Finite Difference Schemes as Algebraic Correspondences between Layers
Malykh, Mikhail; Sevastianov, Leonid
2018-02-01
For some differential equations, especially for Riccati equation, new finite difference schemes are suggested. These schemes define protective correspondences between the layers. Calculation using these schemes can be extended to the area beyond movable singularities of exact solution without any error accumulation.
Finite-difference schemes for anisotropic diffusion
Energy Technology Data Exchange (ETDEWEB)
Es, Bram van, E-mail: es@cwi.nl [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)
2014-09-01
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.
Non Standard Finite Difference Scheme for Mutualistic Interaction Description
Gabbriellini, Gianluca
2012-01-01
One of the more interesting themes of the mathematical ecology is the description of the mutualistic interaction between two interacting species. Based on continuous-time model developed by Holland and DeAngelis 2009 for consumer-resource mutualism description, this work deals with the application of the Mickens Non Standard Finite Difference method to transform the continuous-time scheme into a discrete-time one. It has been proved that the Mickens scheme is dynamically consistent with the o...
High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains
Fisher, Travis C.; Carpenter, Mark H.
2013-01-01
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.
Sman, van der R.G.M.
2006-01-01
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
The finite precision computation and the nonconvergence of difference scheme
Pengfei, Wang; Jianping, Li
2008-01-01
The authors show that the round-off error can break the consistency which is the premise of using the difference equation to replace the original differential equations. We therefore proposed a theoretical approach to investigate this effect, and found that the difference scheme can not guarantee the convergence of the actual compute result to the analytical one. A conservation scheme experiment is applied to solve a simple linear differential equation satisfing the LAX equivalence theorem in...
A perturbational h4 exponential finite difference scheme for the convective diffusion equation
International Nuclear Information System (INIS)
Chen, G.Q.; Gao, Z.; Yang, Z.F.
1993-01-01
A perturbational h 4 compact exponential finite difference scheme with diagonally dominant coefficient matrix and upwind effect is developed for the convective diffusion equation. Perturbations of second order are exerted on the convective coefficients and source term of an h 2 exponential finite difference scheme proposed in this paper based on a transformation to eliminate the upwind effect of the convective diffusion equation. Four numerical examples including one- to three-dimensional model equations of fluid flow and a problem of natural convective heat transfer are given to illustrate the excellent behavior of the present exponential schemes. Besides, the h 4 accuracy of the perturbational scheme is verified using double precision arithmetic
Directory of Open Access Journals (Sweden)
Peng Jiang
2013-01-01
Full Text Available The authors attempt to construct the exact finite-difference schemes for linear stochastic differential equations with constant coefficients. The explicit solutions to Itô and Stratonovich linear stochastic differential equations with constant coefficients are adopted with the view of providing exact finite-difference schemes to solve them. In particular, the authors utilize the exact finite-difference schemes of Stratonovich type linear stochastic differential equations to solve the Kubo oscillator that is widely used in physics. Further, the authors prove that the exact finite-difference schemes can preserve the symplectic structure and first integral of the Kubo oscillator. The authors also use numerical examples to prove the validity of the numerical methods proposed in this paper.
Accuracy of spectral and finite difference schemes in 2D advection problems
DEFF Research Database (Denmark)
Naulin, V.; Nielsen, A.H.
2003-01-01
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....
Four-level conservative finite-difference schemes for Boussinesq paradigm equation
Kolkovska, N.
2013-10-01
In this paper a two-parametric family of four level conservative finite difference schemes is constructed for the multidimensional Boussinesq paradigm equation. The schemes are explicit in the sense that no inner iterations are needed for evaluation of the numerical solution. The preservation of the discrete energy with this method is proved. The schemes have been numerically tested on one soliton propagation model and two solitons interaction model. The numerical experiments demonstrate that the proposed family of schemes has second order of convergence in space and time steps in the discrete maximal norm.
International Nuclear Information System (INIS)
Kriventsev, Vladimir
2000-09-01
Most of thermal hydraulic processes in nuclear engineering can be described by general convection-diffusion equations that are often can be simulated numerically with finite-difference method (FDM). An effective scheme for finite-difference discretization of such equations is presented in this report. The derivation of this scheme is based on analytical solutions of a simplified one-dimensional equation written for every control volume of the finite-difference mesh. These analytical solutions are constructed using linearized representations of both diffusion coefficient and source term. As a result, the Efficient Finite-Differencing (EFD) scheme makes it possible to significantly improve the accuracy of numerical method even using mesh systems with fewer grid nodes that, in turn, allows to speed-up numerical simulation. EFD has been carefully verified on the series of sample problems for which either analytical or very precise numerical solutions can be found. EFD has been compared with other popular FDM schemes including novel, accurate (as well as sophisticated) methods. Among the methods compared were well-known central difference scheme, upwind scheme, exponential differencing and hybrid schemes of Spalding. Also, newly developed finite-difference schemes, such as the the quadratic upstream (QUICK) scheme of Leonard, the locally analytic differencing (LOAD) scheme of Wong and Raithby, the flux-spline scheme proposed by Varejago and Patankar as well as the latest LENS discretization of Sakai have been compared. Detailed results of this comparison are given in this report. These tests have shown a high efficiency of the EFD scheme. For most of sample problems considered EFD has demonstrated the numerical error that appeared to be in orders of magnitude lower than that of other discretization methods. Or, in other words, EFD has predicted numerical solution with the same given numerical error but using much fewer grid nodes. In this report, the detailed
Stability of finite difference schemes for generalized von Foerster equations with renewal
Directory of Open Access Journals (Sweden)
Henryk Leszczyński
2014-01-01
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.
High-order asynchrony-tolerant finite difference schemes for partial differential equations
Aditya, Konduri; Donzis, Diego A.
2017-12-01
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.
A multigrid algorithm for the cell-centered finite difference scheme
Ewing, Richard E.; Shen, Jian
1993-01-01
In this article, we discuss a non-variational V-cycle multigrid algorithm based on the cell-centered finite difference scheme for solving a second-order elliptic problem with discontinuous coefficients. Due to the poor approximation property of piecewise constant spaces and the non-variational nature of our scheme, one step of symmetric linear smoothing in our V-cycle multigrid scheme may fail to be a contraction. Again, because of the simple structure of the piecewise constant spaces, prolongation and restriction are trivial; we save significant computation time with very promising computational results.
A hybrid finite-volume and finite difference scheme for depth-integrated non-hydrostatic model
Yin, Jing; Sun, Jia-wen; Wang, Xing-gang; Yu, Yong-hai; Sun, Zhao-chen
2017-06-01
A depth-integrated, non-hydrostatic model with hybrid finite difference and finite volume numerical algorithm is proposed in this paper. By utilizing a fraction step method, the governing equations are decomposed into hydrostatic and non-hydrostatic parts. The first part is solved by using the finite volume conservative discretization method, whilst the latter is considered by solving discretized Poisson-type equations with the finite difference method. The second-order accuracy, both in time and space, of the finite volume scheme is achieved by using an explicit predictor-correction step and linear construction of variable state in cells. The fluxes across the cell faces are computed in a Godunov-based manner by using MUSTA scheme. Slope and flux limiting technique is used to equip the algorithm with total variation dimensioning property for shock capturing purpose. Wave breaking is treated as a shock by switching off the non-hydrostatic pressure in the steep wave front locally. The model deals with moving wet/dry front in a simple way. Numerical experiments are conducted to verify the proposed model.
Application of the symplectic finite-difference time-domain scheme to electromagnetic simulation
International Nuclear Information System (INIS)
Sha, Wei; Huang, Zhixiang; Wu, Xianliang; Chen, Mingsheng
2007-01-01
An explicit fourth-order finite-difference time-domain (FDTD) scheme using the symplectic integrator is applied to electromagnetic simulation. A feasible numerical implementation of the symplectic FDTD (SFDTD) scheme is specified. In particular, new strategies for the air-dielectric interface treatment and the near-to-far-field (NFF) transformation are presented. By using the SFDTD scheme, both the radiation and the scattering of three-dimensional objects are computed. Furthermore, the energy-conserving characteristic hold for the SFDTD scheme is verified under long-term simulation. Numerical results suggest that the SFDTD scheme is more efficient than the traditional FDTD method and other high-order methods, and can save computational resources
Computational Aero-Acoustic Using High-order Finite-Difference Schemes
DEFF Research Database (Denmark)
Zhu, Wei Jun; Shen, Wen Zhong; Sørensen, Jens Nørkær
2007-01-01
are solved using the in-house flow solver EllipSys2D/3D which is a second-order finite volume code. The acoustic solution is found by solving the acoustic equations using high-order finite difference schemes. The incompressible flow equations and the acoustic equations are solved at the same time levels......In this paper, a high-order technique to accurately predict flow-generated noise is introduced. The technique consists of solving the viscous incompressible flow equations and inviscid acoustic equations using a incompressible/compressible splitting technique. The incompressible flow equations...
Enhanced finite difference scheme for the neutron diffusion equation using the importance function
International Nuclear Information System (INIS)
Vagheian, Mehran; Vosoughi, Naser; Gharib, Morteza
2016-01-01
Highlights: • An enhanced finite difference scheme for the neutron diffusion equation is proposed. • A seven-step algorithm is considered based on the importance function. • Mesh points are distributed through entire reactor core with respect to the importance function. • The results all proved that the proposed algorithm is highly efficient. - Abstract: Mesh point positions in Finite Difference Method (FDM) of discretization for the neutron diffusion equation can remarkably affect the averaged neutron fluxes as well as the effective multiplication factor. In this study, by aid of improving the mesh point positions, an enhanced finite difference scheme for the neutron diffusion equation is proposed based on the neutron importance function. In order to determine the neutron importance function, the adjoint (backward) neutron diffusion calculations are performed in the same procedure as for the forward calculations. Considering the neutron importance function, the mesh points can be improved through the entire reactor core. Accordingly, in regions with greater neutron importance, density of mesh elements is higher than that in regions with less importance. The forward calculations are then performed for both of the uniform and improved non-uniform mesh point distributions and the results (the neutron fluxes along with the corresponding eigenvalues) for the two cases are compared with each other. The results are benchmarked against the reference values (with fine meshes) for Kang and Rod Bundle BWR benchmark problems. These benchmark cases revealed that the improved non-uniform mesh point distribution is highly efficient.
Development and application of a third order scheme of finite differences centered in mesh
International Nuclear Information System (INIS)
Delfin L, A.; Alonso V, G.; Valle G, E. del
2003-01-01
In this work the development of a third order scheme of finite differences centered in mesh is presented and it is applied in the numerical solution of those diffusion equations in multi groups in stationary state and X Y geometry. Originally this scheme was developed by Hennart and del Valle for the monoenergetic diffusion equation with a well-known source and they show that the one scheme is of third order when comparing the numerical solution with the analytical solution of a model problem using several mesh refinements and boundary conditions. The scheme by them developed it also introduces the application of numeric quadratures to evaluate the rigidity matrices and of mass that its appear when making use of the finite elements method of Galerkin. One of the used quadratures is the open quadrature of 4 points, no-standard, of Newton-Cotes to evaluate in approximate form the elements of the rigidity matrices. The other quadrature is that of 3 points of Radau that it is used to evaluate the elements of all the mass matrices. One of the objectives of these quadratures are to eliminate the couplings among the Legendre moments 0 and 1 associated to the left and right faces as those associated to the inferior and superior faces of each cell of the discretization. The other objective is to satisfy the particles balance in weighed form in each cell. In this work it expands such development to multiplicative means considering several energy groups. There are described diverse details inherent to the technique, particularly those that refer to the simplification of the algebraic systems that appear due to the space discretization. Numerical results for several test problems are presented and are compared with those obtained with other nodal techniques. (Author)
Directory of Open Access Journals (Sweden)
G. F. Sun
2015-01-01
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.
A simple finite-difference scheme for handling topography with the first-order wave equation
Mulder, W.A.; Huiskes, M.J.
2017-01-01
One approach to incorporate topography in seismic finite-difference codes is a local modification of the difference operators near the free surface. An earlier paper described an approach for modelling irregular boundaries in a constant-density acoustic finite-difference code, based on the
A simple finite-difference scheme for handling topography with the second-order wave equation
Mulder, W.A.
2017-01-01
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
Simulations of viscous and compressible gas-gas flows using high-order finite difference schemes
Capuano, M.; Bogey, C.; Spelt, P. D. M.
2018-05-01
A computational method for the simulation of viscous and compressible gas-gas flows is presented. It consists in solving the Navier-Stokes equations associated with a convection equation governing the motion of the interface between two gases using high-order finite-difference schemes. A discontinuity-capturing methodology based on sensors and a spatial filter enables capturing shock waves and deformable interfaces. One-dimensional test cases are performed as validation and to justify choices in the numerical method. The results compare well with analytical solutions. Shock waves and interfaces are accurately propagated, and remain sharp. Subsequently, two-dimensional flows are considered including viscosity and thermal conductivity. In Richtmyer-Meshkov instability, generated on an air-SF6 interface, the influence of the mesh refinement on the instability shape is studied, and the temporal variations of the instability amplitude is compared with experimental data. Finally, for a plane shock wave propagating in air and impacting a cylindrical bubble filled with helium or R22, numerical Schlieren pictures obtained using different grid refinements are found to compare well with experimental shadow-photographs. The mass conservation is verified from the temporal variations of the mass of the bubble. The mean velocities of pressure waves and bubble interface are similar to those obtained experimentally.
Application of compact finite-difference schemes to simulations of stably stratified fluid flows
Czech Academy of Sciences Publication Activity Database
Bodnár, Tomáš; Beneš, L.; Fraunie, P.; Kozel, Karel
2012-01-01
Roč. 219, č. 7 (2012), s. 3336-3353 ISSN 0096-3003 Institutional support: RVO:61388998 Keywords : stratification * finite- difference * finite-volume * Runge-Kutta Subject RIV: BA - General Mathematics Impact factor: 1.349, year: 2012 http://www.sciencedirect.com/science/article/pii/S0096300311010988
De Hon, B. P.; Arnold, J. M.
2016-01-01
Time-domain 3-D lattice Green's function (LGF) sequences can be evaluated using a single-lattice point recurrence scheme, and play an important role in finite-difference Green's function diakoptics. Asymptotically, at large distances, the LGFs in three dimensions can be described in terms of six
Mickens, Ronald E.
1989-01-01
A family of conditionally stable, forward Euler finite difference equations can be constructed for the simplest equation of Schroedinger type, namely u sub t - iu sub xx. Generalization of this result to physically realistic Schroedinger type equations is presented.
International Nuclear Information System (INIS)
Tan, Sirui; Huang, Lianjie
2014-01-01
For modeling scalar-wave propagation in geophysical problems using finite-difference schemes, optimizing the coefficients of the finite-difference operators can reduce numerical dispersion. Most optimized finite-difference schemes for modeling seismic-wave propagation suppress only spatial but not temporal dispersion errors. We develop a novel optimized finite-difference scheme for numerical scalar-wave modeling to control dispersion errors not only in space but also in time. Our optimized scheme is based on a new stencil that contains a few more grid points than the standard stencil. We design an objective function for minimizing relative errors of phase velocities of waves propagating in all directions within a given range of wavenumbers. Dispersion analysis and numerical examples demonstrate that our optimized finite-difference scheme is computationally up to 2.5 times faster than the optimized schemes using the standard stencil to achieve the similar modeling accuracy for a given 2D or 3D problem. Compared with the high-order finite-difference scheme using the same new stencil, our optimized scheme reduces 50 percent of the computational cost to achieve the similar modeling accuracy. This new optimized finite-difference scheme is particularly useful for large-scale 3D scalar-wave modeling and inversion
A simple finite-difference scheme for handling topography with the first-order wave equation
Mulder, W. A.; Huiskes, M. J.
2017-07-01
One approach to incorporate topography in seismic finite-difference codes is a local modification of the difference operators near the free surface. An earlier paper described an approach for modelling irregular boundaries in a constant-density acoustic finite-difference code, based on the second-order formulation of the wave equation that only involves the pressure. Here, a similar method is considered for the first-order formulation in terms of pressure and particle velocity, using a staggered finite-difference discretization both in space and in time. In one space dimension, the boundary conditions consist in imposing antisymmetry for the pressure and symmetry for particle velocity components. For the pressure, this means that the solution values as well as all even derivatives up to a certain order are zero on the boundary. For the particle velocity, all odd derivatives are zero. In 2D, the 1-D assumption is used along each coordinate direction, with antisymmetry for the pressure along the coordinate and symmetry for the particle velocity component parallel to that coordinate direction. Since the symmetry or antisymmetry should hold along the direction normal to the boundary rather than along the coordinate directions, this generates an additional numerical error on top of the time stepping errors and the errors due to the interior spatial discretization. Numerical experiments in 2D and 3D nevertheless produce acceptable results.
Energy Technology Data Exchange (ETDEWEB)
Karlsen, Kenneth Hvistendal; Risebro, Nils Henrik
2000-09-01
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)
International Nuclear Information System (INIS)
Saha Ray, S.; Patra, A.
2012-01-01
Highlights: ► In this paper fractional neutron point kinetic equation has been analyzed. ► The numerical solution for fractional neutron point kinetic equation is obtained. ► Explicit Finite Difference Method has been applied. ► Supercritical reactivity, critical reactivity and subcritical reactivity analyzed. ► Comparison between fractional and classical neutron density is presented. - Abstract: In the present article, a numerical procedure to efficiently calculate the solution for fractional point kinetics equation in nuclear reactor dynamics is investigated. The Explicit Finite Difference Method is applied to solve the fractional neutron point kinetic equation with the Grunwald–Letnikov (GL) definition (). Fractional Neutron Point Kinetic Model has been analyzed for the dynamic behavior of the neutron motion in which the relaxation time associated with a variation in the neutron flux involves a fractional order acting as exponent of the relaxation time, to obtain the best operation of a nuclear reactor dynamics. Results for neutron dynamic behavior for subcritical reactivity, supercritical reactivity and critical reactivity and also for different values of fractional order have been presented and compared with the classical neutron point kinetic (NPK) equation as well as the results obtained by the learned researchers .
Wang, Hua; Tao, Guo; Shang, Xue-Feng; Fang, Xin-Ding; Burns, Daniel R.
2013-12-01
In acoustic logging-while-drilling (ALWD) finite difference in time domain (FDTD) simulations, large drill collar occupies, most of the fluid-filled borehole and divides the borehole fluid into two thin fluid columns (radius ˜27 mm). Fine grids and large computational models are required to model the thin fluid region between the tool and the formation. As a result, small time step and more iterations are needed, which increases the cumulative numerical error. Furthermore, due to high impedance contrast between the drill collar and fluid in the borehole (the difference is >30 times), the stability and efficiency of the perfectly matched layer (PML) scheme is critical to simulate complicated wave modes accurately. In this paper, we compared four different PML implementations in a staggered grid finite difference in time domain (FDTD) in the ALWD simulation, including field-splitting PML (SPML), multiaxial PML(MPML), non-splitting PML (NPML), and complex frequency-shifted PML (CFS-PML). The comparison indicated that NPML and CFS-PML can absorb the guided wave reflection from the computational boundaries more efficiently than SPML and M-PML. For large simulation time, SPML, M-PML, and NPML are numerically unstable. However, the stability of M-PML can be improved further to some extent. Based on the analysis, we proposed that the CFS-PML method is used in FDTD to eliminate the numerical instability and to improve the efficiency of absorption in the PML layers for LWD modeling. The optimal values of CFS-PML parameters in the LWD simulation were investigated based on thousands of 3D simulations. For typical LWD cases, the best maximum value of the quadratic damping profile was obtained using one d 0. The optimal parameter space for the maximum value of the linear frequency-shifted factor ( α 0) and the scaling factor ( β 0) depended on the thickness of the PML layer. For typical formations, if the PML thickness is 10 grid points, the global error can be reduced to <1
Kim, Jae Wook
2013-05-01
This paper proposes a novel systematic approach for the parallelization of pentadiagonal compact finite-difference schemes and filters based on domain decomposition. The proposed approach allows a pentadiagonal banded matrix system to be split into quasi-disjoint subsystems by using a linear-algebraic transformation technique. As a result the inversion of pentadiagonal matrices can be implemented within each subdomain in an independent manner subject to a conventional halo-exchange process. The proposed matrix transformation leads to new subdomain boundary (SB) compact schemes and filters that require three halo terms to exchange with neighboring subdomains. The internode communication overhead in the present approach is equivalent to that of standard explicit schemes and filters based on seven-point discretization stencils. The new SB compact schemes and filters demand additional arithmetic operations compared to the original serial ones. However, it is shown that the additional cost becomes sufficiently low by choosing optimal sizes of their discretization stencils. Compared to earlier published results, the proposed SB compact schemes and filters successfully reduce parallelization artifacts arising from subdomain boundaries to a level sufficiently negligible for sophisticated aeroacoustic simulations without degrading parallel efficiency. The overall performance and parallel efficiency of the proposed approach are demonstrated by stringent benchmark tests.
A convergent 2D finite-difference scheme for the Dirac–Poisson system and the simulation of graphene
International Nuclear Information System (INIS)
Brinkman, D.; Heitzinger, C.; Markowich, P.A.
2014-01-01
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
A convergent 2D finite-difference scheme for the Dirac-Poisson system and the simulation of graphene
Brinkman, Daniel; Heitzinger, Clemens Heitzinger; Markowich, Peter A.
2014-01-01
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.
A novel 2.5D finite difference scheme for simulations of resistivity logging in anisotropic media
Zeng, Shubin; Chen, Fangzhou; Li, Dawei; Chen, Ji; Chen, Jiefu
2018-03-01
The objective of this study is to develop a method to model 3D resistivity well logging problems in 2D formation with anisotropy, known as 2.5D modeling. The traditional 1D forward modeling extensively used in practice lacks the capability of modeling 2D formation. A 2.5D finite difference method (FDM) solving all the electric and magnetic field components simultaneously is proposed. Compared to other previous 2.5D FDM schemes, this method is more straightforward in modeling fully anisotropic media and easy to be implemented. Fourier transform is essential to this FDM scheme, and by employing Gauss-Legendre (GL) quadrature rule the computational time of this step can be greatly reduced. In the numerical examples, we first demonstrate the validity of the FDM scheme with GL rule by comparing with 1D forward modeling for layered anisotropic problems, and then we model a complicated 2D formation case and find that the proposed 2.5D FD scheme is much more efficient than 3D numerical methods.
On a Stable and Consistent Finite Difference Scheme for a Time ...
African Journals Online (AJOL)
NJABS
established time independent Schrodinger Wave Equation (SWE). To develop the stability criterion .... the rate at which signals in the numerical scheme travel will be faster than their real world counterparts and this unrealistic expectation leads ...
Kiessling, Jonas
2014-05-06
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.
An efficient hybrid pseudospectral/finite-difference scheme for solving the TTI pure P-wave equation
Zhan, Ge
2013-02-19
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.
An efficient hybrid pseudospectral/finite-difference scheme for solving the TTI pure P-wave equation
International Nuclear Information System (INIS)
Zhan, Ge; Pestana, Reynam C; Stoffa, Paul L
2013-01-01
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. (paper)
Finite-volume scheme for anisotropic diffusion
Energy Technology Data Exchange (ETDEWEB)
Es, Bram van, E-mail: bramiozo@gmail.com [Centrum Wiskunde & Informatica, P.O. Box 94079, 1090GB Amsterdam (Netherlands); FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, The Netherlands" 1 (Netherlands); Koren, Barry [Eindhoven University of Technology (Netherlands); Blank, Hugo J. de [FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, The Netherlands" 1 (Netherlands)
2016-02-01
In this paper, we apply a special finite-volume scheme, limited to smooth temperature distributions and Cartesian grids, to test the importance of connectivity of the finite volumes. The area of application is nuclear fusion plasma with field line aligned temperature gradients and extreme anisotropy. We apply the scheme to the anisotropic heat-conduction equation, and compare its results with those of existing finite-volume schemes for anisotropic diffusion. Also, we introduce a general model adaptation of the steady diffusion equation for extremely anisotropic diffusion problems with closed field lines.
Yang, Lei; Yan, Hongyong; Liu, Hong
2017-03-01
Implicit staggered-grid finite-difference (ISFD) scheme is competitive for its great accuracy and stability, whereas its coefficients are conventionally determined by the Taylor-series expansion (TE) method, leading to a loss in numerical precision. In this paper, we modify the TE method using the minimax approximation (MA), and propose a new optimal ISFD scheme based on the modified TE (MTE) with MA method. The new ISFD scheme takes the advantage of the TE method that guarantees great accuracy at small wavenumbers, and keeps the property of the MA method that keeps the numerical errors within a limited bound at the same time. Thus, it leads to great accuracy for numerical solution of the wave equations. We derive the optimal ISFD coefficients by applying the new method to the construction of the objective function, and using a Remez algorithm to minimize its maximum. Numerical analysis is made in comparison with the conventional TE-based ISFD scheme, indicating that the MTE-based ISFD scheme with appropriate parameters can widen the wavenumber range with high accuracy, and achieve greater precision than the conventional ISFD scheme. The numerical modeling results also demonstrate that the MTE-based ISFD scheme performs well in elastic wave simulation, and is more efficient than the conventional ISFD scheme for elastic modeling.
El-Amin, Mohamed
2011-05-14
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.
Settle, Sean O.
2013-01-01
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.
Steger, J. L.; Dougherty, F. C.; Benek, J. A.
1983-01-01
A mesh system composed of multiple overset body-conforming grids is described for adapting finite-difference procedures to complex aircraft configurations. In this so-called 'chimera mesh,' a major grid is generated about a main component of the configuration and overset minor grids are used to resolve all other features. Methods for connecting overset multiple grids and modifications of flow-simulation algorithms are discussed. Computational tests in two dimensions indicate that the use of multiple overset grids can simplify the task of grid generation without an adverse effect on flow-field algorithms and computer code complexity.
International Nuclear Information System (INIS)
Aruchunan, E.
2015-01-01
In this paper, we have examined the effectiveness of the quarter-sweep iteration concept on conjugate gradient normal residual (CGNR) iterative method by using composite Simpson's (CS) and finite difference (FD) discretization schemes in solving Fredholm integro-differential equations. For comparison purposes, Gauss- Seidel (GS) and the standard or full- and half-sweep CGNR methods namely FSCGNR and HSCGNR are also presented. To validate the efficacy of the proposed method, several analyses were carried out such as computational complexity and percentage reduction on the proposed and existing methods. (author)
Additive operator-difference schemes splitting schemes
Vabishchevich, Petr N
2013-01-01
Applied mathematical modeling isconcerned with solving unsteady problems. This bookshows how toconstruct additive difference schemes to solve approximately unsteady multi-dimensional problems for PDEs. Two classes of schemes are highlighted: methods of splitting with respect to spatial variables (alternating direction methods) and schemes of splitting into physical processes. Also regionally additive schemes (domain decomposition methods)and unconditionally stable additive schemes of multi-component splitting are considered for evolutionary equations of first and second order as well as for sy
Kumari, Komal; Donzis, Diego
2017-11-01
Highly resolved computational simulations on massively parallel machines are critical in understanding the physics of a vast number of complex phenomena in nature governed by partial differential equations. Simulations at extreme levels of parallelism present many challenges with communication between processing elements (PEs) being a major bottleneck. In order to fully exploit the computational power of exascale machines one needs to devise numerical schemes that relax global synchronizations across PEs. This asynchronous computations, however, have a degrading effect on the accuracy of standard numerical schemes.We have developed asynchrony-tolerant (AT) schemes that maintain order of accuracy despite relaxed communications. We show, analytically and numerically, that these schemes retain their numerical properties with multi-step higher order temporal Runge-Kutta schemes. We also show that for a range of optimized parameters,the computation time and error for AT schemes is less than their synchronous counterpart. Stability of the AT schemes which depends upon history and random nature of delays, are also discussed. Support from NSF is gratefully acknowledged.
Kumar, A.; Rudy, D. H.; Drummond, J. P.; Harris, J. E.
