smart Weapons Test Range to benchmark the accuracy achieved in simulating 3-d wave propagation in the vicinity of a topographical anomaly (trench). Synthetic seismograms are generated using a 3-d 8th order staggered grid visco-elastic finite difference code that accounts for topography. The geologic model is based on the Yuma site characterization. The size of these calculations required use of the DoD High Performance Computers and parallelized code. Results are compared with field data. Preliminary results show an excellent match with field data using the 3-d fdtd technique.

  13. Cortical bone stress distribution in mandibles with different configurations restored with prefabricated bar-prosthesis protocol: a three-dimensional finite-element analysis. (United States)

    de Almeida, Erika Oliveira; Rocha, Eduardo Passos; Assunção, Wirley Gonçalves; Júnior, Amílcar Chagas Freitas; Anchieta, Rodolfo Bruniera


    To evaluate stress distribution in different horizontal mandibular arch formats restored by protocol-type prostheses using three-dimensional finite element analysis (3D-FEA). A representative model (M) of a completely edentulous mandible restored with a prefabricated bar using four interforaminal implants was created using SolidWorks 2010 software (Inovart, São Paulo, Brazil) and analyzed by Ansys Workbench 10.0 (Swanson Analysis Inc., Houston, PA) to obtain the stress fields. Three mandibular arch sizes were considered for analysis, regular (M), small (MS), and large (ML). Three unilateral posterior loads (L) (150 N) were used: perpendicular to the prefabricated bar (L1); 30° oblique in a buccolingual direction (L2); 30° oblique in a lingual-buccal direction (L3). The maximum and minimum principal stresses (σ(max), σ(min)), the equivalent von Mises (σ(vM)), and the maximum principal strain (σ(max) ) were obtained for type I (M.I) and type II (M.II) cortical bones. Tensile stress was more evident than compression stress in type I and II bone; however, type II bone showed lower stress values. The L2 condition showed highest values for all parameters (σ(vM), σ(max), σ(min), ɛ(max)). The σ(vM) was highest for the large and small mandibular arches. The large arch model had a higher influence on σ(max) values than did the other formats, mainly for type I bone. Vertical and buccolingual loads showed considerable influence on both σ(max) and σ(min) stresses. © 2010 by The American College of Prosthodontists.

  14. Numerical modeling of CO2 sequestration inside a fracture in porous media based on space discretization by means of integral finite difference method (United States)

    Alizadeh Nomeli, M.; Riaz, A.


    Increasing concentration of CO2 as a greenhouse gas in the atmosphere causes global warming and it subsequently perturbs the balance of the life cycle. In order to mitigate the concentration of CO2 in the atmosphere, the sequestration of CO2 into deep geological formations has been investigated theoretically and experimentally in recent decades. Solubility and mineral trapping are the most promising long term solutions to geologic CO2 sequestration, because they prevent its return to the atmosphere. In this study, the CO2 sequestration capacity of both aqueous and mineral phases is evaluated. Mineral alterations, however, are too slow to be modeled experimentally; therefore a numerical model is required. This study presents a model to simulate a reactive fluid within permeable porous media. The problem contains reactive transport modeling between a miscible flow and minerals in post-injection regime. Rates of dissolution and precipitation (PD) of minerals are determined by taking into account the pH of the system, in addition to the consideration of the influence of temperature. We solve fluid convection, diffusion and PD reactions inside a fracture in order to predict the amount of CO2 that can be stored as precipitation of secondary carbonates after specific period of time. The modeling of flow and transport inside the fracture for the mineral trapping purpose is based on space discretization by means of integral finite differences. Dissolution and precipitation of all minerals in simulations presented in the current study are assumed to be kinetically controlled. Therefore the model can monitor changes in porosity and permeability during the simulation from changes in the volume of the fracture.

  15. A combination of experimental and finite element analyses of needle-tissue interaction to compute the stresses and deformations during injection at different angles. (United States)

    Halabian, Mahdi; Beigzadeh, Borhan; Karimi, Alireza; Shirazi, Hadi Asgharzadeh; Shaali, Mohammad Hasan


    One of the main clinical applications of the needles is its practical usage in the femoral vein catheterization. Annually more than two million peoples in the United States are exposed to femoral vein catheterization. How to use the input needles into the femoral vein has a key role in the sense of pain in post-injection and possible injuries, such as tissue damage and bleeding. It has been shown that there might be a correlation between the stresses and deformations due to femoral injection to the tissue and the sense of pain and, consequently, injuries caused by needles. In this study, the stresses and deformations induced by the needle to the femoral tissue were experimentally and numerically investigated in response to an input needle at four different angles, i.e., 30°, 45°, 60°, and 90°, via finite element method. In addition, a set of experimental injections at different angles were carried out to compare the numerical results with that of the experimental ones, namely pain score. The results revealed that by increasing the angle of injection up to 60°, the strain at the interaction site of the needle-tissue is increased accordingly while a significant falling is observed at the angle of 90°. In contrast, the stress due to injection was decreased at the region of needle-tissue interaction with showing the lowest one at the angle of 90°. Experimental results were also well confirmed the numerical observations since the lowest pain score was seen at the angle of 90°. The results suggest that the most effective angle of injection would be 90° due to a lower amount of stresses and deformations compared to the other angles of injection. These findings may have implications not only for understating the stresses and deformations induced during injection around the needle-tissue interaction, but also to give an outlook to the doctors to implement the most suitable angle of injection in order to reduce the pain as well as post injury of the patients.

  16. Analytical modeling, finite-difference simulation and experimental validation of air-coupled ultrasound beam refraction and damping through timber laminates, with application to non-destructive testing. (United States)

    Sanabria, Sergio J; Furrer, Roman; Neuenschwander, Jürg; Niemz, Peter; Schütz, Philipp


    Reliable non-destructive testing (NDT) ultrasound systems for timber composite structures require quantitative understanding of the propagation of ultrasound beams in wood. A finite-difference time-domain (FDTD) model is described, which incorporates local anisotropy variations of stiffness, damping and density in timber elements. The propagation of pulsed air-coupled ultrasound (ACU) beams in normal and slanted incidence configurations is reproduced by direct definition of material properties (gas, solid) at each model pixel. First, the model was quantitatively validated against analytical derivations. Time-varying wavefronts in unbounded timber with curved growth rings were accurately reproduced, as well as the acoustic properties (velocity, attenuation, beam skewing) of ACU beams transmitted through timber lamellas. An experimental sound field imaging (SFI) setup was implemented at NDT frequencies (120 kHz), which for specific beam incidence positions allows spatially resolved ACU field characterization at the receiver side. The good agreement of experimental and modeled beam shifts across timber laminates allowed extrapolation of the inner propagation paths. The modeling base is an orthotropic stiffness dataset for the desired wood species. In cross-grain planes, beam skewing leads to position-dependent wave paths. They are well-described in terms of the growth ring curvature, which is obtained by visual observation of the laminate. Extraordinary refraction phenomena were observed, which lead to well-collimated quasi-shear wave coupling at grazing beam incidence angles. The anisotropic damping in cross-grain planes is satisfactorily explained in terms of the known anisotropic stiffness dataset and a constant loss tangent. The incorporation of high-resolution density maps (X-ray computed tomography) provided insight into ultrasound scattering effects in the layered growth ring structure. Finally, the combined potential of the FDTD model and the SFI setup for

  17. Finite Coverings by Cones

    NARCIS (Netherlands)

    Tijs, S.H.; Reijnierse, J.H.


    This paper considers analogues of statements concerning compactness and finite coverings, in which the roles of spheres are replaced by cones. Furthermore, one of the finite covering results provides an application in Multi-Objective Programming; infinite sets of alternatives are reduced to finite

  18. Localized solutions for the finite difference semi-discretization of the wave equation [Solutions localisées pour la semi-discrétisation par différences finies de l'équation des ondes


    Marica, Aurora; Zuazua, Enrique


    We study the propagation properties of the solutions of the finite difference space semi-discrete wave equation on a uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that propagate along the corresponding bi-characteristic rays of Geometric Optics with a group velocity arbitrarily close to zero. Our analysis is motivated by control theoretical issues. In particular, the continuous wave equation has the so-called observability property: for a ...