1982-01-01
Several two- and three-dimensional external and internal flow problems solved on the STAR-100 and CYBER-203 vector processing computers are described. The flow field was described by the full Navier-Stokes equations which were then solved by explicit finite-difference algorithms. Problem results and computer system requirements are presented. Program organization and data base structure for three-dimensional computer codes which will eliminate or improve on page faulting, are discussed. Storage requirements for three-dimensional codes are reduced by calculating transformation metric data in each step. As a result, in-core grid points were increased in number by 50% to 150,000, with a 10% execution time increase. An assessment of current and future machine requirements shows that even on the CYBER-205 computer only a few problems can be solved realistically. Estimates reveal that the present situation is more storage limited than compute rate limited, but advancements in both storage and speed are essential to realistically calculate three-dimensional flow.
Directory of Open Access Journals (Sweden)
Alina BOGOI
2016-12-01
Full Text Available Supersonic/hypersonic flows with strong shocks need special treatment in Computational Fluid Dynamics (CFD in order to accurately capture the discontinuity location and his magnitude. To avoid numerical instabilities in the presence of discontinuities, the numerical schemes must generate low dissipation and low dispersion error. Consequently, the algorithms used to calculate the time and space-derivatives, should exhibit a low amplitude and phase error. This paper focuses on the comparison of the numerical results obtained by simulations with some high resolution numerical schemes applied on linear and non-linear one-dimensional conservation low. The analytical solutions are provided for all benchmark tests considering smooth periodical conditions. All the schemes converge to the proper weak solution for linear flux and smooth initial conditions. However, when the flux is non-linear, the discontinuities may develop from smooth initial conditions and the shock must be correctly captured. All the schemes accurately identify the shock position, with the price of the numerical oscillation in the vicinity of the sudden variation. We believe that the identification of this pure numerical behavior, without physical relevance, in 1D case is extremely useful to avoid problems related to the stability and convergence of the solution in the general 3D case.
Yu, Guojun
2012-10-01
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.
Yu, Guojun; Yu, Bo; Sun, Shuyu; Tao, Wenquan
2012-01-01
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.
Directory of Open Access Journals (Sweden)
A. R. Appadu
2013-01-01
for which the Reynolds number is 2 or 4. Some errors are computed, namely, the error rate with respect to the L1 norm, dispersion, and dissipation errors. We have both dissipative and dispersive errors, and this indicates that the methods generate artificial dispersion, though the partial differential considered is not dispersive. It is seen that the Lax-Wendroff and NSFD are quite good methods to approximate the 1D advection-diffusion equation at some values of k and h. Two optimisation techniques are then implemented to find the optimal values of k when h=0.02 for the Lax-Wendroff and NSFD schemes, and this is validated by numerical experiments.
International Nuclear Information System (INIS)
Zhao, S.; Lardjane, N.; Fedioun, I.
2014-01-01
Improved WENO schemes, Z, M, and their combination MZ, originally designed to capture sharper discontinuities than the classical fifth order Jiang-Shu scheme does, are evaluated for the purpose of implicit large eddy simulation of free shear flows. 1D Fourier analysis of errors reveals the built-in filter and dissipative properties of the schemes, which are subsequently applied to the canonical Rayleigh-Taylor and Taylor-Green flows. Large eddy simulations of a transonic non-reacting and a supersonic reacting air/H2 jets are then performed at resolution 128 * 128 * 512, showing no significant difference in the flow statistics. However, the computational time varies from one scheme to the other, the Z scheme providing the smaller wall-time due to larger allowed time steps. (authors)
An introduction to the UNCLE finite element scheme
International Nuclear Information System (INIS)
Enderby, J.A.
1983-01-01
UNCLE is a completely general finite element scheme which provides common input, output, equation-solving and other facilities for a family of finite element codes for linear and non-linear stress analysis, heat transfer etc. This report describes the concepts on which UNCLE is based and gives a general account of the facilities provided. (author)
A Note on Symplectic, Multisymplectic Scheme in Finite Element Method
Institute of Scientific and Technical Information of China (English)
GUO Han-Ying; JI Xiao-Mei; LI Yu-Qi; WU Ke
2001-01-01
We find that with uniform mesh, the numerical schemes derived from finite element method can keep a preserved symplectic structure in one-dimensional case and a preserved multisymplectic structure in two-dimensional case respectively. These results are in fact the intrinsic reason why the numerical experiments show that such finite element algorithms are accurate in practice.``
An introduction to the UNCLE finite element scheme
Energy Technology Data Exchange (ETDEWEB)
Enderby, J A [UK Atomic Energy Authority, Northern Division, Risley Nuclear Power Development Establishment, Risley, Warrington (United Kingdom)
1983-05-01
UNCLE is a completely general finite element scheme which provides common input, output, equation-solving and other facilities for a family of finite element codes for linear and non-linear stress analysis, heat transfer etc. This report describes the concepts on which UNCLE is based and gives a general account of the facilities provided. (author)
Mimetic finite difference method
Lipnikov, Konstantin; Manzini, Gianmarco; Shashkov, Mikhail
2014-01-01
The mimetic finite difference (MFD) method mimics fundamental properties of mathematical and physical systems including conservation laws, symmetry and positivity of solutions, duality and self-adjointness of differential operators, and exact mathematical identities of the vector and tensor calculus. This article is the first comprehensive review of the 50-year long history of the mimetic methodology and describes in a systematic way the major mimetic ideas and their relevance to academic and real-life problems. The supporting applications include diffusion, electromagnetics, fluid flow, and Lagrangian hydrodynamics problems. The article provides enough details to build various discrete operators on unstructured polygonal and polyhedral meshes and summarizes the major convergence results for the mimetic approximations. Most of these theoretical results, which are presented here as lemmas, propositions and theorems, are either original or an extension of existing results to a more general formulation using polyhedral meshes. Finally, flexibility and extensibility of the mimetic methodology are shown by deriving higher-order approximations, enforcing discrete maximum principles for diffusion problems, and ensuring the numerical stability for saddle-point systems.
Energy Technology Data Exchange (ETDEWEB)
Kim, S. [Purdue Univ., West Lafayette, IN (United States)
1994-12-31
Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.
Fourier analysis of finite element preconditioned collocation schemes
Deville, Michel O.; Mund, Ernest H.
1990-01-01
The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.
Conservative Semidiscrete Difference Schemes for Timoshenko Systems
Júnior, D. S. Almeida
2014-01-01
We present a parameterized family of finite-difference schemes to analyze the energy properties for linearly elastic constant-coefficient Timoshenko systems considering shear deformation and rotatory inertia. We derive numerical energies showing the positivity, and the energy conservation property and we show how to avoid a numerical anomaly known as locking phenomenon on shear force. Our method of proof relies on discrete multiplier techniques.
Finite difference techniques for nonlinear hyperbolic conservation laws
International Nuclear Information System (INIS)
Sanders, R.
1985-01-01
The present study is concerned with numerical approximations to the initial value problem for nonlinear systems of conservative laws. Attention is given to the development of a class of conservation form finite difference schemes which are based on the finite volume method (i.e., the method of averages). These schemes do not fit into the classical framework of conservation form schemes discussed by Lax and Wendroff (1960). The finite volume schemes are specifically intended to approximate solutions of multidimensional problems in the absence of rectangular geometries. In addition, the development is reported of different schemes which utilize the finite volume approach for time discretization. Particular attention is given to local time discretization and moving spatial grids. 17 references
Energy Technology Data Exchange (ETDEWEB)
Delfin L, A.; Alonso V, G. [ININ, 52045 Ocoyoacac, Estado de Mexico (Mexico); Valle G, E. del [IPN-ESFM, 07738 Mexico D.F. (Mexico)]. e-mail: adl@nuclear.inin.mx
2003-07-01
In this work the development of a third order scheme of finite differences centered in mesh is presented and it is applied in the numerical solution of those diffusion equations in multi groups in stationary state and X Y geometry. Originally this scheme was developed by Hennart and del Valle for the monoenergetic diffusion equation with a well-known source and they show that the one scheme is of third order when comparing the numerical solution with the analytical solution of a model problem using several mesh refinements and boundary conditions. The scheme by them developed it also introduces the application of numeric quadratures to evaluate the rigidity matrices and of mass that its appear when making use of the finite elements method of Galerkin. One of the used quadratures is the open quadrature of 4 points, no-standard, of Newton-Cotes to evaluate in approximate form the elements of the rigidity matrices. The other quadrature is that of 3 points of Radau that it is used to evaluate the elements of all the mass matrices. One of the objectives of these quadratures are to eliminate the couplings among the Legendre moments 0 and 1 associated to the left and right faces as those associated to the inferior and superior faces of each cell of the discretization. The other objective is to satisfy the particles balance in weighed form in each cell. In this work it expands such development to multiplicative means considering several energy groups. There are described diverse details inherent to the technique, particularly those that refer to the simplification of the algebraic systems that appear due to the space discretization. Numerical results for several test problems are presented and are compared with those obtained with other nodal techniques. (Author)
Cai, Xiaohui; Liu, Yang; Ren, Zhiming
2018-06-01
Reverse-time migration (RTM) is a powerful tool for imaging geologically complex structures such as steep-dip and subsalt. However, its implementation is quite computationally expensive. Recently, as a low-cost solution, the graphic processing unit (GPU) was introduced to improve the efficiency of RTM. In the paper, we develop three ameliorative strategies to implement RTM on GPU card. First, given the high accuracy and efficiency of the adaptive optimal finite-difference (FD) method based on least squares (LS) on central processing unit (CPU), we study the optimal LS-based FD method on GPU. Second, we develop the CPU-based hybrid absorbing boundary condition (ABC) to the GPU-based one by addressing two issues of the former when introduced to GPU card: time-consuming and chaotic threads. Third, for large-scale data, the combinatorial strategy for optimal checkpointing and efficient boundary storage is introduced for the trade-off between memory and recomputation. To save the time of communication between host and disk, the portable operating system interface (POSIX) thread is utilized to create the other CPU core at the checkpoints. Applications of the three strategies on GPU with the compute unified device architecture (CUDA) programming language in RTM demonstrate their efficiency and validity.
Hybrid finite difference/finite element immersed boundary method.
E Griffith, Boyce; Luo, Xiaoyu
2017-12-01
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.
Call Admission Scheme for Multidimensional Traffic Assuming Finite Handoff User
Directory of Open Access Journals (Sweden)
Md. Baitul Al Sadi
2017-01-01
Full Text Available Usually, the number of users within a cell in a mobile cellular network is considered infinite; hence, M/M/n/k model is appropriate for new originated traffic, but the number of ongoing calls around a cell is always finite. Hence, the traffic model of handoff call will be M/M/n/k/N. In this paper, a K-dimensional traffic model of a mobile cellular network is proposed using the combination of limited and unlimited users case. A new call admission scheme (CAS is proposed based on both thinning scheme and fading condition. The fading condition of the wireless channel access to a handoff call is prioritized compared to newly originated calls.
International Nuclear Information System (INIS)
Ishiguro, Misako; Higuchi, Kenji
1983-01-01
The finite element method is applied in Galerkin-type approximation to three-dimensional neutron diffusion equations of fast reactors. A hexagonal element scheme is adopted for treating the hexagonal lattice which is typical for fast reactors. The validity of the scheme is verified by applying the scheme as well as alternative schemes to the neutron diffusion calculation of a gas-cooled fast reactor of actual scale. The computed results are compared with corresponding values obtained using the currently applied triangular-element and also with conventional finite difference schemes. The hexagonal finite element scheme is found to yield a reasonable solution to the problem taken up here, with some merit in terms of saving in computing time, but the resulting multiplication factor differs by 1% and the flux by 9% compared with the triangular mesh finite difference scheme. The finite element method, even in triangular element scheme, would appear to incur error in inadmissible amount and which could not be easily eliminated by refining the nodes. (author)
An assessment of unstructured grid finite volume schemes for cold gas hypersonic flow calculations
Directory of Open Access Journals (Sweden)
João Luiz F. Azevedo
2009-06-01
Full Text Available A comparison of five different spatial discretization schemes is performed considering a typical high speed flow application. Flowfields are simulated using the 2-D Euler equations, discretized in a cell-centered finite volume procedure on unstructured triangular meshes. The algorithms studied include a central difference-type scheme, and 1st- and 2nd-order van Leer and Liou flux-vector splitting schemes. These methods are implemented in an efficient, edge-based, unstructured grid procedure which allows for adaptive mesh refinement based on flow property gradients. Details of the unstructured grid implementation of the methods are presented together with a discussion of the data structure and of the adaptive refinement strategy. The application of interest is the cold gas flow through a typical hypersonic inlet. Results for different entrance Mach numbers and mesh topologies are discussed in order to assess the comparative performance of the various spatial discretization schemes.
Nonstandard Finite Difference Method Applied to a Linear Pharmacokinetics Model
Directory of Open Access Journals (Sweden)
Oluwaseun Egbelowo
2017-05-01
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.
Evaluation of Callable Bonds: Finite Difference Methods, Stability and Accuracy.
Buttler, Hans-Jurg
1995-01-01
The purpose of this paper is to evaluate numerically the semi-American callable bond by means of finite difference methods. This study implies three results. First, the numerical error is greater for the callable bond price than for the straight bond price, and too large for real applications Secondly, the numerical accuracy of the callable bond price computed for the relevant range of interest rates depends entirely on the finite difference scheme which is chosen for the boundary points. Thi...
Liu, Meilin; Bagci, Hakan
2011-01-01
A discontinuous Galerkin finite element method (DG-FEM) with a highly-accurate time integration scheme is presented. The scheme achieves its high accuracy using numerically constructed predictor-corrector integration coefficients. Numerical results
Finite element and finite difference methods in electromagnetic scattering
Morgan, MA
2013-01-01
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
A finite difference method for free boundary problems
Fornberg, Bengt
2010-01-01
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
Finite difference computing with PDEs a modern software approach
Langtangen, Hans Petter
2017-01-01
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.
Constructing space difference schemes which satisfy a cell entropy inequality
Merriam, Marshal L.
1989-01-01
A numerical methodology for solving convection problems is presented, using finite difference schemes which satisfy the second law of thermodynamics on a cell-by-cell basis in addition to the usual conservation laws. It is shown that satisfaction of a cell entropy inequality is sufficient, in some cases, to guarantee nonlinear stability. Some details are given for several one-dimensional problems, including the quasi-one-dimensional Euler equations applied to flow in a nozzle.
Explicit Finite Difference Methods for the Delay Pseudoparabolic Equations
Directory of Open Access Journals (Sweden)
I. Amirali
2014-01-01
Full Text Available Finite difference technique is applied to numerical solution of the initial-boundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities two-level difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stable and convergent of order two in space and of order one in time. The error estimates are obtained in the discrete norm. Some numerical results confirming the expected behavior of the method are shown.
A Modified Computational Scheme for the Stochastic Perturbation Finite Element Method
Directory of Open Access Journals (Sweden)
Feng Wu
Full Text Available Abstract A modified computational scheme of the stochastic perturbation finite element method (SPFEM is developed for structures with low-level uncertainties. The proposed scheme can provide second-order estimates of the mean and variance without differentiating the system matrices with respect to the random variables. When the proposed scheme is used, it involves finite analyses of deterministic systems. In the case of one random variable with a symmetric probability density function, the proposed computational scheme can even provide a result with fifth-order accuracy. Compared with the traditional computational scheme of SPFEM, the proposed scheme is more convenient for numerical implementation. Four numerical examples demonstrate that the proposed scheme can be used in linear or nonlinear structures with correlated or uncorrelated random variables.
Modelling of a 400 kW natural gas diffusion flame using finite-rate chemistry schemes
International Nuclear Information System (INIS)
Mueller, Christian; Kremer, Hans; Brink, Anders; Kilpinen, Pia; Hupa, Mikko
1999-01-01
The Eddy-Dissipation Combustion Model combined with three different reaction mechanisms is applied to simulate a fuel-rich 400 kW natural gas diffusion flame. The chemical schemes include a global 2-step and a global 4-step approach as well as a reduced 4-step mechanism systematically derived from an elementary scheme. The species and temperature distributions resulting from the different schemes are studied in detail and compared to each other and to experiments. Furthermore the method of implementing finite-rate chemistry to the Eddy-Dissipation Combustion Model is discussed. (author)
High-resolution finite-difference algorithms for conservation laws
International Nuclear Information System (INIS)
Towers, J.D.
1987-01-01
A new class of Total Variation Decreasing (TVD) schemes for 2-dimensional scalar conservation laws is constructed using either flux-limited or slope-limited numerical fluxes. The schemes are proven to have formal second-order accuracy in regions where neither u/sub x/ nor y/sub y/ vanishes. A new class of high-resolution large-time-step TVD schemes is constructed by adding flux-limited correction terms to the first-order accurate large-time-step version of the Engquist-Osher scheme. The use of the transport-collapse operator in place of the exact solution operator for the construction of difference schemes is studied. The production of spurious extrema by difference schemes is studied. A simple condition guaranteeing the nonproduction of spurious extrema is derived. A sufficient class of entropy inequalities for a conservation law with a flux having a single inflection point is presented. Finite-difference schemes satisfying a discrete version of each entropy inequality are only first-order accurate
Group foliation of finite difference equations
Thompson, Robert; Valiquette, Francis
2018-06-01
Using the theory of equivariant moving frames, a group foliation method for invariant finite difference equations is developed. This method is analogous to the group foliation of differential equations and uses the symmetry group of the equation to decompose the solution process into two steps, called resolving and reconstruction. Our constructions are performed algorithmically and symbolically by making use of discrete recurrence relations among joint invariants. Applications to invariant finite difference equations that approximate differential equations are given.
A finite difference method for free boundary problems
Fornberg, Bengt
2010-04-01
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.
International Nuclear Information System (INIS)
Benasser Algehawi, Mohammed; Samsudin, Azman
2010-01-01
We present a method to extract key pairs needed for the Identity Based Encryption (IBE) scheme from extended Chebyshev polynomial over finite fields Z p . Our proposed scheme relies on the hard problem and the bilinear property of the extended Chebyshev polynomial over Z p . The proposed system is applicable, secure, and reliable.
International Nuclear Information System (INIS)
Fedon-Magnaud, C.; Hennart, J.P.; Lautard, J.J.
1983-03-01
An unified formulation of non conforming finite elements with quadrature formula and simple nodal scheme is presented. The theoretical convergence is obtained for the previous scheme when the mesh is refined. Numerical tests are provided in order to bear out the theorical results
Liu, Meilin
2011-07-01
A discontinuous Galerkin finite element method (DG-FEM) with a highly-accurate time integration scheme is presented. The scheme achieves its high accuracy using numerically constructed predictor-corrector integration coefficients. Numerical results show that this new time integration scheme uses considerably larger time steps than the fourth-order Runge-Kutta method when combined with a DG-FEM using higher-order spatial discretization/basis functions for high accuracy. © 2011 IEEE.
An implicit finite-difference operator for the Helmholtz equation
Chu, Chunlei; Stoffa, Paul L.
2012-01-01
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.
An implicit finite-difference operator for the Helmholtz equation
Chu, Chunlei
2012-07-01
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.
International Nuclear Information System (INIS)
Xing Yulong; Shu Chiwang
2006-01-01
Hyperbolic balance laws have steady state solutions in which the flux gradients are nonzero but are exactly balanced by the source term. In our earlier work [J. Comput. Phys. 208 (2005) 206-227; J. Sci. Comput., accepted], we designed a well-balanced finite difference weighted essentially non-oscillatory (WENO) scheme, which at the same time maintains genuine high order accuracy for general solutions, to a class of hyperbolic systems with separable source terms including the shallow water equations, the elastic wave equation, the hyperbolic model for a chemosensitive movement, the nozzle flow and a two phase flow model. In this paper, we generalize high order finite volume WENO schemes and Runge-Kutta discontinuous Galerkin (RKDG) finite element methods to the same class of hyperbolic systems to maintain a well-balanced property. Finite volume and discontinuous Galerkin finite element schemes are more flexible than finite difference schemes to treat complicated geometry and adaptivity. However, because of a different computational framework, the maintenance of the well-balanced property requires different technical approaches. After the description of our well-balanced high order finite volume WENO and RKDG schemes, we perform extensive one and two dimensional simulations to verify the properties of these schemes such as the exact preservation of the balance laws for certain steady state solutions, the non-oscillatory property for general solutions with discontinuities, and the genuine high order accuracy in smooth regions
Implicit and fully implicit exponential finite difference methods
Indian Academy of Sciences (India)
Burgers' equation; exponential finite difference method; implicit exponential finite difference method; ... This paper describes two new techniques which give improved exponential finite difference solutions of Burgers' equation. ... Current Issue
Electron-phonon coupling from finite differences
Monserrat, Bartomeu
2018-02-01
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.
Botti, Lorenzo; Paliwal, Nikhil; Conti, Pierangelo; Antiga, Luca; Meng, Hui
2018-06-01
Image-based computational fluid dynamics (CFD) has shown potential to aid in the clinical management of intracranial aneurysms (IAs) but its adoption in the clinical practice has been missing, partially due to lack of accuracy assessment and sensitivity analysis. To numerically solve the flow-governing equations CFD solvers generally rely on two spatial discretization schemes: Finite Volume (FV) and Finite Element (FE). Since increasingly accurate numerical solutions are obtained by different means, accuracies and computational costs of FV and FE formulations cannot be compared directly. To this end, in this study we benchmark two representative CFD solvers in simulating flow in a patient-specific IA model: (1) ANSYS Fluent, a commercial FV-based solver and (2) VMTKLab multidGetto, a discontinuous Galerkin (dG) FE-based solver. The FV solver's accuracy is improved by increasing the spatial mesh resolution (134k, 1.1m, 8.6m and 68.5m tetrahedral element meshes). The dGFE solver accuracy is increased by increasing the degree of polynomials (first, second, third and fourth degree) on the base 134k tetrahedral element mesh. Solutions from best FV and dGFE approximations are used as baseline for error quantification. On average, velocity errors for second-best approximations are approximately 1cm/s for a [0,125]cm/s velocity magnitude field. Results show that high-order dGFE provide better accuracy per degree of freedom but worse accuracy per Jacobian non-zero entry as compared to FV. Cross-comparison of velocity errors demonstrates asymptotic convergence of both solvers to the same numerical solution. Nevertheless, the discrepancy between under-resolved velocity fields suggests that mesh independence is reached following different paths. This article is protected by copyright. All rights reserved.
A High-Accuracy Linear Conservative Difference Scheme for Rosenau-RLW Equation
Directory of Open Access Journals (Sweden)
Jinsong Hu
2013-01-01
Full Text Available We study the initial-boundary value problem for Rosenau-RLW equation. We propose a three-level linear finite difference scheme, which has the theoretical accuracy of Oτ2+h4. The scheme simulates two conservative properties of original problem well. The existence, uniqueness of difference solution, and a priori estimates in infinite norm are obtained. Furthermore, we analyze the convergence and stability of the scheme by energy method. At last, numerical experiments demonstrate the theoretical results.
Five-point Element Scheme of Finite Analytic Method for Unsteady Groundwater Flow
Institute of Scientific and Technical Information of China (English)
Xiang Bo; Mi Xiao; Ji Changming; Luo Qingsong
2007-01-01
In order to improve the finite analytic method's adaptability for irregular unit, by using coordinates rotation technique this paper establishes a five-point element scheme of finite analytic method. It not only solves unsteady groundwater flow equation but also gives the boundary condition. This method can be used to calculate the three typical questions of groundwater. By compared with predecessor's computed result, the result of this method is more satisfactory.
Finite difference order doubling in two dimensions
International Nuclear Information System (INIS)
Killingbeck, John P; Jolicard, Georges
2008-01-01
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
International Nuclear Information System (INIS)
Botchorishvili, Ramaz; Pironneau, Olivier
2003-01-01
We develop here a new class of finite volume schemes on unstructured meshes for scalar conservation laws with stiff source terms. The schemes are of equilibrium type, hence with uniform bounds on approximate solutions, valid in cell entropy inequalities and exact for some equilibrium states. Convergence is investigated in the framework of kinetic schemes. Numerical tests show high computational efficiency and a significant advantage over standard cell centered discretization of source terms. Equilibrium type schemes produce accurate results even on test problems for which the standard approach fails. For some numerical tests they exhibit exponential type convergence rate. In two of our numerical tests an equilibrium type scheme with 441 nodes on a triangular mesh is more accurate than a standard scheme with 5000 2 grid points
Saad, Bilal Mohammed; Saad, Mazen Naufal B M
2014-01-01
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.
Saad, Bilal Mohammed
2014-06-28
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.
The finite-difference and finite-element modeling of seismic wave propagation and earthquake motion
International Nuclear Information System (INIS)
Moczo, P.; Kristek, J.; Pazak, P.; Balazovjech, M.; Moczo, P.; Kristek, J.; Galis, M.
2007-01-01
Numerical modeling of seismic wave propagation and earthquake motion is an irreplaceable tool in investigation of the Earth's structure, processes in the Earth, and particularly earthquake phenomena. Among various numerical methods, the finite-difference method is the dominant method in the modeling of earthquake motion. Moreover, it is becoming more important in the seismic exploration and structural modeling. At the same time we are convinced that the best time of the finite-difference method in seismology is in the future. This monograph provides tutorial and detailed introduction to the application of the finite difference (FD), finite-element (FE), and hybrid FD-FE methods to the modeling of seismic wave propagation and earthquake motion. The text does not cover all topics and aspects of the methods. We focus on those to which we have contributed. We present alternative formulations of equation of motion for a smooth elastic continuum. We then develop alternative formulations for a canonical problem with a welded material interface and free surface. We continue with a model of an earthquake source. We complete the general theoretical introduction by a chapter on the constitutive laws for elastic and viscoelastic media, and brief review of strong formulations of the equation of motion. What follows is a block of chapters on the finite-difference and finite-element methods. We develop FD targets for the free surface and welded material interface. We then present various FD schemes for a smooth continuum, free surface, and welded interface. We focus on the staggered-grid and mainly optimally-accurate FD schemes. We also present alternative formulations of the FE method. We include the FD and FE implementations of the traction-at-split-nodes method for simulation of dynamic rupture propagation. The FD modeling is applied to the model of the deep sedimentary Grenoble basin, France. The FD and FE methods are combined in the hybrid FD-FE method. The hybrid
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
2012-01-01
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...
Optimal 25-Point Finite-Difference Subgridding Techniques for the 2D Helmholtz Equation
Directory of Open Access Journals (Sweden)
Tingting Wu
2016-01-01
Full Text Available We present an optimal 25-point finite-difference subgridding scheme for solving the 2D Helmholtz equation with perfectly matched layer (PML. This scheme is second order in accuracy and pointwise consistent with the equation. Subgrids are used to discretize the computational domain, including the interior domain and the PML. For the transitional node in the interior domain, the finite difference equation is formulated with ghost nodes, and its weight parameters are chosen by a refined choice strategy based on minimizing the numerical dispersion. Numerical experiments are given to illustrate that the newly proposed schemes can produce highly accurate seismic modeling results with enhanced efficiency.
Elementary introduction to finite difference equations
International Nuclear Information System (INIS)
White, J.W.
1976-01-01
An elementary description is given of the basic vocabulary and concepts associated with finite difference modeling. The material discussed is biased toward the types of large computer programs used at the Lawrence Livermore Laboratory. Particular attention is focused on truncation error and how it can be affected by zoning patterns. The principle of convergence is discussed, and convergence as a tool for improving calculational accuracy and efficiency is emphasized
A parallel finite-difference method for computational aerodynamics
International Nuclear Information System (INIS)
Swisshelm, J.M.