  19. Finite quantum gauge theories (United States)

    Modesto, Leonardo; Piva, Marco; Rachwał, Lesław


    We explicitly compute the one-loop exact beta function for a nonlocal extension of the standard gauge theory, in particular, Yang-Mills and QED. The theory, made of a weakly nonlocal kinetic term and a local potential of the gauge field, is unitary (ghost-free) and perturbatively super-renormalizable. Moreover, in the action we can always choose the potential (consisting of one "killer operator") to make zero the beta function of the running gauge coupling constant. The outcome is a UV finite theory for any gauge interaction. Our calculations are done in D =4 , but the results can be generalized to even or odd spacetime dimensions. We compute the contribution to the beta function from two different killer operators by using two independent techniques, namely, the Feynman diagrams and the Barvinsky-Vilkovisky traces. By making the theories finite, we are able to solve also the Landau pole problems, in particular, in QED. Without any potential, the beta function of the one-loop super-renormalizable theory shows a universal Landau pole in the running coupling constant in the ultraviolet regime (UV), regardless of the specific higher-derivative structure. However, the dressed propagator shows neither the Landau pole in the UV nor the singularities in the infrared regime (IR).


    Directory of Open Access Journals (Sweden)



    Full Text Available The application of finite element method is analytical when solutions can not be applied for deeper study analyzes static, dynamic or other types of requirements in different points of the structures .In practice it is necessary to know the behavior of the structure or certain parts components of the machine under the influence of certain factors static and dynamic . The application of finite element in the optimization of components leads to economic growth , to increase reliability and durability organs studied, thus the machine itself.

  1. Finite dust clusters in dusty plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Melzer, A; Buttenschoen, B; Miksch, T; Passvogel, M [Institute of Physics, Ernst-Moritz-Arndt-Universitaet Greifswald, Felix-Hausdorff-Str. 6, 17489 Greifswald (Germany); Block, D; Arp, O; Piel, A, E-mail: melzer@physik.uni-greifswald.d [IEAP, Christian-Albrechts-Universitaet Kiel, Olshausenstr. 40-60, 24098 Kiel (Germany)


    We review recent experiments on the formation of finite systems of charged microspheres in dusty plasmas. There, finite arrangements of these dust clusters can be studied in different geometries ranging from 1D to 3D. The structure and the mode dynamics in these systems will be discussed.

  2. Analysis of stress in bone and microimplants during en-masse retraction of maxillary and mandibular anterior teeth with different insertion angulations: a 3-dimensional finite element analysis study. (United States)

    Jasmine, M Issa Fathima; Yezdani, A Arif; Tajir, Faisal; Venu, R Murali


    The proper angle of microimplant insertion is important for cortical anchorage, patient safety, and biomechanical control. However, the actual impact of different insertion angulations on stability is unknown. To perform 3-dimensional finite element analysis, finite element models of a maxilla and a mandible with types D3 and D2 bone quality, and of microimplants with a diameter of 1.3 mm and lengths of 8 and 7 mm were generated. The microimplants were inserted at 30°, 45°, 60°, and 90° to the bone surface. A simulated horizontal orthodontic force of 200 g was applied to the center of the microimplant head, and stress distribution and its magnitude were analyzed with a 3-dimensional finite element analysis program. The maximum von Mises stresses in the microimplant and the cortical bone decreased as the insertion angle increased. Analysis of the stress distribution in the cortical and cancellous bones showed that the stress was absorbed mostly in the cortical bone, and little was transmitted to the cancellous bone. The maximum von Mises stress was higher in type D3 bone quality than type D2 bone quality. Placement of microimplants at a 90° angulation in the bone reduces the stress concentration, thereby increasing the likelihood of implant stabilization. Perpendicular insertion offers more stability to orthodontic loading. Copyright © 2012 American Association of Orthodontists. Published by Mosby, Inc. All rights reserved.