1989-01-01
A finite-difference scheme for solving complex three-dimensional aerodynamic flow on parallel-processing supercomputers is presented. The method consists of a basic flow solver with multigrid convergence acceleration, embedded grid refinements, and a zonal equation scheme. Multitasking and vectorization have been incorporated into the algorithm. Results obtained include multiprocessed flow simulations from the Cray X-MP and Cray-2. Speedups as high as 3.3 for the two-dimensional case and 3.5 for segments of the three-dimensional case have been achieved on the Cray-2. The entire solver attained a factor of 2.7 improvement over its unitasked version on the Cray-2. The performance of the parallel algorithm on each machine is analyzed. 14 refs
Traoré, Philippe; Ahipo, Yves Marcel; Louste, Christophe
2009-08-01
In this paper an improved finite volume scheme to discretize diffusive flux on a non-orthogonal mesh is proposed. This approach, based on an iterative technique initially suggested by Khosla [P.K. Khosla, S.G. Rubin, A diagonally dominant second-order accurate implicit scheme, Computers and Fluids 2 (1974) 207-209] and known as deferred correction, has been intensively utilized by Muzaferija [S. Muzaferija, Adaptative finite volume method for flow prediction using unstructured meshes and multigrid approach, Ph.D. Thesis, Imperial College, 1994] and later Fergizer and Peric [J.H. Fergizer, M. Peric, Computational Methods for Fluid Dynamics, Springer, 2002] to deal with the non-orthogonality of the control volumes. Using a more suitable decomposition of the normal gradient, our scheme gives accurate solutions in geometries where the basic idea of Muzaferija fails. First the performances of both schemes are compared for a Poisson problem solved in quadrangular domains where control volumes are increasingly skewed in order to test their robustness and efficiency. It is shown that convergence properties and the accuracy order of the solution are not degraded even on extremely skewed mesh. Next, the very stable behavior of the method is successfully demonstrated on a randomly distorted grid as well as on an anisotropically distorted one. Finally we compare the solution obtained for quadrilateral control volumes to the ones obtained with a finite element code and with an unstructured version of our finite volume code for triangular control volumes. No differences can be observed between the different solutions, which demonstrates the effectiveness of our approach.
DEFF Research Database (Denmark)
Fasano, Andrea; Rasmussen, Henrik K.
2017-01-01
A third order accurate, in time and space, finite element scheme for the numerical simulation of three- dimensional time-dependent flow of the molecular stress function type of fluids in a generalized formu- lation is presented. The scheme is an extension of the K-BKZ Lagrangian finite element me...
Renormalization in self-consistent approximation schemes at finite temperature I: theory
International Nuclear Information System (INIS)
Hees, H. van; Knoll, J.
2001-07-01
Within finite temperature field theory, we show that truncated non-perturbative self-consistent Dyson resummation schemes can be renormalized with local counter-terms defined at the vacuum level. The requirements are that the underlying theory is renormalizable and that the self-consistent scheme follows Baym's Φ-derivable concept. The scheme generates both, the renormalized self-consistent equations of motion and the closed equations for the infinite set of counter terms. At the same time the corresponding 2PI-generating functional and the thermodynamic potential can be renormalized, in consistency with the equations of motion. This guarantees the standard Φ-derivable properties like thermodynamic consistency and exact conservation laws also for the renormalized approximation scheme to hold. The proof uses the techniques of BPHZ-renormalization to cope with the explicit and the hidden overlapping vacuum divergences. (orig.)
Integral and finite difference inequalities and applications
Pachpatte, B G
2006-01-01
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
An Elgamal Encryption Scheme of Fibonacci Q-Matrix and Finite State Machine
Directory of Open Access Journals (Sweden)
B. Ravi Kumar
2015-12-01
Full Text Available Cryptography is the science of writing messages in unknown form using mathematical models. In Cryptography, several ciphers were introduced for the encryption schemes. Recent research focusing on designing various mathematical models in such a way that tracing the inverse of the designed mathematical models is infeasible for the eve droppers. In the present work, the ELGamal encryption scheme is executed using the generator of a cyclic group formed by the points on choosing elliptic curve, finite state machines and key matrices obtained from the Fibonacci sequences.
A finite difference, multipoint flux numerical approach to flow in porous media: Numerical examples
Osman, Hossam Omar; Salama, Amgad; Sun, Shuyu; Bao, Kai
2012-01-01
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.
A finite difference, multipoint flux numerical approach to flow in porous media: Numerical examples
Osman, Hossam Omar
2012-06-17
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.
Modeling seismic wave propagation using staggered-grid mimetic finite differences
Directory of Open Access Journals (Sweden)
Freysimar Solano-Feo
2017-04-01
Full Text Available Mimetic finite difference (MFD approximations of continuous gradient and divergence operators satisfy a discrete version of the Gauss-Divergence theorem on staggered grids. On the mimetic approximation of this integral conservation principle, an unique boundary flux operator is introduced that also intervenes on the discretization of a given boundary value problem (BVP. In this work, we present a second-order MFD scheme for seismic wave propagation on staggered grids that discretized free surface and absorbing boundary conditions (ABC with same accuracy order. This scheme is time explicit after coupling a central three-level finite difference (FD stencil for numerical integration. Here, we briefly discuss the convergence properties of this scheme and show its higher accuracy on a challenging test when compared to a traditional FD method. Preliminary applications to 2-D seismic scenarios are also presented and show the potential of the mimetic finite difference method.
Abstract Level Parallelization of Finite Difference Methods
Directory of Open Access Journals (Sweden)
Edwin Vollebregt
1997-01-01
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.
Discrete memory schemes for finite strain thermoplasticity and application to shape memory alloys
International Nuclear Information System (INIS)
Favier, D.; Guelin, P.; Pegon, P.; Nowacki, W.K.
1987-01-01
A theory of finite strain plasticity has been proposed: The scheme of pure hysteresis with mixed transport has been extended to the case of non-rotational kinematics. Secondly, the simple shear case has been studied, taking into account Drucker's recent analysis regarding the 'appropriate simple idealizations for finite plasticity'. Illustrations are provided for general stress/strain paths. Also a new theory of isotropic hyperelasticity has been proposed. The 'reversible' relative Cauchy stress tensor (of type (1,1) and weight one) is defined in the dragged along coordinates as a tensorial isotropic function of the Almansi tensor and of its invariants (through the partial derivatives of the actual scalar density of elastic energy per unit extent of dragged along coordinates). The correspondance between strain and stress paths is then defined in a general form which is particularly convenient for the study of first order effects, limit behaviours, coupling and second order effects. Illustrations are provided. The addition of the pure hysteresis stress contribution σ a and of the reversible contribution σ rev leads to a scheme of 'superelasticity' departure to obtain a provisional scheme of shape memory effects. Some remarks are given regarding some of the possible generalizations of the scheme. (orig./GL)
Finite difference computation of Casimir forces
International Nuclear Information System (INIS)
Pinto, Fabrizio
2016-01-01
In this Invited paper, we begin by a historical introduction to provide a motivation for the classical problems of interatomic force computation and associated challenges. This analysis will lead us from early theoretical and experimental accomplishments to the integration of these fascinating interactions into the operation of realistic, next-generation micro- and nanodevices both for the advanced metrology of fundamental physical processes and in breakthrough industrial applications. Among several powerful strategies enabling vastly enhanced performance and entirely novel technological capabilities, we shall specifically consider Casimir force time-modulation and the adoption of non-trivial geometries. As to the former, the ability to alter the magnitude and sign of the Casimir force will be recognized as a crucial principle to implement thermodynamical nano-engines. As to the latter, we shall first briefly review various reported computational approaches. We shall then discuss the game-changing discovery, in the last decade, that standard methods of numerical classical electromagnetism can be retooled to formulate the problem of Casimir force computation in arbitrary geometries. This remarkable development will be practically illustrated by showing that such an apparently elementary method as standard finite-differencing can be successfully employed to numerically recover results known from the Lifshitz theory of dispersion forces in the case of interacting parallel-plane slabs. Other geometries will be also be explored and consideration given to the potential of non-standard finite-difference methods. Finally, we shall introduce problems at the computational frontier, such as those including membranes deformed by Casimir forces and the effects of anisotropic materials. Conclusions will highlight the dramatic transition from the enduring perception of this field as an exotic application of quantum electrodynamics to the recent demonstration of a human climbing
Determination of finite-difference weights using scaled binomial windows
Chu, Chunlei; Stoffa, Paul L.
2012-01-01
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.
Determination of finite-difference weights using scaled binomial windows
Chu, Chunlei
2012-05-01
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.
International Nuclear Information System (INIS)
Surya Mohan, P.; Tarvainen, Tanja; Schweiger, Martin; Pulkkinen, Aki; Arridge, Simon R.
2011-01-01
Highlights: → We developed a variable order global basis scheme to solve light transport in 3D. → Based on finite elements, the method can be applied to a wide class of geometries. → It is computationally cheap when compared to the fixed order scheme. → Comparisons with local basis method and other models demonstrate its accuracy. → Addresses problems encountered n modeling of light transport in human brain. - Abstract: We propose the P N approximation based on a finite element framework for solving the radiative transport equation with optical tomography as the primary application area. The key idea is to employ a variable order spherical harmonic expansion for angular discretization based on the proximity to the source and the local scattering coefficient. The proposed scheme is shown to be computationally efficient compared to employing homogeneously high orders of expansion everywhere in the domain. In addition the numerical method is shown to accurately describe the void regions encountered in the forward modeling of real-life specimens such as infant brains. The accuracy of the method is demonstrated over three model problems where the P N approximation is compared against Monte Carlo simulations and other state-of-the-art methods.
Boscheri, Walter; Dumbser, Michael
2017-10-01
We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may also include parabolic terms in order to model dissipative transport processes, like molecular viscosity or heat conduction. High order piecewise polynomials of degree N are adopted to represent the discrete solution at each time level and within each spatial control volume of the computational grid, while high order of accuracy in time is achieved by the ADER approach, making use of an element-local space-time Galerkin finite element predictor. A novel nodal solver algorithm based on the HLL flux is derived to compute the velocity for each nodal degree of freedom that describes the current mesh geometry. In our algorithm the spatial mesh configuration can be defined in two different ways: either by an isoparametric approach that generates curved control volumes, or by a piecewise linear decomposition of each spatial control volume into simplex sub-elements. Each technique generates a corresponding number of geometrical degrees of freedom needed to describe the current mesh configuration and which must be considered by the nodal solver for determining the grid velocity. The connection of the old mesh configuration at time tn with the new one at time t n + 1 provides the space-time control volumes on which the governing equations have to be integrated in order to obtain the time evolution of the discrete solution. Our numerical method belongs to the category of so-called direct Arbitrary-Lagrangian-Eulerian (ALE) schemes, where a space-time conservation formulation of the governing PDE system is considered and which already takes into account the new grid geometry (including a possible rezoning step) directly during the computation of the numerical fluxes. We emphasize that our method is a moving mesh method, as opposed to total
Secure diversity-multiplexing tradeoff of zero-forcing transmit scheme at finite-SNR
Rezki, Zouheir
2012-04-01
In this paper, we address the finite Signal-to-Noise Ratio (SNR) Diversity-Multiplexing Tradeoff (DMT) of the Multiple Input Multiple Output (MIMO) wiretap channel, where a Zero-Forcing (ZF) transmit scheme, that intends to send the secret information in the orthogonal space of the eavesdropper channel, is used. First, we introduce the secrecy multiplexing gain at finite-SNR that generalizes the definition at high-SNR. Then, we provide upper and lower bounds on the outage probability under secrecy constraint, from which secrecy diversity gain estimates of ZF are derived. Through asymptotic analysis, we show that the upper bound underestimates the secrecy diversity gain, whereas the lower bound is tight at high-SNR, and thus its related diversity gain estimate is equal to the actual asymptotic secrecy diversity gain of the MIMO wiretap channel. © 2012 IEEE.
Finite Mathematics and Discrete Mathematics: Is There a Difference?
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…
Bound-preserving Legendre-WENO finite volume schemes using nonlinear mapping
Smith, Timothy; Pantano, Carlos
2017-11-01
We present a new method to enforce field bounds in high-order Legendre-WENO finite volume schemes. The strategy consists of reconstructing each field through an intermediate mapping, which by design satisfies realizability constraints. Determination of the coefficients of the polynomial reconstruction involves nonlinear equations that are solved using Newton's method. The selection between the original or mapped reconstruction is implemented dynamically to minimize computational cost. The method has also been generalized to fields that exhibit interdependencies, requiring multi-dimensional mappings. Further, the method does not depend on the existence of a numerical flux function. We will discuss details of the proposed scheme and show results for systems in conservation and non-conservation form. This work was funded by the NSF under Grant DMS 1318161.
Iterative solutions of finite difference diffusion equations
International Nuclear Information System (INIS)
Menon, S.V.G.; Khandekar, D.C.; Trasi, M.S.
1981-01-01
The heterogeneous arrangement of materials and the three-dimensional character of the reactor physics problems encountered in the design and operation of nuclear reactors makes it necessary to use numerical methods for solution of the neutron diffusion equations which are based on the linear Boltzmann equation. The commonly used numerical method for this purpose is the finite difference method. It converts the diffusion equations to a system of algebraic equations. In practice, the size of this resulting algebraic system is so large that the iterative methods have to be used. Most frequently used iterative methods are discussed. They include : (1) basic iterative methods for one-group problems, (2) iterative methods for eigenvalue problems, and (3) iterative methods which use variable acceleration parameters. Application of Chebyshev theorem to iterative methods is discussed. The extension of the above iterative methods to multigroup neutron diffusion equations is also considered. These methods are applicable to elliptic boundary value problems in reactor design studies in particular, and to elliptic partial differential equations in general. Solution of sample problems is included to illustrate their applications. The subject matter is presented in as simple a manner as possible. However, a working knowledge of matrix theory is presupposed. (M.G.B.)
The finite-difference and finite-element modeling of seismic wave propagation and earthquake motion
International Nuclear Information System (INIS)
Moszo, P.; Kristek, J.; Galis, M.; Pazak, P.; Balazovijech, M.
2006-01-01
Numerical modeling of seismic wave propagation and earthquake motion is an irreplaceable tool in investigation of the Earth's structure, processes in the Earth, and particularly earthquake phenomena. Among various numerical methods, the finite-difference method is the dominant method in the modeling of earthquake motion. Moreover, it is becoming more important in the seismic exploration and structural modeling. At the same time we are convinced that the best time of the finite-difference method in seismology is in the future. This monograph provides tutorial and detailed introduction to the application of the finite-difference, finite-element, and hybrid finite-difference-finite-element methods to the modeling of seismic wave propagation and earthquake motion. The text does not cover all topics and aspects of the methods. We focus on those to which we have contributed. (Author)
On the Stability of the Finite Difference based Lattice Boltzmann Method
El-Amin, Mohamed; Sun, Shuyu; Salama, Amgad
2013-01-01
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.
On the Stability of the Finite Difference based Lattice Boltzmann Method
El-Amin, Mohamed
2013-06-01
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.
Implicit time-dependent finite different algorithm for quench simulation
International Nuclear Information System (INIS)
Koizumi, Norikiyo; Takahashi, Yoshikazu; Tsuji, Hiroshi
1994-12-01
A magnet in a fusion machine has many difficulties in its application because of requirement of a large operating current, high operating field and high breakdown voltage. A cable-in-conduit (CIC) conductor is the best candidate to overcome these difficulties. However, there remained uncertainty in a quench event in the cable-in-conduit conductor because of a difficulty to analyze a fluid dynamics equation. Several scientists, then, developed the numerical code for the quench simulation. However, most of them were based on an explicit time-dependent finite difference scheme. In this scheme, a discrete time increment is strictly restricted by CFL (Courant-Friedrichs-Lewy) condition. Therefore, long CPU time was consumed for the quench simulation. Authors, then, developed a new quench simulation code, POCHI1, which is based on an implicit time dependent scheme. In POCHI1, the fluid dynamics equation is linearlized according to a procedure applied by Beam and Warming and then, a tridiagonal system can be offered. Therefore, no iteration is necessary to solve the fluid dynamics equation. This leads great reduction of the CPU time. Also, POCHI1 can cope with non-linear boundary condition. In this study, comparison with experimental results was carried out. The normal zone propagation behavior was investigated in two samples of CIC conductors which had different hydraulic diameters. The measured and simulated normal zone propagation length showed relatively good agreement. However, the behavior of the normal voltage shows a little disagreement. These results indicate necessity to improve the treatment of the heat transfer coefficient in the turbulent flow region and the electric resistivity of the copper stabilizer in high temperature and high field region. (author)
High-order finite difference solution for 3D nonlinear wave-structure interaction
DEFF Research Database (Denmark)
Ducrozet, Guillaume; Bingham, Harry B.; Engsig-Karup, Allan Peter
2010-01-01
This contribution presents our recent progress on developing an efficient fully-nonlinear potential flow model for simulating 3D wave-wave and wave-structure interaction over arbitrary depths (i.e. in coastal and offshore environment). The model is based on a high-order finite difference scheme O...
A parallel adaptive finite difference algorithm for petroleum reservoir simulation
Energy Technology Data Exchange (ETDEWEB)
Hoang, Hai Minh
2005-07-01
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)
A General Finite Element Scheme for Limit State Analysis and Optimization
DEFF Research Database (Denmark)
Damkilde, Lars
1999-01-01
Limit State analysis which is based on a perfect material behaviour is used in many different applications primarily within Structural Engineering and Geotechnics. The calculation methods have not reached the same level of automation such as Finite Element Analysis for elastic structures....... The computer based systems are more ad hoc based and are typically not well-integrated with pre- and postprocessors well-known from commercial Finite Element codes.A finite element based formulation of limit state analysis is presented which allows an easy integration with standard Finite Element codes...... for elastic analysis. In this way the user is able to perform a limit state analysis on the same model used for elastic analysis only adding data for the yield surface.The method is based on the lower-bound theorem and uses stress-based elements with a linearized yield surface. The mathematical problem...
CSIR Research Space (South Africa)
Suliman, Ridhwaan
2012-07-01
Full Text Available -linear deformations are accounted for. As will be demonstrated, the finite volume approach exhibits similar disad- vantages to the linear Q4 finite element formulation when undergoing bending. An enhanced finite volume approach is discussed and compared with finite...
Lu, Qiang; Han, Qing-Long; Zhang, Botao; Liu, Dongliang; Liu, Shirong
2017-12-01
This paper deals with the problem of environmental monitoring by developing an event-triggered finite-time control scheme for mobile sensor networks. The proposed control scheme can be executed by each sensor node independently and consists of two parts: one part is a finite-time consensus algorithm while the other part is an event-triggered rule. The consensus algorithm is employed to enable the positions and velocities of sensor nodes to quickly track the position and velocity of a virtual leader in finite time. The event-triggered rule is used to reduce the updating frequency of controllers in order to save the computational resources of sensor nodes. Some stability conditions are derived for mobile sensor networks with the proposed control scheme under both a fixed communication topology and a switching communication topology. Finally, simulation results illustrate the effectiveness of the proposed control scheme for the problem of environmental monitoring.
International Nuclear Information System (INIS)
Capdevila, R.; Perez-Segarra, C.D.; Oliva, A.
2010-01-01
In the present work four different spatial numerical schemes have been developed with the aim of reducing the false-scattering of the numerical solutions obtained with the discrete ordinates (DOM) and the finite volume (FVM) methods. These schemes have been designed specifically for unstructured meshes by means of the extrapolation of nodal values of intensity on the studied radiative direction. The schemes have been tested and compared in several 3D benchmark test cases using both structured orthogonal and unstructured grids.
de Hon, B.P.; Arnold, J.M.
2015-01-01
The robust and speedy evaluation of lattice Green's functions LGFs) is crucial to the effectiveness of finite-difference Green's function diakoptics schemes. We have recently determined a generic recurrence scheme for the construction of scalar LGF sequences at arbitrary points on a 3-D cubic
Additive Difference Schemes for Filtration Problems in Multilayer Systems
Ayrjan, E A; Pavlush, M; Fedorov, A V
2000-01-01
In the present paper difference schemes for solution of the plane filtration problem in multilayer systems are analyzed within the framework of difference schemes general theory. Attention is paid to splitting the schemes on physical processes of filtration along water-carring layers and vertical motion between layers. Some absolutely stable additive difference schemes are obtained the realization of which needs no software modification. Parallel algorithm connected with the solving of the filtration problem in every water-carring layer on a single processor is constructed. Program realization on the multi-processor system SPP2000 at JINR is discussed.
Chu, Chunlei
2009-01-01
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.
Market behavior and performance of different strategy evaluation schemes.
Baek, Yongjoo; Lee, Sang Hoon; Jeong, Hawoong
2010-08-01
Strategy evaluation schemes are a crucial factor in any agent-based market model, as they determine the agents' strategy preferences and consequently their behavioral pattern. This study investigates how the strategy evaluation schemes adopted by agents affect their performance in conjunction with the market circumstances. We observe the performance of three strategy evaluation schemes, the history-dependent wealth game, the trend-opposing minority game, and the trend-following majority game, in a stock market where the price is exogenously determined. The price is either directly adopted from the real stock market indices or generated with a Markov chain of order ≤2 . Each scheme's success is quantified by average wealth accumulated by the traders equipped with the scheme. The wealth game, as it learns from the history, shows relatively good performance unless the market is highly unpredictable. The majority game is successful in a trendy market dominated by long periods of sustained price increase or decrease. On the other hand, the minority game is suitable for a market with persistent zigzag price patterns. We also discuss the consequence of implementing finite memory in the scoring processes of strategies. Our findings suggest under which market circumstances each evaluation scheme is appropriate for modeling the behavior of real market traders.
Monotone difference schemes for weakly coupled elliptic and parabolic systems
P. Matus (Piotr); F.J. Gaspar Lorenz (Franscisco); L. M. Hieu (Le Minh); V.T.K. Tuyen (Vo Thi Kim)
2017-01-01
textabstractThe present paper is devoted to the development of the theory of monotone difference schemes, approximating the so-called weakly coupled system of linear elliptic and quasilinear parabolic equations. Similarly to the scalar case, the canonical form of the vector-difference schemes is
Energy Technology Data Exchange (ETDEWEB)
Ismagilov, Timur Z., E-mail: ismagilov@academ.org
2015-02-01
This paper presents a second order finite volume scheme for numerical solution of Maxwell's equations with discontinuous dielectric permittivity and magnetic permeability on unstructured meshes. The scheme is based on Godunov scheme and employs approaches of Van Leer and Lax–Wendroff to increase the order of approximation. To keep the second order of approximation near dielectric permittivity and magnetic permeability discontinuities a novel technique for gradient calculation and limitation is applied near discontinuities. Results of test computations for problems with linear and curvilinear discontinuities confirm second order of approximation. The scheme was applied to modelling propagation of electromagnetic waves inside photonic crystal waveguides with a bend.
Finite difference schemes for second order systems describing black holes
International Nuclear Information System (INIS)
Motamed, Mohammad; Kreiss, H-O.; Babiuc, M.; Winicour, J.; Szilagyi, B.
2006-01-01
In the harmonic description of general relativity, the principal part of Einstein's equations reduces to 10 curved space wave equations for the components of the space-time metric. We present theorems regarding the stability of several evolution-boundary algorithms for such equations when treated in second order differential form. The theorems apply to a model black hole space-time consisting of a spacelike inner boundary excising the singularity, a timelike outer boundary and a horizon in between. These algorithms are implemented as stable, convergent numerical codes and their performance is compared in a 2-dimensional excision problem
Finite difference time domain analysis of a chiro plasma
International Nuclear Information System (INIS)
Torres-Silva, H.; Obligado, A.; Reggiani, N.; Sakanaka, P.H.
1995-01-01
The finite difference time-domain (FDTD) method is one of the most widely used computational methods in electromagnetics. Using FDTD, Maxwell's equations are solved directly in the time domain via finite differences and time stepping. The basic approach is relatively easy to understand and is an alternative to the more usual frequency-domain approaches. (author). 5 refs
Exact Finite Differences. The Derivative on Non Uniformly Spaced Partitions
Directory of Open Access Journals (Sweden)
Armando Martínez-Pérez
2017-10-01
Full Text Available We define a finite-differences derivative operation, on a non uniformly spaced partition, which has the exponential function as an exact eigenvector. We discuss some properties of this operator and we propose a definition for the components of a finite-differences momentum operator. This allows us to perform exact discrete calculations.
Mustapha, K.
2017-06-03
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.
Mustapha, K.; Furati, K.; Knio, Omar; Maitre, O. Le
2017-01-01
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.
An efficient coupled polynomial interpolation scheme for shear mode sandwich beam finite element
Directory of Open Access Journals (Sweden)
Litesh N. Sulbhewar
Full Text Available An efficient piezoelectric sandwich beam finite element is presented here. It employs the coupled polynomial field interpolation scheme for field variables which incorporates electromechanical coupling at interpolation level itself; unlike conventional sandwich beam theory (SBT based formulations available in the literature. A variational formulation is used to derive the governing equations, which are used to establish the relationships between field variables. These relations lead to the coupled polynomial field descriptions of variables, unlike conventional SBT formulations which use assumed independent polynomials. The relative axial displacement is expressed only by coupled terms containing contributions from other mechanical and electrical variables, thus eliminating use of the transverse displacement derivative as a degree of freedom. A set of coupled shape function based on these polynomials has shown the improvement in the convergence characteristics of the SBT based formulation. This improvement in the performance is achieved with one nodal degree of freedom lesser than the conventional SBT formulations.
Symplectic finite element scheme: application to a driven problem with a regular singularity
Energy Technology Data Exchange (ETDEWEB)
Pletzer, A. [Ecole Polytechnique Federale, Lausanne (Switzerland). Centre de Recherche en Physique des Plasma (CRPP)
1996-02-01
A new finite element (FE) scheme, based on the decomposition of a second order differential equation into a set of first order symplectic (Hamiltonian) equations, is presented and tested on one-dimensional, driven Sturm-Liouville problem. Error analysis shows improved cubic convergence in the energy norm for piecewise linear `tent` elements, as compared to quadratic convergence for the standard and hybrid FE methods. The convergence deteriorates in the presence of a regular singular point, but can be recovered by appropriate mesh node packing. Optimal mesh packing exponents are derived to ensure cubic (respectively quadratic) convergence with minimal numerical error. A further suppression of the numerical error by a factor proportional to the square of the leading exponent of the singular solution, is achieved for a model problem based on determining the nonideal magnetohydrodynamic stability of a fusion plasma. (author) 7 figs., 14 refs.
Symplectic finite element scheme: application to a driven problem with a regular singularity
International Nuclear Information System (INIS)
Pletzer, A.
1996-02-01
A new finite element (FE) scheme, based on the decomposition of a second order differential equation into a set of first order symplectic (Hamiltonian) equations, is presented and tested on one-dimensional, driven Sturm-Liouville problem. Error analysis shows improved cubic convergence in the energy norm for piecewise linear 'tent' elements, as compared to quadratic convergence for the standard and hybrid FE methods. The convergence deteriorates in the presence of a regular singular point, but can be recovered by appropriate mesh node packing. Optimal mesh packing exponents are derived to ensure cubic (respectively quadratic) convergence with minimal numerical error. A further suppression of the numerical error by a factor proportional to the square of the leading exponent of the singular solution, is achieved for a model problem based on determining the nonideal magnetohydrodynamic stability of a fusion plasma. (author) 7 figs., 14 refs
Chronopoulos, D
2017-01-01
A systematic expression quantifying the wave energy skewing phenomenon as a function of the mechanical characteristics of a non-isotropic structure is derived in this study. A structure of arbitrary anisotropy, layering and geometric complexity is modelled through Finite Elements (FEs) coupled to a periodic structure wave scheme. A generic approach for efficiently computing the angular sensitivity of the wave slowness for each wave type, direction and frequency is presented. The approach does not involve any finite differentiation scheme and is therefore computationally efficient and not prone to the associated numerical errors. Copyright © 2016 Elsevier B.V. All rights reserved.
A perturbative study of two four-quark operators in finite volume renormalization schemes
Palombi, Filippo; Sint, S
2006-01-01
Starting from the QCD Schroedinger functional (SF), we define a family of renormalization schemes for two four-quark operators, which are, in the chiral limit, protected against mixing with other operators. With the appropriate flavour assignments these operators can be interpreted as part of either the $\\Delta F=1$ or $\\Delta F=2$ effective weak Hamiltonians. In view of lattice QCD with Wilson-type quarks, we focus on the parity odd components of the operators, since these are multiplicatively renormalized both on the lattice and in continuum schemes. We consider 9 different SF schemes and relate them to commonly used continuum schemes at one-loop order of perturbation theory. In this way the two-loop anomalous dimensions in the SF schemes can be inferred. As a by-product of our calculation we also obtain the one-loop cutoff effects in the step-scaling functions of the respective renormalization constants, for both O(a) improved and unimproved Wilson quarks. Our results will be needed in a separate study of ...
Differences exist across insurance schemes in China post-consolidation.