  3. Finite element procedures

    CERN Document Server

    Bathe, Klaus-Jürgen


    Finite element procedures are now an important and frequently indispensable part of engineering analyses and scientific investigations. This book focuses on finite element procedures that are very useful and are widely employed. Formulations for the linear and nonlinear analyses of solids and structures, fluids, and multiphysics problems are presented, appropriate finite elements are discussed, and solution techniques for the governing finite element equations are given. The book presents general, reliable, and effective procedures that are fundamental and can be expected to be in use for a long time. The given procedures form also the foundations of recent developments in the field.

  4. Finite Discrete Gabor Analysis

    DEFF Research Database (Denmark)

    Søndergaard, Peter Lempel


    frequency bands at certain times. Gabor theory can be formulated for both functions on the real line and for discrete signals of finite length. The two theories are largely the same because many aspects come from the same underlying theory of locally compact Abelian groups. The two types of Gabor systems...... on the real line to be well approximated by finite and discrete Gabor frames. This method of approximation is especially attractive because efficient numerical methods exists for doing computations with finite, discrete Gabor systems. This thesis presents new algorithms for the efficient computation of finite...

  5. Fractional finite Fourier transform. (United States)

    Khare, Kedar; George, Nicholas


    We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.

  6. Three-dimensional finite element analysis of the stress distribution pattern in a mandibular first molar tooth restored with five different restorative materials. (United States)

    D'souza, Kathleen Manuela; Aras, Meena Ajay


    Badly broken or structurally compromised posterior teeth are frequently associated with crown/root fracture. Numerous restorative materials have been used to fabricate indirect full-coverage restorations for such teeth. This study aims to evaluate and compare the effect of restorative materials on the stress distribution pattern in a mandibular first molar tooth, under varying loading conditions and to compare the stress distribution pattern in five commonly used indirect restorative materials. Five three-dimensional finite element models representing a mandibular first molar tooth restored with crowns of gold, porcelain fused to metal, composite (Artglass), alumina-based zirconia (In-Ceram Zirconia [ICZ]), and double-layered zirconia-based materials (zirconia core veneered with porcelain, Lava) were constructed, using a Finite Element Analysis Software (ANSYS version 10; ANSYS Inc., Canonsburg, PA, USA). Two loading conditions were applied, simulating maximum bite force of 600 N axially and normal masticatory bite force of 225 N axially and nonaxially. Both all-ceramic crowns allowed the least amount of stress distribution to the surrounding tooth structure. In maximum bite force-simulation test, alumina-based all-ceramic crown displayed the highest von Mises stresses (123.745 MPa). In the masticatory bite force-simulation test, both all-ceramic crowns (122.503-133.13 MPa) displayed the highest von Mises stresses. ICZ crown displayed the highest peak von Mises stress values under maximum and masticatory bite forces. ICZ and Lava crowns also allowed the least amount of stress distribution to the surrounding tooth structure, which is indicative of a favorable response of the underlying tooth structure to the overlying full-coverage indirect restorative material. These results suggest that ICZ and Lava crowns can be recommended for clinical use in cases of badly damaged teeth.

  7. A three-dimensional upwind finite element point implicit unstructured grid Euler solver (United States)

    Thareja, Rajiv R.; Morgan, Ken; Peraire, Jaime; Peiro, Joaquin


    A three-dimensional upwind finite element technique that uses cell-centered quantities and implicit and/or explicit time marching was developed for computing hypersonic inviscid flows using adaptive unstructured grids. This technique was used to predict shock interference on a swept cylinder. An attempt was made to determine the flowfield and, in particular, the pressure augmentation caused by an impinging shock on the swept leading edge of a cowl lip of an engine inlet.

  8. Gradient Calculation Methods on Arbitrary Polyhedral Unstructured Meshes for Cell-Centered CFD Solvers (United States)

    Sozer, Emre; Brehm, Christoph; Kiris, Cetin C.