Directory of Open Access Journals (Sweden)
Yang Li
Full Text Available In China, the basic insurance system consists of three schemes: the UEBMI (Urban Employee Basic Medical Insurance, URBMI (Urban Resident Basic Medical Insurance, and NCMS (New Cooperative Medical Scheme, across which significant differences have been observed. Since 2009, the central government has been experimenting with consolidating these schemes in selected areas. This study examines whether differences still exist across schemes after the consolidation.A survey was conducted in the city of Suzhou, collecting data on subjects 45 years old and above with at least one inpatient or outpatient treatment during a period of twelve months. Analysis on 583 subjects was performed comparing subjects' characteristics across insurance schemes. A resampling-based method was applied to compute the predicted gross medical cost, OOP (out-of-pocket cost, and insurance reimbursement rate.Subjects under different insurance schemes differ in multiple aspects. For inpatient treatments, subjects under the URBMI have the highest observed and predicted gross and OOP costs, while those under the UEBMI have the lowest. For outpatient treatments, subjects under the UEBMI and URBMI have comparable costs, while those under the NCMS have much lower costs. Subjects under the NCMS also have a much lower reimbursement rate.Differences still exist across schemes in medical costs and insurance reimbursement rate post-consolidation. Further investigations are needed to identify the causes, and interventions are needed to eliminate such differences.
Convergent Difference Schemes for Hamilton-Jacobi equations
Duisembay, Serikbolsyn
2018-01-01
In this thesis, we consider second-order fully nonlinear partial differential equations of elliptic type. Our aim is to develop computational methods using convergent difference schemes for stationary Hamilton-Jacobi equations with Dirichlet
Finite element analysis of thermal stress distribution in different ...
African Journals Online (AJOL)
Nigerian Journal of Clinical Practice • Jan-Feb 2016 • Vol 19 • Issue 1. Abstract ... Key words: Amalgam, finite element method, glass ionomer cement, resin composite, thermal stress ... applications for force analysis and assessment of different.
Comparison of different precondtioners for nonsymmtric finite volume element methods
Energy Technology Data Exchange (ETDEWEB)
Mishev, I.D.
1996-12-31
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.
Raeli, Alice; Bergmann, Michel; Iollo, Angelo
2018-02-01
We consider problems governed by a linear elliptic equation with varying coefficients across internal interfaces. The solution and its normal derivative can undergo significant variations through these internal boundaries. We present a compact finite-difference scheme on a tree-based adaptive grid that can be efficiently solved using a natively parallel data structure. The main idea is to optimize the truncation error of the discretization scheme as a function of the local grid configuration to achieve second-order accuracy. Numerical illustrations are presented in two and three-dimensional configurations.
Five-point form of the nodal diffusion method and comparison with finite-difference
International Nuclear Information System (INIS)
Azmy, Y.Y.
1988-01-01
Nodal Methods have been derived, implemented and numerically tested for several problems in physics and engineering. In the field of nuclear engineering, many nodal formalisms have been used for the neutron diffusion equation, all yielding results which were far more computationally efficient than conventional Finite Difference (FD) and Finite Element (FE) methods. However, not much effort has been devoted to theoretically comparing nodal and FD methods in order to explain the very high accuracy of the former. In this summary we outline the derivation of a simple five-point form for the lowest order nodal method and compare it to the traditional five-point, edge-centered FD scheme. The effect of the observed differences on the accuracy of the respective methods is established by considering a simple test problem. It must be emphasized that the nodal five-point scheme derived here is mathematically equivalent to previously derived lowest order nodal methods. 7 refs., 1 tab
Optimal variable-grid finite-difference modeling for porous media
International Nuclear Information System (INIS)
Liu, Xinxin; Yin, Xingyao; Li, Haishan
2014-01-01
Numerical modeling of poroelastic waves by the finite-difference (FD) method is more expensive than that of acoustic or elastic waves. To improve the accuracy and computational efficiency of seismic modeling, variable-grid FD methods have been developed. In this paper, we derived optimal staggered-grid finite difference schemes with variable grid-spacing and time-step for seismic modeling in porous media. FD operators with small grid-spacing and time-step are adopted for low-velocity or small-scale geological bodies, while FD operators with big grid-spacing and time-step are adopted for high-velocity or large-scale regions. The dispersion relations of FD schemes were derived based on the plane wave theory, then the FD coefficients were obtained using the Taylor expansion. Dispersion analysis and modeling results demonstrated that the proposed method has higher accuracy with lower computational cost for poroelastic wave simulation in heterogeneous reservoirs. (paper)
A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension
Energy Technology Data Exchange (ETDEWEB)
Garrick, Daniel P. [Department of Aerospace Engineering, Iowa State University, Ames, IA (United States); Owkes, Mark [Department of Mechanical and Industrial Engineering, Montana State University, Bozeman, MT (United States); Regele, Jonathan D., E-mail: jregele@iastate.edu [Department of Aerospace Engineering, Iowa State University, Ames, IA (United States)
2017-06-15
Shock waves are often used in experiments to create a shear flow across liquid droplets to study secondary atomization. Similar behavior occurs inside of supersonic combustors (scramjets) under startup conditions, but it is challenging to study these conditions experimentally. In order to investigate this phenomenon further, a numerical approach is developed to simulate compressible multiphase flows under the effects of surface tension forces. The flow field is solved via the compressible multicomponent Euler equations (i.e., the five equation model) discretized with the finite volume method on a uniform Cartesian grid. The solver utilizes a total variation diminishing (TVD) third-order Runge–Kutta method for time-marching and second order TVD spatial reconstruction. Surface tension is incorporated using the Continuum Surface Force (CSF) model. Fluxes are upwinded with a modified Harten–Lax–van Leer Contact (HLLC) approximate Riemann solver. An interface compression scheme is employed to counter numerical diffusion of the interface. The present work includes modifications to both the HLLC solver and the interface compression scheme to account for capillary force terms and the associated pressure jump across the gas–liquid interface. A simple method for numerically computing the interface curvature is developed and an acoustic scaling of the surface tension coefficient is proposed for the non-dimensionalization of the model. The model captures the surface tension induced pressure jump exactly if the exact curvature is known and is further verified with an oscillating elliptical droplet and Mach 1.47 and 3 shock-droplet interaction problems. The general characteristics of secondary atomization at a range of Weber numbers are also captured in a series of simulations.
Implicit finite-difference simulations of seismic wave propagation
Chu, Chunlei; Stoffa, Paul L.
2012-01-01
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.
Implicit finite-difference simulations of seismic wave propagation
Chu, Chunlei
2012-03-01
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.
Dey, C.; Dey, S. K.
1983-01-01
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.
Optimized difference schemes for multidimensional hyperbolic partial differential equations
Directory of Open Access Journals (Sweden)
Adrian Sescu
2009-04-01
Full Text Available In numerical solutions to hyperbolic partial differential equations in multidimensions, in addition to dispersion and dissipation errors, there is a grid-related error (referred to as isotropy error or numerical anisotropy that affects the directional dependence of the wave propagation. Difference schemes are mostly analyzed and optimized in one dimension, wherein the anisotropy correction may not be effective enough. In this work, optimized multidimensional difference schemes with arbitrary order of accuracy are designed to have improved isotropy compared to conventional schemes. The derivation is performed based on Taylor series expansion and Fourier analysis. The schemes are restricted to equally-spaced Cartesian grids, so the generalized curvilinear transformation method and Cartesian grid methods are good candidates.
Convergent Difference Schemes for Hamilton-Jacobi equations
Duisembay, Serikbolsyn
2018-05-07
In this thesis, we consider second-order fully nonlinear partial differential equations of elliptic type. Our aim is to develop computational methods using convergent difference schemes for stationary Hamilton-Jacobi equations with Dirichlet and Neumann type boundary conditions in arbitrary two-dimensional domains. First, we introduce the notion of viscosity solutions in both continuous and discontinuous frameworks. Next, we review Barles-Souganidis approach using monotone, consistent, and stable schemes. In particular, we show that these schemes converge locally uniformly to the unique viscosity solution of the first-order Hamilton-Jacobi equations under mild assumptions. To solve the scheme numerically, we use Euler map with some initial guess. This iterative method gives the viscosity solution as a limit. Moreover, we illustrate our numerical approach in several two-dimensional examples.
Keslerová, Radka; Trdlička, David
2015-09-01
This work deals with the numerical modelling of steady flows of incompressible viscous and viscoelastic fluids through the three dimensional channel with T-junction. The fundamental system of equations is the system of generalized Navier-Stokes equations for incompressible fluids. This system is based on the system of balance laws of mass and momentum for incompressible fluids. Two different mathematical models for the stress tensor are used for simulation of Newtonian and Oldroyd-B fluids flow. Numerical solution of the described models is based on cetral finite volume method using explicit Runge-Kutta time integration.
On the spectral properties of random finite difference operators
International Nuclear Information System (INIS)
Kunz, H.; Souillard, B.
1980-01-01
We study a class of random finite difference operators, a typical example of which is the finite difference Schroedinger operator with a random potential which arises in solid state physics in the tight binding approximation. We obtain with probability one, in various situations, the exact location of the spectrum, and criterions for a given part in the spectrum to be pure point or purely continuous, or for the static electric conductivity to vanish. A general formalism is developped which transforms the study of these random operators into that of the asymptotics of a multiple integral constructed from a given recipe. Finally we apply our criterions and formalism to prove that, with probability one, the one-dimensional finite difference Schroedinger operator with a random potential has pure point spectrum and developps no static conductivity. (orig.)
Different radiation impedance models for finite porous materials
DEFF Research Database (Denmark)
Nolan, Melanie; Jeong, Cheol-Ho; Brunskog, Jonas
2015-01-01
The Sabine absorption coefficients of finite absorbers are measured in a reverberation chamber according to the international standard ISO 354. They vary with the specimen size essentially due to diffraction at the specimen edges, which can be seen as the radiation impedance differing from...... the infinite case. Thus, in order to predict the Sabine absorption coefficients of finite porous samples, one can incorporate models of the radiation impedance. In this study, different radiation impedance models are compared with two experimental examples. Thomasson’s model is compared to Rhazi’s method when...
Glazyrina, O. V.; Pavlova, M. F.
2016-11-01
We consider the parabolic inequality with monotone with respect to a gradient space operator, which is depended on integral with respect to space variables solution characteristic. We construct a two-layer differential scheme for this problem with use of penalty method, semidiscretization with respect to time variable method and the finite element method (FEM) with respect to space variables. We proved a convergence of constructed mothod.
International Nuclear Information System (INIS)
Ackroyd, R.T.
1987-01-01
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. (author)
A positive and entropy-satisfying finite volume scheme for the Baer–Nunziato model
Energy Technology Data Exchange (ETDEWEB)
Coquel, Frédéric, E-mail: frederic.coquel@cmap.polytechnique.fr [CMAP, École Polytechnique CNRS, UMR 7641, Route de Saclay, F-91128 Palaiseau cedex (France); Hérard, Jean-Marc, E-mail: jean-marc.herard@edf.fr [EDF-R& D, Département MFEE, 6 Quai Watier, F-78401 Chatou Cedex (France); Saleh, Khaled, E-mail: saleh@math.univ-lyon1.fr [Université de Lyon, CNRS UMR 5208, Université Lyon 1, Institut Camille Jordan, 43 bd 11 novembre 1918, F-69622 Villeurbanne cedex (France)
2017-02-01
We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer–Nunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in for the isentropic Baer–Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing scheme for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound are also proven to be maintained by the numerical scheme. It is also the only scheme for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the numerical method, is satisfied for any admissible equation of state. We provide a numerical study for the convergence of the approximate solutions towards some exact Riemann solutions. The numerical simulations show that the relaxation scheme compares well with two of the most popular existing schemes available for the Baer–Nunziato model, namely Schwendeman–Wahle–Kapila's Godunov-type scheme and Tokareva–Toro's HLLC scheme . The relaxation scheme also shows a higher precision and a lower computational cost (for comparable accuracy) than a standard numerical scheme used in the nuclear industry, namely Rusanov's scheme. Finally, we assess the good behavior of the scheme when approximating vanishing phase solutions.
A positive and entropy-satisfying finite volume scheme for the Baer-Nunziato model
Coquel, Frédéric; Hérard, Jean-Marc; Saleh, Khaled
2017-02-01
We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer-Nunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in [16] for the isentropic Baer-Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing scheme for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound are also proven to be maintained by the numerical scheme. It is also the only scheme for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the numerical method, is satisfied for any admissible equation of state. We provide a numerical study for the convergence of the approximate solutions towards some exact Riemann solutions. The numerical simulations show that the relaxation scheme compares well with two of the most popular existing schemes available for the Baer-Nunziato model, namely Schwendeman-Wahle-Kapila's Godunov-type scheme [39] and Tokareva-Toro's HLLC scheme [44]. The relaxation scheme also shows a higher precision and a lower computational cost (for comparable accuracy) than a standard numerical scheme used in the nuclear industry, namely Rusanov's scheme. Finally, we assess the good behavior of the scheme when approximating vanishing phase solutions.
Accuracy of finite-difference modeling of seismic waves : Simulation versus laboratory measurements
Arntsen, B.
2017-12-01
The finite-difference technique for numerical modeling of seismic waves is still important and for some areas extensively used.For exploration purposes is finite-difference simulation at the core of both traditional imaging techniques such as reverse-time migration and more elaborate Full-Waveform Inversion techniques.The accuracy and fidelity of finite-difference simulation of seismic waves are hard to quantify and meaningfully error analysis is really onlyeasily available for simplistic media. A possible alternative to theoretical error analysis is provided by comparing finite-difference simulated data with laboratory data created using a scale model. The advantage of this approach is the accurate knowledge of the model, within measurement precision, and the location of sources and receivers.We use a model made of PVC immersed in water and containing horizontal and tilted interfaces together with several spherical objects to generateultrasonic pressure reflection measurements. The physical dimensions of the model is of the order of a meter, which after scaling represents a model with dimensions of the order of 10 kilometer and frequencies in the range of one to thirty hertz.We find that for plane horizontal interfaces the laboratory data can be reproduced by the finite-difference scheme with relatively small error, but for steeply tilted interfaces the error increases. For spherical interfaces the discrepancy between laboratory data and simulated data is sometimes much more severe, to the extent that it is not possible to simulate reflections from parts of highly curved bodies. The results are important in view of the fact that finite-difference modeling is often at the core of imaging and inversion algorithms tackling complicatedgeological areas with highly curved interfaces.
International Nuclear Information System (INIS)
Farhanieh, B.; Amanifard, N.; Ghorbanian, K.
2002-01-01
An unsteady two-dimensional numerical investigation was performed on the viscous flow passing through a multi-blade cascade. A Cartesian finite-volume approach was linked to Van-Leer's and Roe's flux splitting schemes to evaluate inviscid flux terms. To prevent the oscillatory behavior of numerical results and to increase the accuracy, Mon tonic Upstream Scheme for Conservation Laws was added to flux splitting schemes. The Baldwin-Lo max (B L) turbulence model was implemented to solve the turbulent case studies. Implicit solution was also provided using Lower and Upper (L U) decomposition technique to compare with explicit solutions. To validate the numerical procedure, two test cases are prepared and flow over a Na Ca 0012 airfoil was investigated and the pressure coefficients were compared to the reference data. The numerical solver was implemented to study the flow passing over a compressor cascade. The results of various combinations of splitting schemes and the Mon tonic Upstream Scheme for Conventional Laws limiter were compared with each other to find the suitable methods in cascade problems. Finally the convergence histories of implemented schemes were compared to each other to show the behavior of the solver in using various methods before implementation of them in flow instability studies
Boscheri, Walter; Dumbser, Michael; Loubère, Raphaël; Maire, Pierre-Henri
2018-04-01
In this paper we develop a conservative cell-centered Lagrangian finite volume scheme for the solution of the hydrodynamics equations on unstructured multidimensional grids. The method is derived from the Eucclhyd scheme discussed in [47,43,45]. It is second-order accurate in space and is combined with the a posteriori Multidimensional Optimal Order Detection (MOOD) limiting strategy to ensure robustness and stability at shock waves. Second-order of accuracy in time is achieved via the ADER (Arbitrary high order schemes using DERivatives) approach. A large set of numerical test cases is proposed to assess the ability of the method to achieve effective second order of accuracy on smooth flows, maintaining an essentially non-oscillatory behavior on discontinuous profiles, general robustness ensuring physical admissibility of the numerical solution, and precision where appropriate.
Stability and non-standard finite difference method of the generalized Chua's circuit
Radwan, Ahmed G.
2011-08-01
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.
Finite difference discretization of semiconductor drift-diffusion equations for nanowire solar cells
Deinega, Alexei; John, Sajeev
2012-10-01
We introduce a finite difference discretization of semiconductor drift-diffusion equations using cylindrical partial waves. It can be applied to describe the photo-generated current in radial pn-junction nanowire solar cells. We demonstrate that the cylindrically symmetric (l=0) partial wave accurately describes the electronic response of a square lattice of silicon nanowires at normal incidence. We investigate the accuracy of our discretization scheme by using different mesh resolution along the radial direction r and compare with 3D (x, y, z) discretization. We consider both straight nanowires and nanowires with radius modulation along the vertical axis. The charge carrier generation profile inside each nanowire is calculated using an independent finite-difference time-domain simulation.
High-order finite-difference methods for Poisson's equation
van Linde, Hendrik Jan
1971-01-01
In this thesis finite-difference approximations to the three boundary value problems for Poisson’s equation are given, with discretization errors of O(H^3) for the mixed boundary value problem, O(H^3 |ln(h)| for the Neumann problem and O(H^4)for the Dirichlet problem respectively . First an operator
Chebyshev Finite Difference Method for Fractional Boundary Value Problems
Directory of Open Access Journals (Sweden)
Boundary
2015-09-01
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: http://www.ijmex.com 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
Finite difference time domain modelling of particle accelerators
International Nuclear Information System (INIS)
Jurgens, T.G.; Harfoush, F.A.
1989-03-01
Finite Difference Time Domain (FDTD) modelling has been successfully applied to a wide variety of electromagnetic scattering and interaction problems for many years. Here the method is extended to incorporate the modelling of wake fields in particle accelerators. Algorithmic comparisons are made to existing wake field codes, such as MAFIA T3. 9 refs., 7 figs
HEATING-7, Multidimensional Finite-Difference Heat Conduction Analysis
International Nuclear Information System (INIS)
2000-01-01
problems, surface fluxes may be plotted with H7TECPLOT which requires the proprietary software TECPLOT. HEATING 7.3 runs under Windows95 and WindowsNT on PC's. No future modifications are planned for HEATING7. See README.1ST for more information. 2 - Method of solution: Three steady-state solution techniques are available: point-successive over-relaxation iterative method with extrapolation, direct-solution (for one-dimensional or two-dimensional problems), and conjugate gradient. Transient problems may be solved using any one of several finite-difference schemes: Crank-Nicolson implicit, Classical Implicit Procedure (CIP), Classical Explicit Procedure (CEP), or Levy explicit method (which for some circumstances allows a time step greater than the CEP stability criterion.) The solution of the system of equations arising from the implicit techniques is accomplished by point-successive over-relaxation iteration and includes procedures to estimate the optimum acceleration parameter. 3 - Restrictions on the complexity of the problem: All surfaces in a model must be parallel to one of the coordinate axes which makes modeling complex geometries difficult. Transient change of phase problems can only be solved with one of the explicit techniques - an implicit change-of-phase capability has not been implemented
Insights on different participation schemes to meet climate goals
International Nuclear Information System (INIS)
Russ, Peter; Ierland, Tom van
2009-01-01
Models and scenarios to assess greenhouse gas mitigation action have become more diversified and detailed, allowing the simulation of more realistic global climate policy set-ups. In this paper, different participation schemes to meet different levels of radiative forcing are analysed. The focus is on scenarios that are in line with the 2 deg. C target. Typical stylised participation schemes are based either on a perfect global carbon market or delayed participation with targets only for developed countries, no actions by developing countries and no access to credits from offsetting mechanisms in developing countries. This paper adds an intermediate policy scenario assuming a gradual incorporation of all countries, including a gradually developing carbon market, and taking into account the ability to contribute of different parties. Perfect participation by all parties would be optimal, but it is shown that participation schemes involving a gradual and differentiated participation by all parties can substantially decrease global costs and still meet the 2 deg. C target. Carbon markets can compensate in part for those costs incurred by developing countries' own, autonomous mitigation actions that do not generate tradable emission credits.
J.K. Hoogland (Jiri); C.D.D. Neumann
2000-01-01
textabstractIn this article we present a new approach to the numerical valuation of derivative securities. The method is based on our previous work where we formulated the theory of pricing in terms of tradables. The basic idea is to fit a finite difference scheme to exact solutions of the pricing
International Nuclear Information System (INIS)
Lan, Haiqiang; Zhang, Zhongjie
2011-01-01
The finite-difference (FD) method is a powerful tool in seismic wave field modelling for understanding seismic wave propagation in the Earth's interior and interpreting the real seismic data. The accuracy of FD modelling partly depends on the implementation of the free-surface (i.e. traction-free) condition. In the past 40 years, at least six kinds of free-surface boundary condition approximate schemes (such as one-sided, centred finite-difference, composed, new composed, implicit and boundary-modified approximations) have been developed in FD second-order elastodynamic simulation. Herein we simulate seismic wave fields in homogeneous and lateral heterogeneous models using these free-surface boundary condition approximate schemes and evaluate their stability and applicability by comparing with corresponding analytical solutions, and then quantitatively evaluate the accuracies of different approximate schemes from the misfit of the amplitude and phase between the numerical and analytical results. Our results confirm that the composed scheme becomes unstable for the V s /V p ratio less than 0.57, and suggest that (1) the one-sided scheme is only accurate to first order and therefore introduces serious errors for the shorter wavelengths, other schemes are all of second-order precision; (2) the new composed, implicit and boundary-modified schemes are stable even when the V s /V p ratio is less than 0.2; (3) the implicit and boundary-modified schemes are able to deal with laterally varying (heterogeneous) free surface; (4) in the corresponding stability range, the one-sided scheme shows remarkable errors in both phase and amplitude compared to analytical solution (which means larger errors in travel-time and reflection strength), the other five approximate schemes show better performance in travel-time (phase) than strength (amplitude)
The Laguerre finite difference one-way equation solver
Terekhov, Andrew V.
2017-05-01
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.
A strong shock tube problem calculated by different numerical schemes
Lee, Wen Ho; Clancy, Sean P.
1996-05-01
Calculated results are presented for the solution of a very strong shock tube problem on a coarse mesh using (1) MESA code, (2) UNICORN code, (3) Schulz hydro, and (4) modified TVD scheme. The first two codes are written in Eulerian coordinates, whereas methods (3) and (4) are in Lagrangian coordinates. MESA and UNICORN codes are both of second order and use different monotonic advection method to avoid the Gibbs phenomena. Code (3) uses typical artificial viscosity for inviscid flow, whereas code (4) uses a modified TVD scheme. The test problem is a strong shock tube problem with a pressure ratio of 109 and density ratio of 103 in an ideal gas. For no mass-matching case, Schulz hydro is better than TVD scheme. In the case of mass-matching, there is no difference between them. MESA and UNICORN results are nearly the same. However, the computed positions such as the contact discontinuity (i.e. the material interface) are not as accurate as the Lagrangian methods.
A strong shock tube problem calculated by different numerical schemes
International Nuclear Information System (INIS)
Lee, W.H.; Clancy, S.P.
1996-01-01
Calculated results are presented for the solution of a very strong shock tube problem on a coarse mesh using (1) MESA code, (2) UNICORN code, (3) Schulz hydro, and (4) modified TVD scheme. The first two codes are written in Eulerian coordinates, whereas methods (3) and (4) are in Lagrangian coordinates. MESA and UNICORN codes are both of second order and use different monotonic advection method to avoid the Gibbs phenomena. Code (3) uses typical artificial viscosity for inviscid flow, whereas code (4) uses a modified TVD scheme. The test problem is a strong shock tube problem with a pressure ratio of 10 9 and density ratio of 10 3 in an ideal gas. For no mass-matching case, Schulz hydro is better than TVD scheme. In the case of mass-matching, there is no difference between them. MESA and UNICORN results are nearly the same. However, the computed positions such as the contact discontinuity (i.e. the material interface) are not as accurate as the Lagrangian methods. copyright 1996 American Institute of Physics
Transporter taxonomy - a comparison of different transport protein classification schemes.
Viereck, Michael; Gaulton, Anna; Digles, Daniela; Ecker, Gerhard F
2014-06-01
Currently, there are more than 800 well characterized human membrane transport proteins (including channels and transporters) and there are estimates that about 10% (approx. 2000) of all human genes are related to transport. Membrane transport proteins are of interest as potential drug targets, for drug delivery, and as a cause of side effects and drug–drug interactions. In light of the development of Open PHACTS, which provides an open pharmacological space, we analyzed selected membrane transport protein classification schemes (Transporter Classification Database, ChEMBL, IUPHAR/BPS Guide to Pharmacology, and Gene Ontology) for their ability to serve as a basis for pharmacology driven protein classification. A comparison of these membrane transport protein classification schemes by using a set of clinically relevant transporters as use-case reveals the strengths and weaknesses of the different taxonomy approaches.
The mimetic finite difference method for elliptic problems
Veiga, Lourenço Beirão; Manzini, Gianmarco
2014-01-01
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.
Integral equations with difference kernels on finite intervals
Sakhnovich, Lev A
2015-01-01
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...
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 often indispensable. This thesis presents the development of rigorous finite-difference method, a very general tool to solve Maxwell’s equations in arbitrary geometries in three dimensions, with an emphasis on the frequency-domain formulation. Enhanced performance of the perfectly matched layers...... 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...
Temperature Calculation of Annular Fuel Pellet by Finite Difference Method
Energy Technology Data Exchange (ETDEWEB)
Yang, Yong Sik; Bang, Je Geon; Kim, Dae Ho; Kim, Sun Ki; Lim, Ik Sung; Song, Kun Woo [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2009-10-15
KAERI has started an innovative fuel development project for applying dual-cooled annular fuel to existing PWR reactor. In fuel design, fuel temperature is the most important factor which can affect nuclear fuel integrity and safety. Many models and methodologies, which can calculate temperature distribution in a fuel pellet have been proposed. However, due to the geometrical characteristics and cooling condition differences between existing solid type fuel and dual-cooled annular fuel, current fuel temperature calculation models can not be applied directly. Therefore, the new heat conduction model of fuel pellet was established. In general, fuel pellet temperature is calculated by FDM(Finite Difference Method) or FEM(Finite Element Method), because, temperature dependency of fuel thermal conductivity and spatial dependency heat generation in the pellet due to the self-shielding should be considered. In our study, FDM is adopted due to high exactness and short calculation time.
Rezki, Zouheir
2011-06-01
In this paper, we address the finite Signal-to-Noise Ratio (SNR) Diversity-Multiplexing Tradeoff (DMT) of the Multiple Input Multiple Output (MIMO) wiretap channel, where a Zero-Forcing (ZF) transmit scheme, that intends to send the secret information in the orthogonal space of the eavesdropper channel, is used. First, we introduce the secret multiplexing gain at finite-SNR that generalizes the definition at high-SNR. Then, we provide upper and lower bounds on the outage probability under secrecy constraint, from which secret diversity gain estimates of ZF are derived. Through asymptotic analysis, we show that the upper bound underestimates the secret diversity gain, whereas the lower bound is tight at high-SNR, and thus its related diversity gain estimate is equal to the actual asymptotic secret diversity gain of the Multiple-Input Multiple-Output (MIMO) wiretap channel. © 2011 IEEE.
Optimized Finite-Difference Coefficients for Hydroacoustic Modeling
Preston, L. A.
2014-12-01
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.
International Nuclear Information System (INIS)
Galán, J; Verleysen, P; Lebensohn, R A
2014-01-01
A new algorithm for the solution of the deformation of a polycrystalline material using a self-consistent scheme, and its integration as part of the finite element software Abaqus/Standard are presented. The method is based on the original VPSC formulation by Lebensohn and Tomé and its integration with Abaqus/Standard by Segurado et al. The new algorithm has been implemented as a set of Fortran 90 modules, to be used either from a standalone program or from Abaqus subroutines. The new implementation yields the same results as VPSC7, but with a significantly better performance, especially when used in multicore computers. (paper)
Directory of Open Access Journals (Sweden)
W.R. Azzam
2015-08-01
Full Text Available This paper reports the application of using a skirted foundation system to study the behavior of foundations with structural skirts adjacent to a sand slope and subjected to earthquake loading. The effect of the adopted skirts to safeguard foundation and slope from collapse is studied. The skirts effect on controlling horizontal soil movement and decreasing pore water pressure beneath foundations and beside the slopes during earthquake is investigated. 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. A two dimensional plain strain program PLAXIS, (dynamic version is adopted. A series of models for the problem under investigation were run under different skirt depths and lactation from the slope crest. The effect of subgrade relative density and skirts thickness is also discussed. Nodal displacement and element strains were analyzed for the foundation with and without skirts and at different studied parameters. The research results showed a great effectiveness in increasing the overall stability of the slope and foundation. The confined soil footing system by such skirts reduced the foundation acceleration therefore it can be tended to damping element and relieved the transmitted disturbance to the adjacent slope. This technique can be considered as a good method to control the slope deformation and decrease the slope acceleration during earthquakes.
Finite difference program for calculating hydride bed wall temperature profiles
International Nuclear Information System (INIS)
Klein, J.E.
1992-01-01
A QuickBASIC finite difference program was written for calculating one dimensional temperature profiles in up to two media with flat, cylindrical, or spherical geometries. The development of the program was motivated by the need to calculate maximum temperature differences across the walls of the Tritium metal hydrides beds for thermal fatigue analysis. The purpose of this report is to document the equations and the computer program used to calculate transient wall temperatures in stainless steel hydride vessels. The development of the computer code was motivated by the need to calculate maximum temperature differences across the walls of the hydrides beds in the Tritium Facility for thermal fatigue analysis
Secure diversity-multiplexing tradeoff of zero-forcing transmit scheme at finite-SNR
Rezki, Zouheir; Alouini, Mohamed-Slim
2012-01-01
information in the orthogonal space of the eavesdropper channel, is used. First, we introduce the secrecy multiplexing gain at finite-SNR that generalizes the definition at high-SNR. Then, we provide upper and lower bounds on the outage probability under
A computationally efficient 3D finite-volume scheme for violent liquid–gas sloshing
CSIR Research Space (South Africa)
Oxtoby, Oliver F
2015-10-01
Full Text Available We describe a semi-implicit volume-of-fluid free-surface-modelling methodology for flow problems involving violent free-surface motion. For efficient computation, a hybrid-unstructured edge-based vertex-centred finite volume discretisation...
Dispersion analysis for difference schemes: tables of generalized Airy functions
International Nuclear Information System (INIS)
Chin, R.C.Y.; Hedstrom, G.W.
1978-01-01
This papers contains graphs and tables of the function /sup Ai/p,q(/sup alpha,x/) =∫/sup infinity/: infinity (2π) -1 exp]y/sup p//p-αy/sup q//q+ixy]dy and its indefinite integral for p=3,5,7, for q=2,4,6, and for several values of α with α> or =0. It is shown how these tables should influence the choice of an artifical viscosity for a difference scheme for a linear hyperbolic equation
A finite area scheme for shallow granular flows on three-dimensional surfaces
Rauter, Matthias
2017-04-01
Shallow granular flow models have become a popular tool for the estimation of natural hazards, such as landslides, debris flows and avalanches. The shallowness of the flow allows to reduce the three-dimensional governing equations to a quasi two-dimensional system. Three-dimensional flow fields are replaced by their depth-integrated two-dimensional counterparts, which yields a robust and fast method [1]. A solution for a simple shallow granular flow model, based on the so-called finite area method [3] is presented. The finite area method is an adaption of the finite volume method [4] to two-dimensional curved surfaces in three-dimensional space. This method handles the three dimensional basal topography in a simple way, making the model suitable for arbitrary (but mildly curved) topography, such as natural terrain. Furthermore, the implementation into the open source software OpenFOAM [4] is shown. OpenFOAM is a popular computational fluid dynamics application, designed so that the top-level code mimics the mathematical governing equations. This makes the code easy to read and extendable to more sophisticated models. Finally, some hints on how to get started with the code and how to extend the basic model will be given. I gratefully acknowledge the financial support by the OEAW project "beyond dense flow avalanches". Savage, S. B. & Hutter, K. 1989 The motion of a finite mass of granular material down a rough incline. Journal of Fluid Mechanics 199, 177-215. Ferziger, J. & Peric, M. 2002 Computational methods for fluid dynamics, 3rd edn. Springer. Tukovic, Z. & Jasak, H. 2012 A moving mesh finite volume interface tracking method for surface tension dominated interfacial fluid flow. Computers & fluids 55, 70-84. Weller, H. G., Tabor, G., Jasak, H. & Fureby, C. 1998 A tensorial approach to computational continuum mechanics using object-oriented techniques. Computers in physics 12(6), 620-631.
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)
2009-12-19
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)
Investigation of the factorization scheme dependence of finite order perturbative QCD calculations
Czech Academy of Sciences Publication Activity Database
Kolář, Karel
-, č. 11 (2011), 005/1-005/44 ISSN 1126-6708 R&D Projects: GA MŠk LC527 Institutional research plan: CEZ:AV0Z10100502 Keywords : QCD * parton distribution functions * factorization schemes * NLO Monte Carlo event generators Subject RIV: BF - Elementary Particles and High Energy Physics Impact factor: 5.831, year: 2011
Directory of Open Access Journals (Sweden)
Litesh N. Sulbhewar
Full Text Available The convergence characteristic of the conventional two-noded Euler-Bernoulli piezoelectric beam finite element depends on the configuration of the beam cross-section. The element shows slower convergence for the asymmetric material distribution in the beam cross-section due to 'material-locking' caused by extension-bending coupling. Hence, the use of conventional Euler-Bernoulli beam finite element to analyze piezoelectric beams which are generally made of the host layer with asymmetrically surface bonded piezoelectric layers/patches, leads to increased computational effort to yield converged results. Here, an efficient coupled polynomial interpolation scheme is proposed to improve the convergence of the Euler-Bernoulli piezoelectric beam finite elements, by eliminating ill-effects of material-locking. The equilibrium equations, derived using a variational formulation, are used to establish relationships between field variables. These relations are used to find a coupled quadratic polynomial for axial displacement, having contributions from an assumed cubic polynomial for transverse displacement and assumed linear polynomials for layerwise electric potentials. A set of coupled shape functions derived using these polynomials efficiently handles extension-bending and electromechanical couplings at the field interpolation level itself in a variationally consistent manner, without increasing the number of nodal degrees of freedom. The comparison of results obtained from numerical simulation of test problems shows that the convergence characteristic of the proposed element is insensitive to the material configuration of the beam cross-section.
Zhebel, E.; Minisini, S.; Kononov, A.; Mulder, W.A.
2013-01-01
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
Finite difference evolution equations and quantum dynamical semigroups
International Nuclear Information System (INIS)
Ghirardi, G.C.; Weber, T.
1983-12-01
We consider the recently proposed [Bonifacio, Lett. Nuovo Cimento, 37, 481 (1983)] coarse grained description of time evolution for the density operator rho(t) through a finite difference equation with steps tau, and we prove that there exists a generator of the quantum dynamical semigroup type yielding an equation giving a continuous evolution coinciding at all time steps with the one induced by the coarse grained description. The map rho(0)→rho(t) derived in this way takes the standard form originally proposed by Lindblad [Comm. Math. Phys., 48, 119 (1976)], even when the map itself (and, therefore, the corresponding generator) is not bounded. (author)
Finite difference time domain modeling of spiral antennas
Penney, Christopher W.; Beggs, John H.; Luebbers, Raymond J.
1992-01-01
The objectives outlined in the original proposal for this project were to create a well-documented computer analysis model based on the finite-difference, time-domain (FDTD) method that would be capable of computing antenna impedance, far-zone radiation patterns, and radar cross-section (RCS). The ability to model a variety of penetrable materials in addition to conductors is also desired. The spiral antennas under study by this project meet these requirements since they are constructed of slots cut into conducting surfaces which are backed by dielectric materials.
Mimetic Finite Differences for Flow in Fractures from Microseismic Data
Al-Hinai, Omar; Srinivasan, Sanjay; Wheeler, Mary F.
2015-01-01
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.
Mimetic Finite Differences for Flow in Fractures from Microseismic Data
Al-Hinai, Omar
2015-01-01
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.
Balsara, Dinshaw S.; Dumbser, Michael
2015-10-01
Several advances have been reported in the recent literature on divergence-free finite volume schemes for Magnetohydrodynamics (MHD). Almost all of these advances are restricted to structured meshes. To retain full geometric versatility, however, it is also very important to make analogous advances in divergence-free schemes for MHD on unstructured meshes. Such schemes utilize a staggered Yee-type mesh, where all hydrodynamic quantities (mass, momentum and energy density) are cell-centered, while the magnetic fields are face-centered and the electric fields, which are so useful for the time update of the magnetic field, are centered at the edges. Three important advances are brought together in this paper in order to make it possible to have high order accurate finite volume schemes for the MHD equations on unstructured meshes. First, it is shown that a divergence-free WENO reconstruction of the magnetic field can be developed for unstructured meshes in two and three space dimensions using a classical cell-centered WENO algorithm, without the need to do a WENO reconstruction for the magnetic field on the faces. This is achieved via a novel constrained L2-projection operator that is used in each time step as a postprocessor of the cell-centered WENO reconstruction so that the magnetic field becomes locally and globally divergence free. Second, it is shown that recently-developed genuinely multidimensional Riemann solvers (called MuSIC Riemann solvers) can be used on unstructured meshes to obtain a multidimensionally upwinded representation of the electric field at each edge. Third, the above two innovations work well together with a high order accurate one-step ADER time stepping strategy, which requires the divergence-free nonlinear WENO reconstruction procedure to be carried out only once per time step. The resulting divergence-free ADER-WENO schemes with MuSIC Riemann solvers give us an efficient and easily-implemented strategy for divergence-free MHD on
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
2009-01-01
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.
International Nuclear Information System (INIS)
Hees, Hendrik van; Knoll, Joern
2002-01-01
The theoretical concepts for the renormalization of self-consistent Dyson resummations, devised in the first paper of this series, are applied to first example cases of φ 4 theory. In addition to the tadpole (Hartree) approximation, as a novel part the numerical solutions are presented, which include the sunset self-energy diagram into the self-consistent scheme based on the Φ-derivable approximation or the two-particle irreducible effective action concept
International Nuclear Information System (INIS)
Hees, H. van; Knoll, J.
2001-01-01
The theoretical concepts for the renormalization of self-consistent Dyson resummations, deviced in the first paper of this series, are applied to first example cases for the φ 4 -theory. Besides the tadpole (Hartree) approximation as a novel part the numerical solutions are presented which includes the sunset self-energy diagram into the self-consistent scheme based on the Φ-derivable approximation or 2PI effective action concept. (orig.)
Homogenization of Periodic Masonry Using Self-Consistent Scheme and Finite Element Method
Kumar, Nitin; Lambadi, Harish; Pandey, Manoj; Rajagopal, Amirtham
2016-01-01
Masonry is a heterogeneous anisotropic continuum, made up of the brick and mortar arranged in a periodic manner. Obtaining the effective elastic stiffness of the masonry structures has been a challenging task. In this study, the homogenization theory for periodic media is implemented in a very generic manner to derive the anisotropic global behavior of the masonry, through rigorous application of the homogenization theory in one step and through a full three-dimensional behavior. We have considered the periodic Eshelby self-consistent method and the finite element method. Two representative unit cells that represent the microstructure of the masonry wall exactly are considered for calibration and numerical application of the theory.
International Nuclear Information System (INIS)
Chernyshenko, Dmitri; Fangohr, Hans
2015-01-01
In the finite difference method which is commonly used in computational micromagnetics, the demagnetizing field is usually computed as a convolution of the magnetization vector field with the demagnetizing tensor that describes the magnetostatic field of a cuboidal cell with constant magnetization. An analytical expression for the demagnetizing tensor is available, however at distances far from the cuboidal cell, the numerical evaluation of the analytical expression can be very inaccurate. Due to this large-distance inaccuracy numerical packages such as OOMMF compute the demagnetizing tensor using the explicit formula at distances close to the originating cell, but at distances far from the originating cell a formula based on an asymptotic expansion has to be used. In this work, we describe a method to calculate the demagnetizing field by numerical evaluation of the multidimensional integral in the demagnetizing tensor terms using a sparse grid integration scheme. This method improves the accuracy of computation at intermediate distances from the origin. We compute and report the accuracy of (i) the numerical evaluation of the exact tensor expression which is best for short distances, (ii) the asymptotic expansion best suited for large distances, and (iii) the new method based on numerical integration, which is superior to methods (i) and (ii) for intermediate distances. For all three methods, we show the measurements of accuracy and execution time as a function of distance, for calculations using single precision (4-byte) and double precision (8-byte) floating point arithmetic. We make recommendations for the choice of scheme order and integrating coefficients for the numerical integration method (iii). - Highlights: • We study the accuracy of demagnetization in finite difference micromagnetics. • We introduce a new sparse integration method to compute the tensor more accurately. • Newell, sparse integration and asymptotic method are compared for all ranges
Directory of Open Access Journals (Sweden)
Huawei Zhou
2016-10-01
Full Text Available Achieving an effective combination of various temperature control measures is critical for temperature control and crack prevention of concrete dams. This paper presents a procedure for optimizing the temperature control scheme of roller compacted concrete (RCC dams that couples the finite element method (FEM with a sensitivity analysis method. In this study, seven temperature control schemes are defined according to variations in three temperature control measures: concrete placement temperature, water-pipe cooling time, and thermal insulation layer thickness. FEM is employed to simulate the equivalent temperature field and temperature stress field obtained under each of the seven designed temperature control schemes for a typical overflow dam monolith based on the actual characteristics of a RCC dam located in southwestern China. A sensitivity analysis is subsequently conducted to investigate the degree of influence each of the three temperature control measures has on the temperature field and temperature tensile stress field of the dam. Results show that the placement temperature has a substantial influence on the maximum temperature and tensile stress of the dam, and that the placement temperature cannot exceed 15 °C. The water-pipe cooling time and thermal insulation layer thickness have little influence on the maximum temperature, but both demonstrate a substantial influence on the maximum tensile stress of the dam. The thermal insulation thickness is significant for reducing the probability of cracking as a result of high thermal stress, and the maximum tensile stress can be controlled under the specification limit with a thermal insulation layer thickness of 10 cm. Finally, an optimized temperature control scheme for crack prevention is obtained based on the analysis results.
Mesh-size errors in diffusion-theory calculations using finite-difference and finite-element methods
International Nuclear Information System (INIS)
Baker, A.R.
1982-07-01
A study has been performed of mesh-size errors in diffusion-theory calculations using finite-difference and finite-element methods. As the objective was to illuminate the issues, the study was performed for a 1D slab model of a reactor with one neutron-energy group for which analytical solutions were possible. A computer code SLAB was specially written to perform the finite-difference and finite-element calculations and also to obtain the analytical solutions. The standard finite-difference equations were obtained by starting with an expansion of the neutron current in powers of the mesh size, h, and keeping terms as far as h 2 . It was confirmed that these equations led to the well-known result that the criticality parameter varied with the square of the mesh size. An improved form of the finite-difference equations was obtained by continuing the expansion for the neutron current as far as the term in h 4 . In this case, the critical parameter varied as the fourth power of the mesh size. The finite-element solutions for 2 and 3 nodes per element revealed that the criticality parameter varied as the square and fourth power of the mesh size, respectively. Numerical results are presented for a bare reactive core of uniform composition with 2 zones of different uniform mesh and for a reactive core with an absorptive reflector. (author)
Turbulent boundary layer under the control of different schemes.
Qiao, Z X; Zhou, Y; Wu, Z
2017-06-01
This work explores experimentally the control of a turbulent boundary layer over a flat plate based on wall perturbation generated by piezo-ceramic actuators. Different schemes are investigated, including the feed-forward, the feedback, and the combined feed-forward and feedback strategies, with a view to suppressing the near-wall high-speed events and hence reducing skin friction drag. While the strategies may achieve a local maximum drag reduction slightly less than their counterpart of the open-loop control, the corresponding duty cycles are substantially reduced when compared with that of the open-loop control. The results suggest a good potential to cut down the input energy under these control strategies. The fluctuating velocity, spectra, Taylor microscale and mean energy dissipation are measured across the boundary layer with and without control and, based on the measurements, the flow mechanism behind the control is proposed.
Market behavior and performance of different strategy evaluation schemes
Yongjoo Baek; Sang Hoon Lee; Hawoong Jeong
2010-01-01
Strategy evaluation schemes are a crucial factor in any agent-based market model, as they determine the agents' strategy preferences and consequently their behavioral pattern. This study investigates how the strategy evaluation schemes adopted by agents affect their performance in conjunction with the market circumstances. We observe the performance of three strategy evaluation schemes, the history-dependent wealth game, the trend-opposing minority game, and the trend-following majority game,...
International Nuclear Information System (INIS)
Ansanay-Alex, G.
2009-01-01
The development of simulation codes aimed at a precise simulation of fires requires a precise approach of flame front phenomena by using very fine grids. The need to take different spatial scale into consideration leads to a local grid refinement and to a discretization with homogeneous grid for computing time and memory purposes. The author reports the approximation of the non-linear convection term, the scalar advection-diffusion in finite volumes, numerical simulations of a flow in a bent tube, of a three-dimensional laminar flame and of a low Mach number an-isotherm flow. Non conformal finite elements are also presented (Rannacher-Turek and Crouzeix-Raviart elements)
Directory of Open Access Journals (Sweden)
Andranik Tsakanian
2012-05-01
Full Text Available In particle accelerators a preferred direction, the direction of motion, is well defined. If in a numerical calculation the (numerical dispersion in this direction is suppressed, a quite coarse mesh and moderate computational resources can be used to reach accurate results even for extremely short electron bunches. Several approaches have been proposed in the past decades to reduce the accumulated dispersion error in wakefield calculations for perfectly conducting structures. In this paper we extend the TE/TM splitting algorithm to a new hybrid scheme that allows for wakefield calculations in structures with walls of finite conductivity. The conductive boundary is modeled by one-dimensional wires connected to each boundary cell. A good agreement of the numerical simulations with analytical results and other numerical approaches is obtained.
International Nuclear Information System (INIS)
Akeju, T.A.I.; Kelly, D.W.; Zienkiewicz, O.C.; Kanaka Raju, K.
1981-01-01
The eigenvalue equations governing the free vibration of axisymmetric solids are derived by means of a semi-analytical finite element scheme. In particular we investigated the use of an 8-node solid element in structures which exhibit a 'shell-like' behaviour. Bathe-Wilson subspace iteration algorithm is employed for the solution of the equations. The element is shown to give good results for beam and shell vibration problems. It is also utilised to solve a complex solid in the form of an internal component of a modern jet engine. This particular application is of considerable practical importance as the dynamics of such components form a dominant design constraint. (orig./HP)
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)
2017-06-15
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.
Comparison of measured and predicted thermal mixing tests using improved finite difference technique
International Nuclear Information System (INIS)
Hassan, Y.A.; Rice, J.G.; Kim, J.H.
1983-01-01
The numerical diffusion introduced by the use of upwind formulations in the finite difference solution of the flow and energy equations for thermal mixing problems (cold water injection after small break LOCA in a PWR) was examined. The relative importance of numerical diffusion in the flow equations, compared to its effect on the energy equation was demonstrated. The flow field equations were solved using both first order accurate upwind, and second order accurate differencing schemes. The energy equation was treated using the conventional upwind and a mass weighted skew upwind scheme. Results presented for a simple test case showed that, for thermal mixing problems, the numerical diffusion was most significant in the energy equation. The numerical diffusion effect in the flow field equations was much less significant. A comparison of predictions using the skew upwind and the conventional upwind with experimental data from a two dimensional thermal mixing text are presented. The use of the skew upwind scheme showed a significant improvement in the accuracy of the steady state predicted temperatures. (orig./HP)
Acoustic, finite-difference, time-domain technique development
International Nuclear Information System (INIS)
Kunz, K.
1994-01-01
A close analog exists between the behavior of sound waves in an ideal gas and the radiated waves of electromagnetics. This analog has been exploited to obtain an acoustic, finite-difference, time-domain (AFDTD) technique capable of treating small signal vibrations in elastic media, such as air, water, and metal, with the important feature of bending motion included in the behavior of the metal. This bending motion is particularly important when the metal is formed into sheets or plates. Bending motion does not have an analog in electromagnetics, but can be readily appended to the acoustic treatment since it appears as a single additional term in the force equation for plate motion, which is otherwise analogous to the electromagnetic wave equation. The AFDTD technique has been implemented in a code architecture that duplicates the electromagnetic, finite-difference, time-domain technique code. The main difference in the implementation is the form of the first-order coupled differential equations obtained from the wave equation. The gradient of pressure and divergence of velocity appear in these equations in the place of curls of the electric and magnetic fields. Other small changes exist as well, but the codes are essentially interchangeable. The pre- and post-processing for model construction and response-data evaluation of the electromagnetic code, in the form of the TSAR code at Lawrence Livermore National Laboratory, can be used for the acoustic version. A variety of applications is possible, pending validation of the bending phenomenon. The applications include acoustic-radiation-pattern predictions for a submerged object; mine detection analysis; structural noise analysis for cars; acoustic barrier analysis; and symphonic hall/auditorium predictions and speaker enclosure modeling
Jinghai, Zhou; Tianbei, Kang; Fengchi, Wang; Xindong, Wang
2017-11-01
Eight less stirrups in the core area frame joints are simulated by ABAQUS finite element numerical software. The composite reinforcement method is strengthened with carbon fiber and increasing column section, the axial compression ratio of reinforced specimens is 0.3, 0.45 and 0.6 respectively. The results of the load-displacement curve, ductility and stiffness are analyzed, and it is found that the different axial compression ratio has great influence on the bearing capacity of increasing column section strengthening method, and has little influence on carbon fiber reinforcement method. The different strengthening schemes improve the ultimate bearing capacity and ductility of frame joints in a certain extent, composite reinforcement joints strengthening method to improve the most significant, followed by increasing column section, reinforcement method of carbon fiber reinforced joints to increase the minimum.
Computational electrodynamics the finite-difference time-domain method
Taflove, Allen
2005-01-01
This extensively revised and expanded third edition of the Artech House bestseller, Computational Electrodynamics: The Finite-Difference Time-Domain Method, offers engineers the most up-to-date and definitive resource on this critical method for solving Maxwell's equations. The method helps practitioners design antennas, wireless communications devices, high-speed digital and microwave circuits, and integrated optical devices with unsurpassed efficiency. There has been considerable advancement in FDTD computational technology over the past few years, and the third edition brings professionals the very latest details with entirely new chapters on important techniques, major updates on key topics, and new discussions on emerging areas such as nanophotonics. What's more, to supplement the third edition, the authors have created a Web site with solutions to problems, downloadable graphics and videos, and updates, making this new edition the ideal textbook on the subject as well.
Finite-difference modeling of commercial aircraft using TSAR
Energy Technology Data Exchange (ETDEWEB)
Pennock, S.T.; Poggio, A.J.
1994-11-15
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.
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.
1994-11-15
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.
Moving magnets in a micromagnetic finite-difference framework
Rissanen, Ilari; Laurson, Lasse
2018-05-01
We present a method and an implementation for smooth linear motion in a finite-difference-based micromagnetic simulation code, to be used in simulating magnetic friction and other phenomena involving moving microscale magnets. Our aim is to accurately simulate the magnetization dynamics and relative motion of magnets while retaining high computational speed. To this end, we combine techniques for fast scalar potential calculation and cubic b-spline interpolation, parallelizing them on a graphics processing unit (GPU). The implementation also includes the possibility of explicitly simulating eddy currents in the case of conducting magnets. We test our implementation by providing numerical examples of stick-slip motion of thin films pulled by a spring and the effect of eddy currents on the switching time of magnetic nanocubes.
Energy Technology Data Exchange (ETDEWEB)
Saas, L.
2004-05-01
This Thesis deals with sedimentary basin modeling whose goal is the prediction through geological times of the localizations and appraisal of hydrocarbons quantities present in the ground. Due to the natural and evolutionary decomposition of the sedimentary basin in blocks and stratigraphic layers, domain decomposition methods are requested to simulate flows of waters and of hydrocarbons in the ground. Conservations laws are used to model the flows in the ground and form coupled partial differential equations which must be discretized by finite volume method. In this report we carry out a study on finite volume methods on non-matching grids solved by domain decomposition methods. We describe a family of finite volume schemes on non-matching grids and we prove that the associated global discretized problem is well posed. Then we give an error estimate. We give two examples of finite volume schemes on non matching grids and the corresponding theoretical results (Constant scheme and Linear scheme). Then we present the resolution of the global discretized problem by a domain decomposition method using arbitrary interface conditions (for example Robin conditions). Finally we give numerical results which validate the theoretical results and study the use of finite volume methods on non-matching grids for basin modeling. (author)
Modeling of NiTiHf using finite difference method
Farjam, Nazanin; Mehrabi, Reza; Karaca, Haluk; Mirzaeifar, Reza; Elahinia, Mohammad
2018-03-01
NiTiHf is a high temperature and high strength shape memory alloy with transformation temperatures above 100oC. A constitutive model based on Gibbs free energy is developed to predict the behavior of this material. Two different irrecoverable strains including transformation induced plastic strain (TRIP) and viscoplastic strain (VP) are considered when using high temperature shape memory alloys (HTSMAs). The first one happens during transformation at high levels of stress and the second one is related to the creep which is rate-dependent. The developed model is implemented for NiTiHf under uniaxial loading. Finite difference method is utilized to solve the proposed equations. The material parameters in the equations are calibrated from experimental data. Simulation results are captured to investigate the superelastic behavior of NiTiHf. The extracted results are compared with experimental tests of isobaric heating and cooling at different levels of stress and also superelastic tests at different levels of temperature. More results are generated to investigate the capability of the proposed model in the prediction of the irrecoverable strain after full transformation in HTSMAs.
The performance of different cumulus parameterization schemes in ...
Indian Academy of Sciences (India)
Introduction. The Malaysian climate is generally categorized as ... J. Earth Syst. Sci. 121 ... disturbances that influence the weather pattern of ... models to various factors such as the various phys- .... There is also no cloud model in this scheme.
Mapping of the Universe of Knowledge in Different Classification Schemes
Directory of Open Access Journals (Sweden)
M. P. Satija
2017-06-01
Full Text Available Given the variety of approaches to mapping the universe of knowledge that have been presented and discussed in the literature, the purpose of this paper is to systematize their main principles and their applications in the major general modern library classification schemes. We conducted an analysis of the literature on classification and the main classification systems, namely Dewey/Universal Decimal Classification, Cutter’s Expansive Classification, Subject Classification of J.D. Brown, Colon Classification, Library of Congress Classification, Bibliographic Classification, Rider’s International Classification, Bibliothecal Bibliographic Klassification (BBK, and Broad System of Ordering (BSO. We conclude that the arrangement of the main classes can be done following four principles that are not mutually exclusive: ideological principle, social purpose principle, scientific order, and division by discipline. The paper provides examples and analysis of each system. We also conclude that as knowledge is ever-changing, classifications also change and present a different structure of knowledge depending upon the society and time of their design.