    A survey of gradient reconstruction methods for cell-centered data on unstructured meshes is conducted within the scope of accuracy assessment. Formal order of accuracy, as well as error magnitudes for each of the studied methods, are evaluated on a complex mesh of various cell types through consecutive local scaling of an analytical test function. The tests highlighted several gradient operator choices that can consistently achieve 1st order accuracy regardless of cell type and shape. The tests further offered error comparisons for given cell types, leading to the observation that the "ideal" gradient operator choice is not universal. Practical implications of the results are explored via CFD solutions of a 2D inviscid standing vortex, portraying the discretization error properties. A relatively naive, yet largely unexplored, approach of local curvilinear stencil transformation exhibited surprisingly favorable properties

  9. Finite Control in Korean (United States)

    Lee, Kum Young


    This thesis explores finite control in Korean. An overview of the previous studies of control shows that the mainstream literature on control has consistently argued that referential dependence between an overt matrix argument and an embedded null subject is characteristic of non-finite clauses which contain a PRO subject. Moreover, although some…

  10. Designs and finite geometries

    CERN Document Server


    Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics. Designs and Finite Geometries serves as an excellent reference, providing insight into some of the most important research issues in the field.

  11. Finite Virtual State Machines


    Senhadji Navarro, Raouf; García Vargas, Ignacio


    This letter proposes a new model of state machine called Finite Virtual State Machine (FVSM). A memory-based architecture and a procedure for generating FVSM implementations from Finite State Machines (FSMs) are presented. FVSM implementations provide advantages in speed over conventional RAM-based FSM implementations. The results of experiments prove the feasibility of this approach.

  12. On Constructing Finite, Finitely Subadditive Outer Measures, and Submodularity

    Directory of Open Access Journals (Sweden)

    Charles Traina


    functions on the lattice generated by . Lastly, we describe a construction of a finite, finitely subadditive outer measure given an arbitrary family of subsets, ℬ, of and a nonnegative, finite set function defined on ℬ.

  13. Parallel direct solver for finite element modeling of manufacturing processes

    DEFF Research Database (Denmark)

    Nielsen, Chris Valentin; Martins, P.A.F.


    The central processing unit (CPU) time is of paramount importance in finite element modeling of manufacturing processes. Because the most significant part of the CPU time is consumed in solving the main system of equations resulting from finite element assemblies, different approaches have been...... developed to optimize solutions and reduce the overall computational costs of large finite element models....


    Energy Technology Data Exchange (ETDEWEB)



    The author discusses quarkonium spectral functions at finite temperature reconstructed using the Maximum Entropy Method. The author shows in particular that the J/{psi} survives in the deconfined phase up to 1.5T{sub c}.

  15. Finite BMS transformations

    Energy Technology Data Exchange (ETDEWEB)

    Barnich, Glenn [Physique Théorique et Mathématique,Université Libre de Bruxelles and International Solvay Institutes,Campus Plaine C.P. 231, B-1050 Bruxelles (Belgium); Troessaert, Cédric [Centro de Estudios Científicos (CECs),Arturo Prat 514, Valdivia (Chile)


    The action of finite BMS and Weyl transformations on the gravitational data at null infinity is worked out in three and four dimensions in the case of an arbitrary conformal factor for the boundary metric induced on Scri.

  16. Advanced finite element technologies

    CERN Document Server

    Wriggers, Peter


    The book presents an overview of the state of research of advanced finite element technologies. Besides the mathematical analysis, the finite element development and their engineering applications are shown to the reader. The authors give a survey of the methods and technologies concerning efficiency, robustness and performance aspects. The book covers the topics of mathematical foundations for variational approaches and the mathematical understanding of the analytical requirements of modern finite element methods. Special attention is paid to finite deformations, adaptive strategies, incompressible, isotropic or anisotropic material behavior and the mathematical and numerical treatment of the well-known locking phenomenon. Beyond that new results for the introduced approaches are presented especially for challenging nonlinear problems.