Finite-difference solution of the space-angle-lethargy-dependent slowing-down transport equation
Energy Technology Data Exchange (ETDEWEB)
Matausek, M V [Boris Kidric Vinca Institute of Nuclear Sciences, Vinca, Belgrade (Yugoslavia)
1972-07-01
A procedure has been developed for solving the slowing-down transport equation for a cylindrically symmetric reactor system. The anisotropy of the resonance neutron flux is treated by the spherical harmonics formalism, which reduces the space-angle-Iethargy-dependent transport equation to a matrix integro-differential equation in space and lethargy. Replacing further the lethargy transfer integral by a finite-difference form, a set of matrix ordinary differential equations is obtained, with lethargy-and space dependent coefficients. If the lethargy pivotal points are chosen dense enough so that the difference correction term can be ignored, this set assumes a lower block triangular form and can be solved directly by forward block substitution. As in each step of the finite-difference procedure a boundary value problem has to be solved for a non-homogeneous system of ordinary differential equations with space-dependent coefficients, application of any standard numerical procedure, for example, the finite-difference method or the method of adjoint equations, is too cumbersome and would make the whole procedure practically inapplicable. A simple and efficient approximation is proposed here, allowing analytical solution for the space dependence of the spherical-harmonics flux moments, and hence the derivation of the recurrence relations between the flux moments at successive lethargy pivotal points. According to the procedure indicated above a computer code has been developed for the CDC -3600 computer, which uses the KEDAK nuclear data file. The space and lethargy distribution of the resonance neutrons can be computed in such a detailed fashion as the neutron cross-sections are known for the reactor materials considered. The computing time is relatively short so that the code can be efficiently used, either autonomously, or as part of some complex modular scheme. Typical results will be presented and discussed in order to prove and illustrate the applicability of the
Finite differences versus finite elements in slab geometry, even-parity transport theory
International Nuclear Information System (INIS)
Miller, W.F. Jr.; Noh, T.
1993-01-01
There continues to be considerable interest in the application of the even-parity transport equation to problems of radiation transfer and neutron transport. The motivation for this interest arises from several potential advantages of this equation when compared with the more traditional first-order form of the equation. First, assuming that the scalar flux is of primary interest, the angular domain under consideration is one-half of that required for the first-order equation. Thus, for the same degree of accuracy, one would hopefully require substantiably fewer unknown values of the dependent variable to be determined. Secondly, the elliptic-like nature of the set of even-parity equations should allow certain parallel computer architectures to be used more readily. In a recent paper, it was shown that for neutron transport applications in slab geometry, finite differencing the even-parity equation on the cell edges yields algebraic equations with numerical properties that are superior to the traditional diamond difference approach. Specifically, a positive, second-order method with a rapidly convergent iteration approach emerged from cell-edge differencing. Additionally, for radiation transfer problems that are optically thick, it was shown that cell-edge differencing demonstrates better behavior than does diamond-differencing. However, some problems in accuracy could occur due to vacuum boundaries as well as at interfaces between very different types of material regions. These problems emerge from a boundary-layer analysis of the so called open-quotes thickclose quotes diffusion limit. For neutronics calculations, which are the subject of this paper, however, the open-quotes thickclose quotes diffusion limit analysis has little applicability, and the cell-edge differencing derived previously seems to have considerable promise. 13 refs., 2 figs., 3 tabs
Black-Scholes finite difference modeling in forecasting of call warrant prices in Bursa Malaysia
Mansor, Nur Jariah; Jaffar, Maheran Mohd
2014-07-01
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.
Schwing, Alan Michael
For computational fluid dynamics, the governing equations are solved on a discretized domain of nodes, faces, and cells. The quality of the grid or mesh can be a driving source for error in the results. While refinement studies can help guide the creation of a mesh, grid quality is largely determined by user expertise and understanding of the flow physics. Adaptive mesh refinement is a technique for enriching the mesh during a simulation based on metrics for error, impact on important parameters, or location of important flow features. This can offload from the user some of the difficult and ambiguous decisions necessary when discretizing the domain. This work explores the implementation of adaptive mesh refinement in an implicit, unstructured, finite-volume solver. Consideration is made for applying modern computational techniques in the presence of hanging nodes and refined cells. The approach is developed to be independent of the flow solver in order to provide a path for augmenting existing codes. It is designed to be applicable for unsteady simulations and refinement and coarsening of the grid does not impact the conservatism of the underlying numerics. The effect on high-order numerical fluxes of fourth- and sixth-order are explored. Provided the criteria for refinement is appropriately selected, solutions obtained using adapted meshes have no additional error when compared to results obtained on traditional, unadapted meshes. In order to leverage large-scale computational resources common today, the methods are parallelized using MPI. Parallel performance is considered for several test problems in order to assess scalability of both adapted and unadapted grids. Dynamic repartitioning of the mesh during refinement is crucial for load balancing an evolving grid. Development of the methods outlined here depend on a dual-memory approach that is described in detail. Validation of the solver developed here against a number of motivating problems shows favorable
International Nuclear Information System (INIS)
Potemki, Valeri G.; Borisevich, Valentine D.; Yupatov, Sergei V.
1996-01-01
This paper describes the the next evolution step in development of the direct method for solving systems of Nonlinear Algebraic Equations (SNAE). These equations arise from the finite difference approximation of original nonlinear partial differential equations (PDE). This method has been extended on the SNAE with three variables. The solving SNAE bases on Reiterating General Singular Value Decomposition of rectangular matrix pencils (RGSVD-algorithm). In contrast to the computer algebra algorithm in integer arithmetic based on the reduction to the Groebner's basis that algorithm is working in floating point arithmetic and realizes the reduction to the Kronecker's form. The possibilities of the method are illustrated on the example of solving the one-dimensional diffusion equation for 3-component model isotope mixture in a ga centrifuge. The implicit scheme for the finite difference equations without simplifying the nonlinear properties of the original equations is realized. The technique offered provides convergence to the solution for the single run. The Toolbox SNAE is developed in the framework of the high performance numeric computation and visualization software MATLAB. It includes more than 30 modules in MATLAB language for solving SNAE with two and three variables. (author)
A coarse-mesh nodal method-diffusive-mesh finite difference method
International Nuclear Information System (INIS)
Joo, H.; Nichols, W.R.
1994-01-01
Modern nodal methods have been successfully used for conventional light water reactor core analyses where the homogenized, node average cross sections (XSs) and the flux discontinuity factors (DFs) based on equivalence theory can reliably predict core behavior. For other types of cores and other geometries characterized by tightly-coupled, heterogeneous core configurations, the intranodal flux shapes obtained from a homogenized nodal problem may not accurately portray steep flux gradients near fuel assembly interfaces or various reactivity control elements. This may require extreme values of DFs (either very large, very small, or even negative) to achieve a desired solution accuracy. Extreme values of DFs, however, can disrupt the convergence of the iterative methods used to solve for the node average fluxes, and can lead to a difficulty in interpolating adjacent DF values. Several attempts to remedy the problem have been made, but nothing has been satisfactory. A new coarse-mesh nodal scheme called the Diffusive-Mesh Finite Difference (DMFD) technique, as contrasted with the coarse-mesh finite difference (CMFD) technique, has been developed to resolve this problem. This new technique and the development of a few-group, multidimensional kinetics computer program are described in this paper
Gyrya, V.; Lipnikov, K.
2017-11-01
We present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, we observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.
Finite-difference analysis of shells impacting rigid barriers
International Nuclear Information System (INIS)
Pirotin, S.D.; Witmer, E.A.
1977-01-01
Nuclear power plants must be protected from the adverse effects of missile impacts. A significant category of missile impact involves deformable structures (pressure vessel components, whipping pipes) striking relatively rigid targets (concrete walls, bumpers) which act as protective devices. The response and interaction of these structures is needed to assess the adequacy of these barriers for protecting vital safety related equipment. The present investigation represents an initial attempt to develop an efficient numerical procedure for predicting the deformations and impact force time-histories of shells which impact upon a rigid target. The general large-deflection equations of motion of the shell are expressed in finite-difference form in space and integrated in time through application of the central-difference temporal operator. The effect of material nonlinearities is treated by a mechanical sublayer material model which handles the strain-hardening, Bauschinger, and strain-rate effects. The general adequacy of this shell treatment has been validated by comparing predictions with the results of various experiments in which structures have been subjected to well-defined transient forcing functions (typically high-explosive impulse loading). The 'new' ingredient addressed in the present study involves an accounting for impact interaction and response of both the target structure and the attacking body. (Auth.)
International Nuclear Information System (INIS)
Koteras, J.R.
1996-01-01
The prediction of stresses and displacements around tunnels buried deep within the earth is an important class of geomechanics problems. The material behavior immediately surrounding the tunnel is typically nonlinear. The surrounding mass, even if it is nonlinear, can usually be characterized by a simple linear elastic model. The finite element method is best suited for modeling nonlinear materials of limited volume, while the boundary element method is well suited for modeling large volumes of linear elastic material. A computational scheme that couples the finite element and boundary element methods would seem particularly useful for geomechanics problems. A variety of coupling schemes have been proposed, but they rely on direct solution methods. Direct solution techniques have large storage requirements that become cumbersome for large-scale three-dimensional problems. An alternative to direct solution methods is iterative solution techniques. A scheme has been developed for coupling the finite element and boundary element methods that uses an iterative solution method. This report shows that this coupling scheme is valid for problems where nonlinear material behavior occurs in the finite element region
Xu, Wenying; Wang, Zidong; Ho, Daniel W C
2018-05-01
This paper is concerned with the finite-horizon consensus problem for a class of discrete time-varying multiagent systems with external disturbances and missing measurements. To improve the communication reliability, redundant channels are introduced and the corresponding protocol is constructed for the information transmission over redundant channels. An event-triggered scheme is adopted to determine whether the information of agents should be transmitted to their neighbors. Subsequently, an observer-type event-triggered control protocol is proposed based on the latest received neighbors' information. The purpose of the addressed problem is to design a time-varying controller based on the observed information to achieve the consensus performance in a finite horizon. By utilizing a constrained recursive Riccati difference equation approach, some sufficient conditions are obtained to guarantee the consensus performance, and the controller parameters are also designed. Finally, a numerical example is provided to demonstrate the desired reliability of redundant channels and the effectiveness of the event-triggered control protocol.
Finite element analysis of thermal stress distribution in different ...
African Journals Online (AJOL)
Nigerian Journal of Clinical Practice. Journal Home ... Von Mises and thermal stress distributions were evaluated. Results: In all ... distribution. Key words: Amalgam, finite element method, glass ionomer cement, resin composite, thermal stress ...
Finite-difference numerical simulations of underground explosion cavity decoupling
Aldridge, D. F.; Preston, L. A.; Jensen, R. P.
2012-12-01
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
Non-linear analysis of skew thin plate by finite difference method
International Nuclear Information System (INIS)
Kim, Chi Kyung; Hwang, Myung Hwan
2012-01-01
This paper deals with a discrete analysis capability for predicting the geometrically nonlinear behavior of skew thin plate subjected to uniform pressure. The differential equations are discretized by means of the finite difference method which are used to determine the deflections and the in-plane stress functions of plates and reduced to several sets of linear algebraic simultaneous equations. For the geometrically non-linear, large deflection behavior of the plate, the non-linear plate theory is used for the analysis. An iterative scheme is employed to solve these quasi-linear algebraic equations. Several problems are solved which illustrate the potential of the method for predicting the finite deflection and stress. For increasing lateral pressures, the maximum principal tensile stress occurs at the center of the plate and migrates toward the corners as the load increases. It was deemed important to describe the locations of the maximum principal tensile stress as it occurs. The load-deflection relations and the maximum bending and membrane stresses for each case are presented and discussed
Solution to PDEs using radial basis function finite-differences (RBF-FD) on multiple GPUs
International Nuclear Information System (INIS)
Bollig, Evan F.; Flyer, Natasha; Erlebacher, Gordon
2012-01-01
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.
Evaluation of finite difference and FFT-based solutions of the transport of intensity equation.
Zhang, Hongbo; Zhou, Wen-Jing; Liu, Ying; Leber, Donald; Banerjee, Partha; Basunia, Mahmudunnabi; Poon, Ting-Chung
2018-01-01
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.
Do, Seongju; Li, Haojun; Kang, Myungjoo
2017-06-01
In this paper, we present an accurate and efficient wavelet-based adaptive weighted essentially non-oscillatory (WENO) scheme for hydrodynamics and ideal magnetohydrodynamics (MHD) equations arising from the hyperbolic conservation systems. The proposed method works with the finite difference weighted essentially non-oscillatory (FD-WENO) method in space and the third order total variation diminishing (TVD) Runge-Kutta (RK) method in time. The philosophy of this work is to use the lifted interpolating wavelets as not only detector for singularities but also interpolator. Especially, flexible interpolations can be performed by an inverse wavelet transformation. When the divergence cleaning method introducing auxiliary scalar field ψ is applied to the base numerical schemes for imposing divergence-free condition to the magnetic field in a MHD equation, the approximations to derivatives of ψ require the neighboring points. Moreover, the fifth order WENO interpolation requires large stencil to reconstruct high order polynomial. In such cases, an efficient interpolation method is necessary. The adaptive spatial differentiation method is considered as well as the adaptation of grid resolutions. In order to avoid the heavy computation of FD-WENO, in the smooth regions fixed stencil approximation without computing the non-linear WENO weights is used, and the characteristic decomposition method is replaced by a component-wise approach. Numerical results demonstrate that with the adaptive method we are able to resolve the solutions that agree well with the solution of the corresponding fine grid.
International Nuclear Information System (INIS)
Park, Beom Woo; Joo, Han Gyu
2015-01-01
Highlights: • The stiffness confinement method is combined with multigroup CMFD with SENM nodal kernel. • The systematic methods for determining the shape and amplitude frequencies are established. • Eigenvalue problems instead of fixed source problems are solved in the transient calculation. • It is demonstrated that much larger time step sizes can be used with the SCM–CMFD method. - Abstract: An improved Stiffness Confinement Method (SCM) is formulated within the framework of the coarse mesh finite difference (CMFD) formulation for efficient multigroup spatial kinetics calculation. The algorithm for searching for the amplitude frequency that makes the dynamic eigenvalue unity is developed in a systematic way along with the methods for determining the shape and precursor frequencies. A nodal calculation scheme is established within the CMFD framework to incorporate the cross section changes due to thermal feedback and dynamic frequency update. The conditional nodal update scheme is employed such that the transient calculation is performed mostly with the CMFD formulation and the CMFD parameters are conditionally updated by intermittent nodal calculations. A quadratic representation of amplitude frequency is introduced as another improvement. The performance of the improved SCM within the CMFD framework is assessed by comparing the solution accuracy and computing times for the NEACRP control rod ejection benchmark problems with those obtained with the Crank–Nicholson method with exponential transform (CNET). It is demonstrated that the improved SCM is beneficial for large time step size calculations with stability and accuracy enhancement
International Nuclear Information System (INIS)
Sulbhewar, Litesh N; Raveendranath, P
2014-01-01
An efficient piezoelectric smart beam finite element based on Reddy’s third-order displacement field and layerwise linear potential is presented here. The present formulation is based on the coupled polynomial field interpolation of variables, unlike conventional piezoelectric beam formulations that use independent polynomials. Governing equations derived using a variational formulation are used to establish the relationship between field variables. The resulting expressions are used to formulate coupled shape functions. Starting with an assumed cubic polynomial for transverse displacement (w) and a linear polynomial for electric potential (φ), coupled polynomials for axial displacement (u) and section rotation (θ) are found. This leads to a coupled quadratic polynomial representation for axial displacement (u) and section rotation (θ). The formulation allows accommodation of extension–bending, shear–bending and electromechanical couplings at the interpolation level itself, in a variationally consistent manner. The proposed interpolation scheme is shown to eliminate the locking effects exhibited by conventional independent polynomial field interpolations and improve the convergence characteristics of HSDT based piezoelectric beam elements. Also, the present coupled formulation uses only three mechanical degrees of freedom per node, one less than the conventional formulations. Results from numerical test problems prove the accuracy and efficiency of the present formulation. (paper)
International Nuclear Information System (INIS)
Hua Jinsong; Lin Ping; Liu Chun; Wang Qi
2011-01-01
Highlights: → We study phase-field models for multi-phase flow computation. → We develop an energy-law preserving C0 FEM. → We show that the energy-law preserving method work better. → We overcome unphysical oscillation associated with the Cahn-Hilliard model. - Abstract: We use the idea in to develop the energy law preserving method and compute the diffusive interface (phase-field) models of Allen-Cahn and Cahn-Hilliard type, respectively, governing the motion of two-phase incompressible flows. We discretize these two models using a C 0 finite element in space and a modified midpoint scheme in time. To increase the stability in the pressure variable we treat the divergence free condition by a penalty formulation, under which the discrete energy law can still be derived for these diffusive interface models. Through an example we demonstrate that the energy law preserving method is beneficial for computing these multi-phase flow models. We also demonstrate that when applying the energy law preserving method to the model of Cahn-Hilliard type, un-physical interfacial oscillations may occur. We examine the source of such oscillations and a remedy is presented to eliminate the oscillations. A few two-phase incompressible flow examples are computed to show the good performance of our method.
Madhulatha, A.; Rajeevan, M.
2018-02-01
Main objective of the present paper is to examine the role of various parameterization schemes in simulating the evolution of mesoscale convective system (MCS) occurred over south-east India. Using the Weather Research and Forecasting (WRF) model, numerical experiments are conducted by considering various planetary boundary layer, microphysics, and cumulus parameterization schemes. Performances of different schemes are evaluated by examining boundary layer, reflectivity, and precipitation features of MCS using ground-based and satellite observations. Among various physical parameterization schemes, Mellor-Yamada-Janjic (MYJ) boundary layer scheme is able to produce deep boundary layer height by simulating warm temperatures necessary for storm initiation; Thompson (THM) microphysics scheme is capable to simulate the reflectivity by reasonable distribution of different hydrometeors during various stages of system; Betts-Miller-Janjic (BMJ) cumulus scheme is able to capture the precipitation by proper representation of convective instability associated with MCS. Present analysis suggests that MYJ, a local turbulent kinetic energy boundary layer scheme, which accounts strong vertical mixing; THM, a six-class hybrid moment microphysics scheme, which considers number concentration along with mixing ratio of rain hydrometeors; and BMJ, a closure cumulus scheme, which adjusts thermodynamic profiles based on climatological profiles might have contributed for better performance of respective model simulations. Numerical simulation carried out using the above combination of schemes is able to capture storm initiation, propagation, surface variations, thermodynamic structure, and precipitation features reasonably well. This study clearly demonstrates that the simulation of MCS characteristics is highly sensitive to the choice of parameterization schemes.
A finite-difference contrast source inversion method
International Nuclear Information System (INIS)
Abubakar, A; Hu, W; Habashy, T M; Van den Berg, P M
2008-01-01
We present a contrast source inversion (CSI) algorithm using a finite-difference (FD) approach as its backbone for reconstructing the unknown material properties of inhomogeneous objects embedded in a known inhomogeneous background medium. Unlike the CSI method using the integral equation (IE) approach, the FD-CSI method can readily employ an arbitrary inhomogeneous medium as its background. The ability to use an inhomogeneous background medium has made this algorithm very suitable to be used in through-wall imaging and time-lapse inversion applications. Similar to the IE-CSI algorithm the unknown contrast sources and contrast function are updated alternately to reconstruct the unknown objects without requiring the solution of the full forward problem at each iteration step in the optimization process. The FD solver is formulated in the frequency domain and it is equipped with a perfectly matched layer (PML) absorbing boundary condition. The FD operator used in the FD-CSI method is only dependent on the background medium and the frequency of operation, thus it does not change throughout the inversion process. Therefore, at least for the two-dimensional (2D) configurations, where the size of the stiffness matrix is manageable, the FD stiffness matrix can be inverted using a non-iterative inversion matrix approach such as a Gauss elimination method for the sparse matrix. In this case, an LU decomposition needs to be done only once and can then be reused for multiple source positions and in successive iterations of the inversion. Numerical experiments show that this FD-CSI algorithm has an excellent performance for inverting inhomogeneous objects embedded in an inhomogeneous background medium
Directory of Open Access Journals (Sweden)
Taohua Liu
2017-01-01
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(KlogK. 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.
Nonstandard Finite Difference Variational Integrators for Multisymplectic PDEs
Directory of Open Access Journals (Sweden)
Cuicui Liao
2012-01-01
discretization and a square discretization, respectively. These methods are naturally multisymplectic. Their discrete multisymplectic structures are presented by the multisymplectic form formulas. The convergence of the discretization schemes is discussed. The effectiveness and efficiency of the proposed methods are verified by the numerical experiments.
ORIGINAL ARTICLE Fitted-Stable Finite Difference Method for ...
African Journals Online (AJOL)
Gemechis
two point boundary value problems with the boundary layer at one end (left or right) ... scheme (SCD Method) and its value is obtained using the theory of singular ..... Eq. (15) at the point. N iih xxi. , ,2 ,1 ,0 ,.. = = = and taking the limit as. 0. →.
Yan, Y.; Barth, A.; Beckers, J. M.; Brankart, J. M.; Brasseur, P.; Candille, G.
2017-07-01
In this paper, three incremental analysis update schemes (IAU 0, IAU 50 and IAU 100) are compared in the same assimilation experiments with a realistic eddy permitting primitive equation model of the North Atlantic Ocean using the Ensemble Kalman Filter. The difference between the three IAU schemes lies on the position of the increment update window. The relevance of each IAU scheme is evaluated through analyses on both thermohaline and dynamical variables. The validation of the assimilation results is performed according to both deterministic and probabilistic metrics against different sources of observations. For deterministic validation, the ensemble mean and the ensemble spread are compared to the observations. For probabilistic validation, the continuous ranked probability score (CRPS) is used to evaluate the ensemble forecast system according to reliability and resolution. The reliability is further decomposed into bias and dispersion by the reduced centred random variable (RCRV) score. The obtained results show that 1) the IAU 50 scheme has the same performance as the IAU 100 scheme 2) the IAU 50/100 schemes outperform the IAU 0 scheme in error covariance propagation for thermohaline variables in relatively stable region, while the IAU 0 scheme outperforms the IAU 50/100 schemes in dynamical variables estimation in dynamically active region 3) in case with sufficient number of observations and good error specification, the impact of IAU schemes is negligible. The differences between the IAU 0 scheme and the IAU 50/100 schemes are mainly due to different model integration time and different instability (density inversion, large vertical velocity, etc.) induced by the increment update. The longer model integration time with the IAU 50/100 schemes, especially the free model integration, on one hand, allows for better re-establishment of the equilibrium model state, on the other hand, smooths the strong gradients in dynamically active region.
A finite different field solver for dipole modes
International Nuclear Information System (INIS)
Nelson, E.M.
1992-08-01
A finite element field solver for dipole modes in axisymmetric structures has been written. The second-order elements used in this formulation yield accurate mode frequencies with no spurious modes. Quasi-periodic boundaries are included to allow travelling waves in periodic structures. The solver is useful in applications requiring precise frequency calculations such as detuned accelerator structures for linear colliders. Comparisons are made with measurements and with the popular but less accurate field solver URMEL
Directory of Open Access Journals (Sweden)
Navnit Jha
2014-04-01
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.
Chabory, A.; Hon, de B.P.; Schilders, W.H.A.; Tijhuis, A.G.
2008-01-01
Finite-difference techniques are very popular and versatile numerical tools in computational electromagnetics. In this paper, we propose a preconditioned finite-difference frequency-domain method (FDFD) to model periodic structures in 2D and 3D. The preconditioner follows from a modal decoupling
Chabory, A.; Hon, de B.P.; Schilders, W.H.A.; Tijhuis, A.G.
2008-01-01
Finite-difference techniques are very popular and versatile numerical tools in computational electromagnetics. In this paper, we propose a preconditioned finite-difference frequency-domain method (FDFD) to model periodic structures in 2D and 3D. The preconditioner follows from a modal decoupling
International Nuclear Information System (INIS)
Shtromberger, N.L.
1989-01-01
To design a cyclotron magnetic system the legitimacy of two-dimensional approximations application is discussed. In all the calculations the finite difference method is used, and the linearization method with further use of the gradient conjugation method is used to solve the set of finite-difference equations. 3 refs.; 5 figs
The computation of pressure waves in shock tubes by a finite difference procedure
International Nuclear Information System (INIS)
Barbaro, M.
1988-09-01
A finite difference solution of one-dimensional unsteady isentropic compressible flow equations is presented. The computer program has been tested by solving some cases of the Riemann shock tube problem. Predictions are in good agreement with those presented by other authors. Some inaccuracies may be attributed to the wave smearing consequent of the finite-difference treatment. (author)
Quiney, H. M.; Glushkov, V. N.; Wilson, S.; Sabin,; Brandas, E
2001-01-01
A comparison is made of the accuracy achieved in finite difference and finite basis set approximations to the Dirac equation for the ground state of the hydrogen molecular ion. The finite basis set calculations are carried out using a distributed basis set of Gaussian functions the exponents and
Finite-Time Synchronization of Chaotic Systems with Different Dimension and Secure Communication
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Shouquan Pang
2016-01-01
Full Text Available Finite-time synchronization of chaotic systems with different dimension and secure communication is investigated. It is rigorously proven that global finite-time synchronization can be achieved between three-dimension Lorenz chaotic system and four-dimension Lorenz hyperchaotic system which have certain parameters or uncertain parameters. The electronic circuits of finite-time synchronization using Multisim 12 are designed to verify our conclusion. And the application to the secure communications is also analyzed and discussed.
Panczak, Tim; Ring, Steve; Welch, Mark
1999-01-01
Thermal engineering has long been left out of the concurrent engineering environment dominated by CAD (computer aided design) and FEM (finite element method) software. Current tools attempt to force the thermal design process into an environment primarily created to support structural analysis, which results in inappropriate thermal models. As a result, many thermal engineers either build models "by hand" or use geometric user interfaces that are separate from and have little useful connection, if any, to CAD and FEM systems. This paper describes the development of a new thermal design environment called the Thermal Desktop. This system, while fully integrated into a neutral, low cost CAD system, and which utilizes both FEM and FD methods, does not compromise the needs of the thermal engineer. Rather, the features needed for concurrent thermal analysis are specifically addressed by combining traditional parametric surface based radiation and FD based conduction modeling with CAD and FEM methods. The use of flexible and familiar temperature solvers such as SINDA/FLUINT (Systems Improved Numerical Differencing Analyzer/Fluid Integrator) is retained.
SLIC: an interactive mesh generator for finite element and finite difference application programs
International Nuclear Information System (INIS)
Gerhard, M.A.; Greenlaw, R.C.
1979-01-01
Computers with extended memory, such as the CDC STAR 100 and the CRAY 1 with mega-word capacities, are greatly enlarging the size of finite element problems which can be solved. The cost of developing and testing large meshes can be prohibitive unless one uses a computer program for mesh generation and plotting. SLIC is an interactive mesh program which builds and plots 2- and 3-D continuum meshes from interactive terminal or disc input. The user inputs coordinates for certain key points and enters commands which complete the description of the geometry. Entire surfaces and volumes are then generated from the geometric skeleton. SLIC allows the user to correct input errors and saves the corrected command list for later reuse. The mesh can be plotted on a video display at any stage of development to evaluate the work in progress. Output is in the form of an input file to a user-selected computer code. Among the available output types are ADINA, SAP4, and NIKE2D. 11 figures
International Nuclear Information System (INIS)
Runca, E.; Melli, P.; Sardei, F.
1985-01-01
A finite-difference scheme and a Galerkin scheme are compared with respect to a very accurate solution describing time-dependent advection and diffusion of air pollutants from a line source in an atmosphere vertically stratified and limited by an inversion layer. The accurate solution was achieved by applying the finite-difference scheme on a very refined grid with a very small time step. The grid size and time step were defined according to stability and accuracy criteria discussed in the text. It is found that for the problem considered the two methods can be considered equally accurate. However, the Galerkin method gives a better approximation in the vicinity of the source. This was assumed to be partly due to the different way the source term is taken into account in the two methods. Improvement of the accuracy of the finite-difference scheme was achieved by approximating, at every step, the contribution of the source term by a Gaussian puff moving and diffusing with the velocity and diffusivity of the source location, instead of utilizing a stepwise function for the numerical approximation of the delta function representing the source term
Gao, Longfei
2018-02-22
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.
Gao, Longfei; Keyes, David E.
2018-01-01
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.
Energy Technology Data Exchange (ETDEWEB)
Bettaibi, Soufiene, E-mail: Bettaibisoufiene@gmail.com [UR: Rayonnement Thermique, Faculté des Sciences de Tunis, Université de Tunis El Manar, 2092 Tunis (Tunisia); Kuznik, Frédéric [INSA-Lyon, CETHIL, F-69621 Villeurbanne (France); Université de Lyon, CNRS, UMR5008, F-69622 Villeurbanne (France); Sediki, Ezeddine [UR: Rayonnement Thermique, Faculté des Sciences de Tunis, Université de Tunis El Manar, 2092 Tunis (Tunisia)
2014-06-27
Highlights: • Mixed convection heat transfer in 2D lid-driven cavity is studied numerically. • Hybrid scheme with multiple relaxation time lattice Boltzmann method is used to obtain the velocity field. • Finite difference method is used to compute the temperature. • Effect of both Richardson and Reynolds numbers for mixed convection is studied. - Abstract: Mixed convection heat transfer in two-dimensional lid-driven rectangular cavity filled with air (Pr=0.71) is studied numerically. A hybrid scheme with multiple relaxation time lattice Boltzmann method (MRT-LBM) is used to obtain the velocity field while the temperature field is deduced from energy balance equation by using the finite difference method (FDM). The main objective of this work is to investigate the model effectiveness for mixed convection flow simulation. Results are presented in terms of streamlines, isotherms and Nusselt numbers. Excellent agreement is obtained between our results and previous works. The different comparisons demonstrate the robustness and the accuracy of our proposed approach.
Pressure transient analysis in single and two-phase water by finite difference methods
International Nuclear Information System (INIS)
Berry, G.F.; Daley, J.G.
1977-01-01
An important consideration in the design of LMFBR steam generators is the possibility of leakage from a steam generator water tube. The ensuing sodium/water reaction will be largely controlled by the amount of water available at the leak site, thus analysis methods treating this event must have the capability of accurately modeling pressure transients through all states of water occurring in a steam generator, whether single or two-phase. The equation systems of the present model consist of the conservation equations together with an equation of state for one-dimensional homogeneous flow. These equations are then solved using finite difference techniques with phase considerations and non-equilibrium effects being treated through the equation of state. The basis for water property computation is Keenan's 'fundamental equation of state' which is applicable to single-phase water at pressures less than 1000 bars and temperatures less than 1300 0 C. This provides formulations allowing computation of any water property to any desired precision. Two-phase properties are constructed from values on the saturation line. The use of formulations permits the direct calculation of any thermodynamic property (or property derivative) to great precision while requiring very little computer storage, but does involve considerable computation time. For this reason an optional calculation scheme based on the method of 'transfinite interpolation' is included to give rapid computation in selected regions with decreased precision. The conservation equations were solved using the second order Lax-Wendroff scheme which includes wall friction, allows the formation of shocks and locally supersonic flow. Computational boundary conditions were found from a method-of-characteristics solution at the reservoir and receiver ends. The local characteristics were used to interpolate data from inside the pipe to the boundary
Parsani, Matteo
2013-04-10
Explicit Runge--Kutta schemes with large stable step sizes are developed for integration of high-order spectral difference spatial discretizations on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard explicit Runge--Kutta schemes available in the literature. Furthermore, they have a small principal error norm and admit a low-storage implementation. The advantages of the new schemes are demonstrated through application to the Euler equations and the linearized Euler equations.
Parsani, Matteo; Ketcheson, David I.; Deconinck, W.
2013-01-01
Explicit Runge--Kutta schemes with large stable step sizes are developed for integration of high-order spectral difference spatial discretizations on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard explicit Runge--Kutta schemes available in the literature. Furthermore, they have a small principal error norm and admit a low-storage implementation. The advantages of the new schemes are demonstrated through application to the Euler equations and the linearized Euler equations.
Brinkman, Daniel
2013-05-01
We present and discuss a mathematical model for the operation of bilayer organic photovoltaic devices. Our model couples drift-diffusion-recombination equations for the charge carriers (specifically, electrons and holes) with a reaction-diffusion equation for the excitons/polaron pairs and Poisson\\'s equation for the self-consistent electrostatic potential. The material difference (i.e. the HOMO/LUMO gap) of the two organic substrates forming the bilayer device is included as a work-function potential. Firstly, we perform an asymptotic analysis of the scaled one-dimensional stationary state system: (i) with focus on the dynamics on the interface and (ii) with the goal of simplifying the bulk dynamics away from the interface. Secondly, we present a two-dimensional hybrid discontinuous Galerkin finite element numerical scheme which is very well suited to resolve: (i) the material changes, (ii) the resulting strong variation over the interface, and (iii) the necessary upwinding in the discretization of drift-diffusion equations. Finally, we compare the numerical results with the approximating asymptotics. © 2013 World Scientific Publishing Company.
Syed, S. A.; Chiappetta, L. M.
1985-01-01
A methodological evaluation for two-finite differencing schemes for computer-aided gas turbine design is presented. The two computational schemes include; a Bounded Skewed Finite Differencing Scheme (BSUDS); and a Quadratic Upwind Differencing Scheme (QSDS). In the evaluation, the derivations of the schemes were incorporated into two-dimensional and three-dimensional versions of the Teaching Axisymmetric Characteristics Heuristically (TEACH) computer code. Assessments were made according to performance criteria for the solution of problems of turbulent, laminar, and coannular turbulent flow. The specific performance criteria used in the evaluation were simplicity, accuracy, and computational economy. It is found that the BSUDS scheme performed better with respect to the criteria than the QUDS. Some of the reasons for the more successful performance BSUDS are discussed.
International Nuclear Information System (INIS)
Wang Shumin; Duyn, Jeff H
2008-01-01
A hybrid method that combines the finite-difference time-domain (FDTD) method and the finite-element time-domain (FETD) method is presented for simulating radio-frequency (RF) coils in magnetic resonance imaging. This method applies a high-fidelity FETD method to RF coils, while the human body is modeled with a low-cost FDTD method. Since the FDTD and the FETD methods are applied simultaneously, the dynamic interaction between RF coils and the human body is fully accounted for. In order to simplify the treatment of the highly irregular FDTD/FETD interface, composite elements are proposed. Two examples are provided to demonstrate the validity and effectiveness of the hybrid method in high-field receive-and-transmit coil design. This approach is also applicable to general bio-electromagnetic simulations
Systematic Differences Across Evaluation Schemes and Educational Choice
DEFF Research Database (Denmark)
Rangvid, Beatrice Schindler
2015-01-01
Using large-scale register data from Denmark in a difference-in-differences framework, I analyse whether systematic disparities between internal teacher scores and external exam scores in the school-leaving certiﬁcates are linked to pupil characteristics. Such differences may mat- ter for post......-school. The corresponding increase for pupils with low educated parents is 4% points, closing 13% of the high-school enrolment gap to pupils with high educated parents....
Systematic Differences across Evaluation Schemes and Educational Choice
DEFF Research Database (Denmark)
Rangvid, Beatrice Schindler
Using large scale register data from Denmark in a difference-in-differences framework, I analyze whether systematic disparities between internal teacher scores and external exam scores in the school leaving certificates are linked to pupil characteristics. Such differences may be particularly con......-SES pupils’ predicted probability to enroll in high-school, closing almost 10% of the high-school enrolment gap to high-SES pupils. Increases for boys and migrant pupils are modest....
Itkin, Andrey
2017-01-01
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...
A Finite-Difference Solution of Solute Transport through a Membrane Bioreactor
Directory of Open Access Journals (Sweden)
B. Godongwana
2015-01-01
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.
Shishkin, G. I.
2015-11-01
An initial-boundary value problem is considered for a singularly perturbed parabolic convection-diffusion equation with a perturbation parameter ɛ (ɛ ∈ (0, 1]) multiplying the highest order derivative. The stability of a standard difference scheme based on monotone approximations of the problem on a uniform mesh is analyzed, and the behavior of discrete solutions in the presence of perturbations is examined. The scheme does not converge ɛ-uniformly in the maximum norm as the number of its grid nodes is increased. When the solution of the difference scheme converges, which occurs if N -1 ≪ ɛ and N -1 0 ≪ 1, where N and N 0 are the numbers of grid intervals in x and t, respectively, the scheme is not ɛ-uniformly well conditioned or stable to data perturbations in the grid problem and to computer perturbations. For the standard difference scheme in the presence of data perturbations in the grid problem and/or computer perturbations, conditions on the "parameters" of the difference scheme and of the computer (namely, on ɛ, N, N 0, admissible data perturbations in the grid problem, and admissible computer perturbations) are obtained that ensure the convergence of the perturbed solutions. Additionally, the conditions are obtained under which the perturbed numerical solution has the same order of convergence as the solution of the unperturbed standard difference scheme.
Kirk, Benjamin S.; Bova, Stephen W.; Bond, Ryan B.
2011-01-01
Presentation topics include background and motivation; physical modeling including governing equations and thermochemistry; finite element formulation; results of inviscid thermal nonequilibrium chemically reacting flow and viscous thermal equilibrium chemical reacting flow; and near-term effort.
A high-order solver for aerodynamic flow simulations and comparison of different numerical schemes
Mikhaylov, Sergey; Morozov, Alexander; Podaruev, Vladimir; Troshin, Alexey
2017-11-01
An implementation of high order of accuracy Discontinuous Galerkin method is presented. Reconstruction is done for the conservative variables. Gradients are calculated using the BR2 method. Coordinate transformations are done by serendipity elements. In computations with schemes of order higher than 2, curvature of the mesh lines is taken into account. A comparison with finite volume methods is performed, including WENO method with linear weights and single quadrature point on a cell side. The results of the following classical tests are presented: subsonic flow around a circular cylinder in an ideal gas, convection of two-dimensional isentropic vortex, and decay of the Taylor-Green vortex.
Energy Technology Data Exchange (ETDEWEB)
Dattoli, Giuseppe; Torre, Amalia [ENEA, Centro Ricerche Frascati, Rome (Italy). Dipt. Innovazione; Ottaviani, Pier Luigi [ENEA, Centro Ricerche Bologna (Italy); Vasquez, Luis [Madris, Univ. Complutense (Spain). Dept. de Matemateca Aplicado
1997-10-01
The finite-difference based integration method for evolution-line equations is discussed in detail and framed within the general context of the evolution operator picture. Exact analytical methods are described to solve evolution-like equations in a quite general physical context. The numerical technique based on the factorization formulae of exponential operator is then illustrated and applied to the evolution-operator in both classical and quantum framework. Finally, the general view to the finite differencing schemes is provided, displaying the wide range of applications from the classical Newton equation of motion to the quantum field theory.
Comparison between different encoding schemes for synthetic aperture imaging
DEFF Research Database (Denmark)
Nikolov, Svetoslav; Jensen, Jørgen Arendt
2002-01-01
and spatio-temporal encoding was investigated. Experiments on wire phantom in water were carried out to quantify the gain from the different encodings. The gain in SNR using an FM modulated pulse is 12 dB. The penetration depth of the images was studied using tissue mimicking phantom with frequency dependent......Synthetic transmit aperture ultrasound (STAU) imaging can create images with as low as 2 emissions, making it attractive for 3D real-time imaging. Two are the major problems to be solved: (1) complexity of the hardware involved, and (2) poor image quality due to low signal to noise ratio (SNR). We...... attenuation of 0.5 dB/(cm MHz). The combination of spatial and temporal encoding have highest penetration depth. Images to a depth of 110 mm, can successfully be made with contrast resolution comparable to that of a linear array image. The in-vivo scans show that the motion artifacts do not significantly...
Rocklin, Gabriel J; Mobley, David L; Dill, Ken A; Hünenberger, Philippe H
2013-11-14
The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges -5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol(-1)) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non-periodic PB
Energy Technology Data Exchange (ETDEWEB)
Rocklin, Gabriel J. [Department of Pharmaceutical Chemistry, University of California San Francisco, 1700 4th St., San Francisco, California 94143-2550, USA and Biophysics Graduate Program, University of California San Francisco, 1700 4th St., San Francisco, California 94143-2550 (United States); Mobley, David L. [Departments of Pharmaceutical Sciences and Chemistry, University of California Irvine, 147 Bison Modular, Building 515, Irvine, California 92697-0001, USA and Department of Chemistry, University of New Orleans, 2000 Lakeshore Drive, New Orleans, Louisiana 70148 (United States); Dill, Ken A. [Laufer Center for Physical and Quantitative Biology, 5252 Stony Brook University, Stony Brook, New York 11794-0001 (United States); Hünenberger, Philippe H., E-mail: phil@igc.phys.chem.ethz.ch [Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH, 8093 Zürich (Switzerland)
2013-11-14
The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges −5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol{sup −1}) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non
Rocklin, Gabriel J.; Mobley, David L.; Dill, Ken A.; Hünenberger, Philippe H.
2013-11-01
The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges -5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol-1) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non-periodic PB
Chu, Chunlei; Stoffa, Paul L.
2012-01-01
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
On the raising and lowering difference operators for eigenvectors of the finite Fourier transform
International Nuclear Information System (INIS)
Atakishiyeva, M K; Atakishiyev, N M
2015-01-01
We construct explicit forms of raising and lowering difference operators that govern eigenvectors of the finite (discrete) Fourier transform. Some of the algebraic properties of these operators are also examined. (paper)
Stability and non-standard finite difference method of the generalized Chua's circuit
Radwan, Ahmed G.; Moaddy, K.; Momani, Shaher M.
2011-01-01
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
Energy Technology Data Exchange (ETDEWEB)
Swegle, J.W.; Hicks, D.L.
1979-05-01
An anisotropic constitutive relation was incorporated into the Lagrangian finite-difference wavecode TOODY. The details of the implementation of the constitutive relation in the wavecode and an example of its use are discussed. 4 figures, 1 table.
Natarajan, Murali; Fairlie, T. Duncan; Dwyer Cianciolo, Alicia; Smith, Michael D.
2015-01-01
We use the mesoscale modeling capability of Mars Weather Research and Forecasting (MarsWRF) model to study the sensitivity of the simulated Martian lower atmosphere to differences in the parameterization of the planetary boundary layer (PBL). Characterization of the Martian atmosphere and realistic representation of processes such as mixing of tracers like dust depend on how well the model reproduces the evolution of the PBL structure. MarsWRF is based on the NCAR WRF model and it retains some of the PBL schemes available in the earth version. Published studies have examined the performance of different PBL schemes in NCAR WRF with the help of observations. Currently such assessments are not feasible for Martian atmospheric models due to lack of observations. It is of interest though to study the sensitivity of the model to PBL parameterization. Typically, for standard Martian atmospheric simulations, we have used the Medium Range Forecast (MRF) PBL scheme, which considers a correction term to the vertical gradients to incorporate nonlocal effects. For this study, we have also used two other parameterizations, a non-local closure scheme called Yonsei University (YSU) PBL scheme and a turbulent kinetic energy closure scheme called Mellor- Yamada-Janjic (MYJ) PBL scheme. We will present intercomparisons of the near surface temperature profiles, boundary layer heights, and wind obtained from the different simulations. We plan to use available temperature observations from Mini TES instrument onboard the rovers Spirit and Opportunity in evaluating the model results.
Macías-Díaz, J E; Macías, Siegfried; Medina-Ramírez, I E
2013-12-01
In this manuscript, we present a computational model to approximate the solutions of a partial differential equation which describes the growth dynamics of microbial films. The numerical technique reported in this work is an explicit, nonlinear finite-difference methodology which is computationally implemented using Newton's method. Our scheme is compared numerically against an implicit, linear finite-difference discretization of the same partial differential equation, whose computer coding requires an implementation of the stabilized bi-conjugate gradient method. Our numerical results evince that the nonlinear approach results in a more efficient approximation to the solutions of the biofilm model considered, and demands less computer memory. Moreover, the positivity of initial profiles is preserved in the practice by the nonlinear scheme proposed. Copyright © 2013 Elsevier Ltd. All rights reserved.
Gerya, T.; Duretz, T.; May, D. A.
2012-04-01
We present new 2D adaptive mesh refinement (AMR) algorithm based on stress-conservative finite-differences formulated for non-uniform rectangular staggered grid. The refinement approach is based on a repetitive cell splitting organized via a quad-tree construction (every parent cell is split into 4 daughter cells of equal size). Irrespective of the level of resolution every cell has 5 staggered nodes (2 horizontal velocities, 2 vertical velocities and 1 pressure) for which respective governing equations, boundary conditions and interpolation equations are formulated. The connectivity of the grid is achieved via cross-indexing of grid cells and basic nodal points located in their corners: four corner nodes are indexed for every cell and up to 4 surrounding cells are indexed for every node. The accuracy of the approach depends critically on the formulation of the stencil used at the "hanging" velocity nodes located at the boundaries between different levels of resolution. Most accurate results are obtained for the scheme based on the volume flux balance across the resolution boundary combined with stress-based interpolation of velocity orthogonal to the boundary. We tested this new approach with a number of 2D variable viscosity analytical solutions. Our tests demonstrate that the adaptive staggered grid formulation has convergence properties similar to those obtained in case of a standard, non-adaptive staggered grid formulation. This convergence is also achieved when resolution boundary crosses sharp viscosity contrast interfaces. The convergence rates measured are found to be insensitive to scenarios when the transition in grid resolution crosses sharp viscosity contrast interfaces. We compared various grid refinement strategies based on distribution of different field variables such as viscosity, density and velocity. According to these tests the refinement allows for significant (0.5-1 order of magnitude) increase in the computational accuracy at the same
Directory of Open Access Journals (Sweden)
Marcin Krzeszowiec
2015-03-01
Full Text Available Computer simulations of physical phenomena are at the moment common both in science and industry. The possibility of finding approximate solutions for complicated systems of differential equations, mathematically describing issues in the fields of mechanics, physics or chemistry, allows for shorten design and research time, often significantly reducing the need for expensive experimental studies or costly production of prototypes. However, the mentioned prevalence of these methods, particularly the Finite Element Method, resulted in analysis outcomes to be often in advance regarded as accurate ones. The purpose of the article is to showcase, on a simple stress analysis problem, how parameters such as the density of the finite element mesh, finite element formulation or integration scheme significantly influence on the simulation results and how easy it is to end up with the results that do not hold any physical sense, despite the fact that all the basic assumptions of correct analysis (suitable boundary conditions, total system energy stored etc. have been met. The results of this study can serve as a warning against premature conclusion drawing from calculations carried out by means of FEM simulation.[b]Keywords[/b]: computational mechanics, finite element method, shell elements, numerical integration
International Nuclear Information System (INIS)
Popov, Pavel P.; Pope, Stephen B.
2014-01-01
This work addresses the issue of particle mass consistency in Large Eddy Simulation/Probability Density Function (LES/PDF) methods for turbulent reactive flows. Numerical schemes for the implicit and explicit enforcement of particle mass consistency (PMC) are introduced, and their performance is examined in a representative LES/PDF application, namely the Sandia–Sydney Bluff-Body flame HM1. A new combination of interpolation schemes for velocity and scalar fields is found to better satisfy PMC than multilinear and fourth-order Lagrangian interpolation. A second-order accurate time-stepping scheme for stochastic differential equations (SDE) is found to improve PMC relative to Euler time stepping, which is the first time that a second-order scheme is found to be beneficial, when compared to a first-order scheme, in an LES/PDF application. An explicit corrective velocity scheme for PMC enforcement is introduced, and its parameters optimized to enforce a specified PMC criterion with minimal corrective velocity magnitudes
Optimized low-order explicit Runge-Kutta schemes for high- order spectral difference method
Parsani, Matteo
2012-01-01
Optimal explicit Runge-Kutta (ERK) schemes with large stable step sizes are developed for method-of-lines discretizations based on the spectral difference (SD) spatial discretization on quadrilateral grids. These methods involve many stages and provide the optimal linearly stable time step for a prescribed SD spectrum and the minimum leading truncation error coefficient, while admitting a low-storage implementation. Using a large number of stages, the new ERK schemes lead to efficiency improvements larger than 60% over standard ERK schemes for 4th- and 5th-order spatial discretization.
Neutron-proton mass difference in finite nuclei and the Nolen-Schiffer anomaly
International Nuclear Information System (INIS)
Meissner, U.G.; Rakhimov, A.M.; Wirzba, A.; Yakhshiev, U.T.
2008-01-01
The neutron-proton mass difference in finite nuclei is studied in the framework of a medium-modified Skyrme model. The possible interplay between the effective nucleon mass in finite nuclei and the Nolen-Schiffer anomaly is discussed. In particular, we find that a correct description of the properties of mirror nuclei leads to a stringent restriction of possible modifications of the nucleon's effective mass in nuclei. (orig.)
田中, 英一; TANAKA, Eiichi; 山本, 創太; YAMAMOTO, Sota; 坂本, 誠二; SAKAMOTO, Seiji; 中西, 孝文; NAKANISHI, Takafumi; 原田, 敦; HARADA, Atsushi; 水野, 雅士; MIZUNO, Masashi
2004-01-01
This paper is concerned with an individual finite element modeling system for femur and biomechanical evaluations of the influences of loading conditions, bone shape and bone density on risks of hip fracture. Firstly, a method to construct an individual finite element model by morphological parameters that represent femoral shapes was developed. Using the models with different shapes constructed by this method, the effects of fall direction, posture of upper body, femur shape and bone density...
Byun, Chansup; Guruswamy, Guru P.; Kutler, Paul (Technical Monitor)
1994-01-01
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.
Efficiency of High-Order Accurate Difference Schemes for the Korteweg-de Vries Equation
Directory of Open Access Journals (Sweden)
Kanyuta Poochinapan
2014-01-01
Full Text Available Two numerical models to obtain the solution of the KdV equation are proposed. Numerical tools, compact fourth-order and standard fourth-order finite difference techniques, are applied to the KdV equation. The fundamental conservative properties of the equation are preserved by the finite difference methods. Linear stability analysis of two methods is presented by the Von Neumann analysis. The new methods give second- and fourth-order accuracy in time and space, respectively. The numerical experiments show that the proposed methods improve the accuracy of the solution significantly.
Novel UEP LT Coding Scheme with Feedback Based on Different Degree Distributions
Directory of Open Access Journals (Sweden)
Li Ya-Fang
2016-01-01
Full Text Available Traditional unequal error protection (UEP schemes have some limitations and problems, such as the poor UEP performance of high priority data and the seriously sacrifice of low priority data in decoding property. Based on the reasonable applications of different degree distributions in LT codes, this paper puts forward a novel UEP LT coding scheme with a simple feedback to compile these data packets separately. Simulation results show that the proposed scheme can effectively protect high priority data, and improve the transmission efficiency of low priority data from 2.9% to 22.3%. Furthermore, it is fairly suitable to apply this novel scheme to multicast and broadcast environments since only a simple feedback introduced.
Renewable energy investments under different support schemes: A real options approach
DEFF Research Database (Denmark)
Boomsma, Trine Krogh; Meade, Nigel; Fleten, Stein-Erik
2012-01-01
-in tariff encourages earlier investment. Nevertheless, as investment has been undertaken, renewable energy certificate trading creates incentives for larger projects. In our baseline scenario and taking the fixed feed-in tariff as a base, the revenue required to trigger investments is 61% higher......This paper adopts a real options approach to analyze investment timing and capacity choice for renewable energy projects under different support schemes. The main purpose is to examine investment behavior under the most extensively employed support schemes, namely, feed-in tariffs and renewable...... energy certificate trading. We consider both multiple sources of uncertainty under each support scheme and uncertainty with respect to any change of support scheme, and we obtain both analytical (when possible) and numerical solutions. In a Nordic case study based on wind power, we find that the feed...
Directory of Open Access Journals (Sweden)
E. A. Levchuk
2018-01-01
Full Text Available Numerical modeling of electronic state evolution due to non-uniform external electric field in the structure metal-insulator-semiconductor with solitary donor center is carried out. Considering a nanometer disc-shaped gate as a source of the electric field, the problem for the Laplace equation in multilayered medium is solved numerically to determine the distribution of the gate potential. The energy spectrum of a bound electron is calculated from the problem for the stationary Schrödinger equation. Finite difference schemes are constructed to solve both the problems. Difference scheme for the Schrödinger equation takes into account cusp condition for the wave function at the donor location. To solve the problem for the Laplace equation, asymptotic boundary conditions for approximating the external field potential at large distances from the gate in different layers are suggested. These conditions allow to reduce the calculation domain for the electrostatic problem essentially. The effect of the boundary conditions on the accuracy of calculating the potential and energies is investigated. Using the developed difference schemes, the dependences of the energy spectrum of the bound electron on the gate potential are calculated, and the values of critical potential at which the wave function of the electron is relocated are determined. It has been found on the basis of calculation results, that governing parameter for the description of electronic behavior is the potential difference between the donor and semiconductor surface. It has been shown that critical potential difference does not depend on dielectric thickness and permittivity.
International Nuclear Information System (INIS)
Peery, J.S.; Best, F.R.
1987-01-01
A model to simulate heat pipe rapid transients has been developed. This model uses a one-dimensional development of the continuity and momentum equations to solve for the velocity and pressure distributions in both the liquid and vapor regions. A two-dimensional development of the energy equation is used to determine the temperature distributions in the liquid and vapor regions, as well as in the walls of the heat pipe. The vapor and liquid regions are coupled through mass and energy transfer due to evaporation and condensation. The model used for this phenomenon is based on the physical conditions of the vapor and liquid for a given node. However, this model for evaporation and condensation not only causes the energy equation to be nonlinear but also constrains the time step to 10 -4 seconds for convergence to be reached. The model has been run for small transients up to 2 seconds to produce temperature distributions and demonstrate the convergence difficulties associated with the evaporation/condensation model used
DEFF Research Database (Denmark)
Mashayekhi, Sima; Hugger, Jens
2015-01-01
Several nonlinear Black-Scholes models have been proposed to take transaction cost, large investor performance and illiquid markets into account. One of the most comprehensive models introduced by Barles and Soner in [4] considers transaction cost in the hedging strategy and risk from an illiquid...
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 ...
Gaburro, Elena; Castro, Manuel J.; Dumbser, Michael
2018-06-01
In this work, we present a novel second-order accurate well-balanced arbitrary Lagrangian-Eulerian (ALE) finite volume scheme on moving nonconforming meshes for the Euler equations of compressible gas dynamics with gravity in cylindrical coordinates. The main feature of the proposed algorithm is the capability of preserving many of the physical properties of the system exactly also on the discrete level: besides being conservative for mass, momentum and total energy, also any known steady equilibrium between pressure gradient, centrifugal force, and gravity force can be exactly maintained up to machine precision. Perturbations around such equilibrium solutions are resolved with high accuracy and with minimal dissipation on moving contact discontinuities even for very long computational times. This is achieved by the novel combination of well-balanced path-conservative finite volume schemes, which are expressly designed to deal with source terms written via non-conservative products, with ALE schemes on moving grids, which exhibit only very little numerical dissipation on moving contact waves. In particular, we have formulated a new HLL-type and a novel Osher-type flux that are both able to guarantee the well balancing in a gas cloud rotating around a central object. Moreover, to maintain a high level of quality of the moving mesh, we have adopted a nonconforming treatment of the sliding interfaces that appear due to the differential rotation. A large set of numerical tests has been carried out in order to check the accuracy of the method close and far away from the equilibrium, both, in one- and two-space dimensions.
Comparative study of numerical schemes of TVD3, UNO3-ACM and optimized compact scheme
Lee, Duck-Joo; Hwang, Chang-Jeon; Ko, Duck-Kon; Kim, Jae-Wook
1995-01-01
Three different schemes are employed to solve the benchmark problem. The first one is a conventional TVD-MUSCL (Monotone Upwind Schemes for Conservation Laws) scheme. The second scheme is a UNO3-ACM (Uniformly Non-Oscillatory Artificial Compression Method) scheme. The third scheme is an optimized compact finite difference scheme modified by us: the 4th order Runge Kutta time stepping, the 4th order pentadiagonal compact spatial discretization with the maximum resolution characteristics. The problems of category 1 are solved by using the second (UNO3-ACM) and third (Optimized Compact) schemes. The problems of category 2 are solved by using the first (TVD3) and second (UNO3-ACM) schemes. The problem of category 5 is solved by using the first (TVD3) scheme. It can be concluded from the present calculations that the Optimized Compact scheme and the UN03-ACM show good resolutions for category 1 and category 2 respectively.
Directory of Open Access Journals (Sweden)
B. U. Musa
2017-04-01
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.
Gao, Longfei
2017-10-26
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.
Gao, Longfei; Ketcheson, David; Keyes, David
2018-02-01
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.