  17. Numerical stability of finite difference algorithms for electrochemical kinetic simulations: Matrix stability analysis of the classic explicit, fully implicit and Crank-Nicolson methods and typical problems involving mixed boundary conditions

    DEFF Research Database (Denmark)

    Bieniasz, Leslaw K.; Østerby, Ole; Britz, Dieter


    The stepwise numerical stability of the classic explicit, fully implicit and Crank-Nicolson finite difference discretizations of example diffusional initial boundary value problems from electrochemical kinetics has been investigated using the matrix method of stability analysis. Special attention...... has been paid to the effect of the discretization of the mixed, linear boundary condition with time-dependent coefficients on stability, assuming the two-point forward-difference approximations for the gradient at the left boundary (electrode). Under accepted assumptions one obtains the usual...... stability criteria for the classic explicit and fully implicit methods. The Crank-Nicolson method turns out to be only conditionally stable in contrast to the current thought regarding this method....

  18. A combined finite volume-nonconforming finite element scheme for compressible two phase flow in porous media

    KAUST Repository

    Saad, Bilal Mohammed


    We propose and analyze a combined finite volume-nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. The diffusion term, which can be anisotropic and heterogeneous, is discretized by piecewise linear nonconforming triangular finite elements. The other terms are discretized by means of a cell-centered finite volume scheme on a dual mesh, where the dual volumes are constructed around the sides of the original mesh. The relative permeability of each phase is decentred according the sign of the velocity at the dual interface. This technique also ensures the validity of the discrete maximum principle for the saturation under a non restrictive shape regularity of the space mesh and the positiveness of all transmissibilities. Next, a priori estimates on the pressures and a function of the saturation that denote capillary terms are established. These stabilities results lead to some compactness arguments based on the use of the Kolmogorov compactness theorem, and allow us to derive the convergence of a subsequence of the sequence of approximate solutions to a weak solution of the continuous equations, provided the mesh size tends to zero. The proof is given for the complete system when the density of the each phase depends on its own pressure. © 2014 Springer-Verlag Berlin Heidelberg.

  19. Automation of finite element methods

    CERN Document Server

    Korelc, Jože


    New finite elements are needed as well in research as in industry environments for the development of virtual prediction techniques. The design and implementation of novel finite elements for specific purposes is a tedious and time consuming task, especially for nonlinear formulations. The automation of this process can help to speed up this process considerably since the generation of the final computer code can be accelerated by order of several magnitudes. This book provides the reader with the required knowledge needed to employ modern automatic tools like AceGen within solid mechanics in a successful way. It covers the range from the theoretical background, algorithmic treatments to many different applications. The book is written for advanced students in the engineering field and for researchers in educational and industrial environments.

  20. Why and how of finite elements

    Energy Technology Data Exchange (ETDEWEB)

    Ackroyd, R.T. (UKAEA Risley Nuclear Power Development Establishment)


    The development of the finite element method is traced to show how ideas from structural and fluid mechanics, the calculus of variations, functional analysis and the calculus of finite differences have been forged to provide a tool which minimizes the mismatch between the behaviour of a continuous system and that of a discrete model of the system assembled from finite elements. Geometrical flexibility of the model is achieved by the use of polygonal and curved elements. The behaviour of any point of an element is described in terms of its behaviour at discrete points or nodes of the element. In treating neutron transport the finite element method can be applied to phase-space, or the spatial dependence can be treated by the use of finite elements in conjuction with expansions in orthogonal functions for the directional dependence. The maximum principle for the second-order even-parity Boltzmann equations is used to demonstrate the precision and flexibility of the finite element method by solving the problems of a doglegged duct in a shield and a cylindrical fuel element in a square lattice cell. The geometrical interpretation of the boundary-free maximum principle with the aid of a suitable Hilbert space then leads to completely boundary-free weighted residual or Galerkin schemes for both the first- and second-order forms of the Boltzmann equation. Imposing essential boundary conditions leads to classical schemes, a sketch of finite element treatments of the multigroup Boltzmann equation is given.