Perfectly Matched Layer for the Wave Equation Finite Difference Time Domain Method
Miyazaki, Yutaka; Tsuchiya, Takao
2012-07-01
The perfectly matched layer (PML) is introduced into the wave equation finite difference time domain (WE-FDTD) method. The WE-FDTD method is a finite difference method in which the wave equation is directly discretized on the basis of the central differences. The required memory of the WE-FDTD method is less than that of the standard FDTD method because no particle velocity is stored in the memory. In this study, the WE-FDTD method is first combined with the standard FDTD method. Then, Berenger's PML is combined with the WE-FDTD method. Some numerical demonstrations are given for the two- and three-dimensional sound fields.
Estimation of seasonal atmospheric stability and mixing height by using different schemes
International Nuclear Information System (INIS)
Essa, K.S.M.; Embaby, M.; Mubarak, F.; Kamel, I.
2007-01-01
Different atmospheric stability schemes were used to characterize the plume growth (dispersion coefficients σ) in the lateral and vertical directions to determine the concentration distribution of pollutants through the PBL. The PBL is the region in which surface friction has a large effect on the mixing of pollutants. It is also suffer large fluctuation in temperature and wind and its depth (mixing depth) changes over a diurnal cycle. In this study, four months of surface meteorological parameters were used (to represent different seasons) to determine seasonal stability, classification. Five different stability schemes were estimated based on temperature gradient, standard deviation of the horizontal wind direction fluctuation, gradient and Bulk Richardson numbers and Monin-Obukhov length. Friction velocity, (u * ) for each stability scheme was estimated for characterizing the hourly, mixing height for each stability class. Also, plume rise was estimated for each stability class depending on the availability of meteorological parameters
Colera, Manuel; Pérez-Saborid, Miguel
2017-09-01
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.
Gerke, Kirill M.
2018-01-17
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.
Gerke, Kirill M.; Vasilyev, Roman V.; Khirevich, Siarhei; Collins, Daniel; Karsanina, Marina V.; Sizonenko, Timofey O.; Korost, Dmitry V.; Lamontagne, Sébastien; Mallants, Dirk
2018-05-01
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.
Wu, Zedong
2018-04-05
Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media is crucial to seismic modeling, imaging and inversion. Actually, it represents the core computation cost of these highly advanced seismic processing methods. However, the conventional finite-difference method suffers from severe numerical dispersion errors and S-wave artifacts when solving the acoustic wave equation for anisotropic media. We propose a method to obtain the finite-difference coefficients by comparing its numerical dispersion with the exact form. We find the optimal finite difference coefficients that share the dispersion characteristics of the exact equation with minimal dispersion error. The method is extended to solve the acoustic wave equation in transversely isotropic (TI) media without S-wave artifacts. Numerical examples show that the method is is highly accurate and efficient.
Formulation of coarse mesh finite difference to calculate mathematical adjoint flux
International Nuclear Information System (INIS)
Pereira, Valmir; Martinez, Aquilino Senra; Silva, Fernando Carvalho da
2002-01-01
The objective of this work is the obtention of the mathematical adjoint flux, having as its support the nodal expansion method (NEM) for coarse mesh problems. Since there are difficulties to evaluate this flux by using NEM. directly, a coarse mesh finite difference program was developed to obtain this adjoint flux. The coarse mesh finite difference formulation (DFMG) adopted uses results of the direct calculation (node average flux and node face averaged currents) obtained by NEM. These quantities (flux and currents) are used to obtain the correction factors which modify the classical finite differences formulation . Since the DFMG formulation is also capable of calculating the direct flux it was also tested to obtain this flux and it was verified that it was able to reproduce with good accuracy both the flux and the currents obtained via NEM. In this way, only matrix transposition is needed to calculate the mathematical adjoint flux. (author)
Interactive finite difference preprocessor for three-dimensional fluid flow systems. [PREFLO
Energy Technology Data Exchange (ETDEWEB)
Kleinstreuer, C. (Rensselaer Polytechnic Inst., Troy, NY); Patterson, M.R.
1981-06-01
A preprocessor, called PREFLO, consisting of data processing modules combined with a flexible finite difference grid generator is described. This economical, interactive computer code is a useful research tool contributing significantly to the accurate analysis and modeling of large and/or geometrically complex flow systems. PREFLO (PREprocessor for fluid FLOw problems), written in FORTRAN IV, consists of four modules which in turn call various subroutines. The main programs accomplish the following tasks: (1) system identification and selection of appropriate finite difference algorithms; (2) input devices for storage of natural flow boundaries; (3) interactive generation of finite difference meshes and display of computer graphics; (4) preparation of all data files for the source program. The computation of the velocity field near a power plant site is outlined to illustrate the capabilities and application of PREFLO.
Relative and Absolute Error Control in a Finite-Difference Method Solution of Poisson's Equation
Prentice, J. S. C.
2012-01-01
An algorithm for error control (absolute and relative) in the five-point finite-difference method applied to Poisson's equation is described. The algorithm is based on discretization of the domain of the problem by means of three rectilinear grids, each of different resolution. We discuss some hardware limitations associated with the algorithm,…
A real options approach to analyse wind energy investments under different support schemes
DEFF Research Database (Denmark)
Kitzing, Lena; Juul, Nina; Drud, Michael Stolbjerg Leni
2016-01-01
are combined into a single stochastic process, which allows for analytical (closed-form) solutions. The approach is well suited for quantitative policy analysis, such as the comparison of different support schemes. A case study for offshore wind in the Baltic Sea quantifies differences in investment incentives...... under feed-in tariffs, feed-in premiums and tradable green certificates. Investors can under certificate schemes require up to 3% higher profit margins than under tariffs due to higher variance in profits. Feed-in tariffs may lead to 15% smaller project sizes. This trade-off between faster deployment...... on investment incentives also depends on correlations between the underlying stochastic factors. The results may help investors to make informed investment decisions and policy makers to strategically design renewable support and develop tailor-made incentive schemes....
International Nuclear Information System (INIS)
Kopsakangas-Savolainen, Maria; Svento, Rauli
2010-01-01
We compare the welfare effects of different regulation schemes of electricity distribution utilities. The compared regulation schemes are Fixed Price regulation, Cost of Service regulation, Menu of Cost-Contingent Contracts and Simple Menu of Contracts. In our calculations we utilize the information of a firm's potential to improve cost efficiency. The firm-specific cost information of Finnish electricity distribution utilities is obtained by using various Stochastic Frontier models. Our basic result is that welfare can be improved by changing the Cost of Service regulation scheme to the Menu of Contracts regulation. Welfare also increases in the case of Fixed Price regulation and Simple Menu of Contract regulation. There is however, a significant difference among regulation regimes on how this improved welfare is distributed to consumers and producers.
Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics
Gedney, Stephen
2011-01-01
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
Analysis of equilibrium in a tokamak by the finite-difference method
International Nuclear Information System (INIS)
Kim, K.E.; Jeun, G.D.
1983-01-01
Ideal magnetohydrodynamic equilibrium in a Tokamak having a small radius with an elongated rectangular cross section is studied by applying the finite-difference method to the Grad-Shafranov equation to determine possible limitations for *b=8*pPsup(2)/Bsup(2). The coupled first-order differential equations resulting from the finite-difference Grad-Shafranov equation is solved by the numarical method:1)We concluded that equilibrium consideration alone gives no limitation even for *b approx.1. 2)We have obtained the equilibrium magnetic field configuration charcterized by a set of three parameters;the aspect ratio, *b,and the safety factor. (Author)
Boscheri, Walter; Dumbser, Michael
2014-10-01
In this paper we present a new family of high order accurate Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear systems of conservative and non-conservative hyperbolic partial differential equations with stiff source terms on moving tetrahedral meshes in three space dimensions. A WENO reconstruction technique is used to achieve high order of accuracy in space, while an element-local space-time Discontinuous Galerkin finite element predictor on moving curved meshes is used to obtain a high order accurate one-step time discretization. Within the space-time predictor the physical element is mapped onto a reference element using a high order isoparametric approach, where the space-time basis and test functions are given by the Lagrange interpolation polynomials passing through a predefined set of space-time nodes. Since our algorithm is cell-centered, the final mesh motion is computed by using a suitable node solver algorithm. A rezoning step as well as a flattener strategy are used in some of the test problems to avoid mesh tangling or excessive element deformations that may occur when the computation involves strong shocks or shear waves. The ALE algorithm presented in this article belongs to the so-called direct ALE methods because the final Lagrangian finite volume scheme is based directly on a space-time conservation formulation of the governing PDE system, with the rezoned geometry taken already into account during the computation of the fluxes. We apply our new high order unstructured ALE schemes to the 3D Euler equations of compressible gas dynamics, for which a set of classical numerical test problems has been solved and for which convergence rates up to sixth order of accuracy in space and time have been obtained. We furthermore consider the equations of classical ideal magnetohydrodynamics (MHD) as well as the non-conservative seven-equation Baer-Nunziato model of compressible multi-phase flows with
Simple Numerical Schemes for the Korteweg-deVries Equation
International Nuclear Information System (INIS)
McKinstrie, C. J.; Kozlov, M.V.
2000-01-01
Two numerical schemes, which simulate the propagation of dispersive non-linear waves, are described. The first is a split-step Fourier scheme for the Korteweg-de Vries (KdV) equation. The second is a finite-difference scheme for the modified KdV equation. The stability and accuracy of both schemes are discussed. These simple schemes can be used to study a wide variety of physical processes that involve dispersive nonlinear waves
Simple Numerical Schemes for the Korteweg-deVries Equation
Energy Technology Data Exchange (ETDEWEB)
C. J. McKinstrie; M. V. Kozlov
2000-12-01
Two numerical schemes, which simulate the propagation of dispersive non-linear waves, are described. The first is a split-step Fourier scheme for the Korteweg-de Vries (KdV) equation. The second is a finite-difference scheme for the modified KdV equation. The stability and accuracy of both schemes are discussed. These simple schemes can be used to study a wide variety of physical processes that involve dispersive nonlinear waves.
Hajipour, Mojtaba; Jajarmi, Amin
2018-02-01
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.
3D Staggered-Grid Finite-Difference Simulation of Acoustic Waves in Turbulent Moving Media
Symons, N. P.; Aldridge, D. F.; Marlin, D.; Wilson, D. K.; Sullivan, P.; Ostashev, V.
2003-12-01
Acoustic wave propagation in a three-dimensional heterogeneous moving atmosphere is accurately simulated with a numerical algorithm recently developed under the DOD Common High Performance Computing Software Support Initiative (CHSSI). Sound waves within such a dynamic environment are mathematically described by a set of four, coupled, first-order partial differential equations governing small-amplitude fluctuations in pressure and particle velocity. The system is rigorously derived from fundamental principles of continuum mechanics, ideal-fluid constitutive relations, and reasonable assumptions that the ambient atmospheric motion is adiabatic and divergence-free. An explicit, time-domain, finite-difference (FD) numerical scheme is used to solve the system for both pressure and particle velocity wavefields. The atmosphere is characterized by 3D gridded models of sound speed, mass density, and the three components of the wind velocity vector. Dependent variables are stored on staggered spatial and temporal grids, and centered FD operators possess 2nd-order and 4th-order space/time accuracy. Accurate sound wave simulation is achieved provided grid intervals are chosen appropriately. The gridding must be fine enough to reduce numerical dispersion artifacts to an acceptable level and maintain stability. The algorithm is designed to execute on parallel computational platforms by utilizing a spatial domain-decomposition strategy. Currently, the algorithm has been validated on four different computational platforms, and parallel scalability of approximately 85% has been demonstrated. Comparisons with analytic solutions for uniform and vertically stratified wind models indicate that the FD algorithm generates accurate results with either a vanishing pressure or vanishing vertical-particle velocity boundary condition. Simulations are performed using a kinematic turbulence wind profile developed with the quasi-wavelet method. In addition, preliminary results are presented
Toet, A.; Hogervorst, M.A.
2003-01-01
We applied a recently introduced universal image quality index Q that quantifies the distortion of a processed image relative to its original version, to assess the performance of different graylevel image fusion schemes. The method is as follows. First, we adopt an original test image as the
Directory of Open Access Journals (Sweden)
Rafail B. Garibov
2017-12-01
Full Text Available The article discusses the model of deformation of fiber-reinforced concrete rectangular plate under the influence of radiation environments. In the calculation of the plate was considered different schemes impact of the applied external loads and radiation environments.
Limperos, Anthony M; Schmierbach, Michael G; Kegerise, Andrew D; Dardis, Frank E
2011-06-01
Many studies have investigated how different technological features impact the experience of playing video games, yet few have focused on how control schemes may affect the play experience. This research employed a between-subjects design to explore the relationship between the type of console played (Nintendo Wii, Playstation 2) and feelings of flow and enjoyment during the game-play experience. Results indicated that participants reported greater feelings of control and enjoyment with a traditional control scheme (Playstation 2) than with the more technologically advanced control scheme (Nintendo Wii). Further mediation analysis showed that enjoyment was driven by the sense of control that participants experienced and not simply by whether they won the game. Theoretical and practical implications are discussed.
Clay, M. P.; Yeung, P. K.; Buaria, D.; Gotoh, T.
2017-11-01
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.
A fast finite-difference algorithm for topology optimization of permanent magnets
Abert, Claas; Huber, Christian; Bruckner, Florian; Vogler, Christoph; Wautischer, Gregor; Suess, Dieter
2017-09-01
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.
ON THE CONSTRUCTION OF PARTIAL DIFFERENCE SCHEMES II: DISCRETE VARIABLES AND SCHWARZIAN LATTICES
Directory of Open Access Journals (Sweden)
Decio Levi
2016-06-01
Full Text Available In the process of constructing invariant difference schemes which approximate partial differential equations we write down a procedure for discretizing a partial differential equation on an arbitrary lattice. An open problem is the meaning of a lattice which does not satisfy the Clairaut–Schwarz–Young theorem. To analyze it we apply the procedure on a simple example, the potential Burgers equation with two different lattices, an orthogonal lattice which is invariant under the symmetries of the equation and satisfies the commutativity of the partial difference operators and an exponential lattice which is not invariant and does not satisfy the Clairaut–Schwarz–Young theorem. A discussion on the numerical results is presented showing the different behavior of both schemes for two different exact solutions and their numerical approximations.
Comparison of finite-difference and variational solutions to advection-diffusion problems
International Nuclear Information System (INIS)
Lee, C.E.; Washington, K.E.
1984-01-01
Two numerical solution methods are developed for 1-D time-dependent advection-diffusion problems on infinite and finite domains. Numerical solutions are compared with analytical results for constant coefficients and various boundary conditions. A finite-difference spectrum method is solved exactly in time for periodic boundary conditions by a matrix operator method and exhibits excellent accuracy compared with other methods, especially at late times, where it is also computationally more efficient. Finite-system solutions are determined from a conservational variational principle with cubic spatial trial functions and solved in time by a matrix operator method. Comparisons of problems with few nodes show excellent agreement with analytical solutions and exhibit the necessity of implementing Lagrangian conservational constraints for physically-correct solutions. (author)
Detailed balance principle and finite-difference stochastic equation in a field theory
International Nuclear Information System (INIS)
Kozhamkulov, T.A.
1986-01-01
A finite-difference equation, which is a generalization of the Langevin equation in field theory, has been obtained basing upon the principle of detailed balance for the Markov chain. Advantages of the present approach as compared with the conventional Parisi-Wu method are shown for examples of an exactly solvable problem of zero-dimensional quantum theory and a simple numerical simulation
The finite-difference time-domain method for electromagnetics with Matlab simulations
Elsherbeni, Atef Z
2016-01-01
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.
Principle of detailed balance and the finite-difference stochastic equation in field theory
International Nuclear Information System (INIS)
Kozhamkulov, T.A.
1986-01-01
The principle of detailed balance for the Markov chain is used to obtain a finite-difference equation which generalizes the Langevin equation in field theory. The advantages of using this approach compared to the conventional Parisi-Wu method are demonstrated for the examples of an exactly solvable problem in zero-dimensional quantum theory and a simple numerical simulation
Chu, Chunlei
2012-01-01
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.
Finite-difference time-domain analysis of time-resolved terahertz spectroscopy experiments
DEFF Research Database (Denmark)
Larsen, Casper; Cooke, David G.; Jepsen, Peter Uhd
2011-01-01
In this paper we report on the numerical analysis of a time-resolved terahertz (THz) spectroscopy experiment using a modified finite-difference time-domain method. Using this method, we show that ultrafast carrier dynamics can be extracted with a time resolution smaller than the duration of the T...
Optimal implicit 2-D finite differences to model wave propagation in poroelastic media
Itzá, Reymundo; Iturrarán-Viveros, Ursula; Parra, Jorge O.
2016-08-01
Numerical modeling of seismic waves in heterogeneous porous reservoir rocks is an important tool for the interpretation of seismic surveys in reservoir engineering. We apply globally optimal implicit staggered-grid finite differences (FD) to model 2-D wave propagation in heterogeneous poroelastic media at a low-frequency range (differentiation involves solving tridiagonal linear systems of equations through Thomas' algorithm.
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.
2011-01-01
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...
Modeling of Nanophotonic Resonators with the Finite-Difference Frequency-Domain Method
DEFF Research Database (Denmark)
Ivinskaya, Aliaksandra; Lavrinenko, Andrei; Shyroki, Dzmitry
2011-01-01
Finite-difference frequency-domain method with perfectly matched layers and free-space squeezing is applied to model open photonic resonators of arbitrary morphology in three dimensions. Treating each spatial dimension independently, nonuniform mesh of continuously varying density can be built ea...
Banks, H T; Birch, Malcolm J; Brewin, Mark P; Greenwald, Stephen E; Hu, Shuhua; Kenz, Zackary R; Kruse, Carola; Maischak, Matthias; Shaw, Simon; Whiteman, John R
2014-04-13
We revisit a method originally introduced by Werder et al. (in Comput. Methods Appl. Mech. Engrg., 190:6685-6708, 2001) for temporally discontinuous Galerkin FEMs applied to a parabolic partial differential equation. In that approach, block systems arise because of the coupling of the spatial systems through inner products of the temporal basis functions. If the spatial finite element space is of dimension D and polynomials of degree r are used in time, the block system has dimension ( r + 1) D and is usually regarded as being too large when r > 1. Werder et al. found that the space-time coupling matrices are diagonalizable over [Formula: see text] for r ⩽ 100, and this means that the time-coupled computations within a time step can actually be decoupled. By using either continuous Galerkin or spectral element methods in space, we apply this DG-in-time methodology, for the first time, to second-order wave equations including elastodynamics with and without Kelvin-Voigt and Maxwell-Zener viscoelasticity. An example set of numerical results is given to demonstrate the favourable effect on error and computational work of the moderately high-order (up to degree 7) temporal and spatio-temporal approximations, and we also touch on an application of this method to an ambitious problem related to the diagnosis of coronary artery disease. Copyright © 2014 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.
Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations
Directory of Open Access Journals (Sweden)
Vladimir P. Gerdt
2006-05-01
Full Text Available In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law form by extra integral relations between unknown functions and their derivatives, and on discretization of the obtained system. The structure of the discrete system depends on numerical approximation methods for the integrals occurring in the enlarged system. As a result of the discretization, a system of linear polynomial difference equations is derived for the unknown functions and their partial derivatives. A difference scheme is constructed by elimination of all the partial derivatives. The elimination can be achieved by selecting a proper elimination ranking and by computing a Gröbner basis of the linear difference ideal generated by the polynomials in the discrete system. For these purposes we use the difference form of Janet-like Gröbner bases and their implementation in Maple. As illustration of the described methods and algorithms, we construct a number of difference schemes for Burgers and Falkowich-Karman equations and discuss their numerical properties.
DEFF Research Database (Denmark)
Raymond, Christopher Mark; Reed, Mark; Bieling, Claudia
2016-01-01
While multiple studies have identified land managers’ preferences for agri-environmental schemes (AES), few approaches exist for integrating different understandings of landscape stewardship into the design of these measures. We compared and contrasted rural land managers’ attitudes toward AES...... to the reduced amount of funding available for entry-level and higher-level stewardship schemes in the UK since 2008, changing funding priorities, perceived overstrict compliance and lack of support for farm succession and new entrants into farming. However, there were differences in concerns across...... understandings of landscape stewardship, with production respondents citing that AES do not encourage food production, whereas environmental and holistic farmers citing that AES do not support the development of a local green food culture and associated social infrastructure. These differences also emerged...
Directory of Open Access Journals (Sweden)
Lei Wang
2015-09-01
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.
Yoneoka, Daisuke; Henmi, Masayuki
2017-11-30
Recently, the number of clinical prediction models sharing the same regression task has increased in the medical literature. However, evidence synthesis methodologies that use the results of these regression models have not been sufficiently studied, particularly in meta-analysis settings where only regression coefficients are available. One of the difficulties lies in the differences between the categorization schemes of continuous covariates across different studies. In general, categorization methods using cutoff values are study specific across available models, even if they focus on the same covariates of interest. Differences in the categorization of covariates could lead to serious bias in the estimated regression coefficients and thus in subsequent syntheses. To tackle this issue, we developed synthesis methods for linear regression models with different categorization schemes of covariates. A 2-step approach to aggregate the regression coefficient estimates is proposed. The first step is to estimate the joint distribution of covariates by introducing a latent sampling distribution, which uses one set of individual participant data to estimate the marginal distribution of covariates with categorization. The second step is to use a nonlinear mixed-effects model with correction terms for the bias due to categorization to estimate the overall regression coefficients. Especially in terms of precision, numerical simulations show that our approach outperforms conventional methods, which only use studies with common covariates or ignore the differences between categorization schemes. The method developed in this study is also applied to a series of WHO epidemiologic studies on white blood cell counts. Copyright © 2017 John Wiley & Sons, Ltd.
An outgoing energy flux boundary condition for finite difference ICRP antenna models
International Nuclear Information System (INIS)
Batchelor, D.B.; Carter, M.D.
1992-11-01
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
Stability analysis of single-phase thermosyphon loops by finite difference numerical methods
International Nuclear Information System (INIS)
Ambrosini, W.
1998-01-01
In this paper, examples of the application of finite difference numerical methods in the analysis of stability of single-phase natural circulation loops are reported. The problem is here addressed for its relevance for thermal-hydraulic system code applications, in the aim to point out the effect of truncation error on stability prediction. The methodology adopted for analysing in a systematic way the effect of various finite difference discretization can be considered the numerical analogue of the usual techniques adopted for PDE stability analysis. Three different single-phase loop configurations are considered involving various kinds of boundary conditions. In one of these cases, an original dimensionless form of the governing equations is proposed, adopting the Reynolds number as a flow variable. This allows for an appropriate consideration of transition between laminar and turbulent regimes, which is not possible with other dimensionless forms, thus enlarging the field of validity of model assumptions. (author). 14 refs., 8 figs
Energy stable and high-order-accurate finite difference methods on staggered grids
O'Reilly, Ossian; Lundquist, Tomas; Dunham, Eric M.; Nordström, Jan
2017-10-01
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.
Liu, Xiaoting; Wong, Hung; Liu, Kai
2016-01-14
Against the achievement of nearly universal coverage for social health insurance for the elderly in China, a problem of inequity among different insurance schemes on health outcomes is still a big challenge for the health care system. Whether various health insurance schemes have divergent effects on health outcome is still a puzzle. Empirical evidence will be investigated in this study. This study employs a nationally representative survey database, the National Survey of the Aged Population in Urban/Rural China, to compare the changes of health outcomes among the elderly before and after the reform. A one-way ANOVA is utilized to detect disparities in health care expenditures and health status among different health insurance schemes. Multiple Linear Regression is applied later to examine the further effects of different insurance plans on health outcomes while controlling for other social determinants. The one-way ANOVA result illustrates that although the gaps in insurance reimbursements between the Urban Employee Basic Medical Insurance (UEBMI) and the other schemes, the New Rural Cooperative Medical Scheme (NCMS) and Urban Residents Basic Medical Insurance (URBMI) decreased, out-of-pocket spending accounts for a larger proportion of total health care expenditures, and the disparities among different insurances enlarged. Results of the Multiple Linear Regression suggest that UEBMI participants have better self-reported health status, physical functions and psychological wellbeing than URBMI and NCMS participants, and those uninsured. URBMI participants report better self-reported health than NCMS ones and uninsured people, while having worse psychological wellbeing compared with their NCMS counterparts. This research contributes to a transformation in health insurance studies from an emphasis on the opportunity-oriented health equity measured by coverage and healthcare accessibility to concern with outcome-based equity composed of health expenditure and health
International Nuclear Information System (INIS)
Koleshko, S.B.
1989-01-01
A three-parametric set of difference schemes is suggested to solve Navier-Stokes equations with the use of the relaxation form of the continuity equation. The initial equations are stated for time increments. Use is made of splitting the operator into one-dimensional forms that reduce calculations to scalar factorizations. Calculated results for steady- and unsteady-state flows in a cavity are presented
A study on different thermodynamic cycle schemes coupled with a high temperature gas-cooled reactor
International Nuclear Information System (INIS)
Qu, Xinhe; Yang, Xiaoyong; Wang, Jie
2017-01-01
Highlights: • The features of three different power generation schemes, including closed Brayton cycle, non-reheating combined cycle and reheating combined cycle, coupled with high temperature gas-cooled reactor (HTGR) were investigated and compared. • The effects and mechanism of reactor core outlet temperature, compression ratio and other key parameters over cycle characteristics were analyzed by the thermodynamic models.. • It is found that reheated combined cycle has the highest efficiency. Reactor outlet temperature and main steam parameters are key factors to improve the cycle’s performance. - Abstract: With gradual increase in reactor outlet temperature, the efficient power conversion technology has become one of developing trends of (very) high temperature gas-cooled reactors (HTGRs). In this paper, different cycle power generation schemes for HTGRs were systematically studied. Physical and mathematical models were established for these three cycle schemes: closed Brayton cycle, simple combined cycle, and reheated combined cycle. The effects and mechanism of key parameters such as reactor core outlet temperature, reactor core inlet temperature and compression ratio on the features of these cycles were analyzed. Then, optimization results were given with engineering restrictive conditions, including pinch point temperature differences. Results revealed that within the temperature range of HTGRs (700–900 °C), the reheated combined cycle had the highest efficiency, while the simple combined cycle had the lowest efficiency (900 °C). The efficiencies of the closed Brayton cycle, simple combined cycle and reheated combined cycle are 49.5%, 46.6% and 50.1%, respectively. These results provide insights on the different schemes of these cycles, and reveal the effects of key parameters on performance of these cycles. It could be helpful to understand and develop a combined cycle coupled with a high temperature reactor in the future.
A practical implicit finite-difference method: examples from seismic modelling
International Nuclear Information System (INIS)
Liu, Yang; Sen, Mrinal K
2009-01-01
We derive explicit and new implicit finite-difference formulae for derivatives of arbitrary order with any order of accuracy by the plane wave theory where the finite-difference coefficients are obtained from the Taylor series expansion. The implicit finite-difference formulae are derived from fractional expansion of derivatives which form tridiagonal matrix equations. Our results demonstrate that the accuracy of a (2N + 2)th-order implicit formula is nearly equivalent to that of a (6N + 2)th-order explicit formula for the first-order derivative, and (2N + 2)th-order implicit formula is nearly equivalent to (4N + 2)th-order explicit formula for the second-order derivative. In general, an implicit method is computationally more expensive than an explicit method, due to the requirement of solving large matrix equations. However, the new implicit method only involves solving tridiagonal matrix equations, which is fairly inexpensive. Furthermore, taking advantage of the fact that many repeated calculations of derivatives are performed by the same difference formula, several parts can be precomputed resulting in a fast algorithm. We further demonstrate that a (2N + 2)th-order implicit formulation requires nearly the same memory and computation as a (2N + 4)th-order explicit formulation but attains the accuracy achieved by a (6N + 2)th-order explicit formulation for the first-order derivative and that of a (4N + 2)th-order explicit method for the second-order derivative when additional cost of visiting arrays is not considered. This means that a high-order explicit method may be replaced by an implicit method of the same order resulting in a much improved performance. Our analysis of efficiency and numerical modelling results for acoustic and elastic wave propagation validates the effectiveness and practicality of the implicit finite-difference method
A real options approach to analyse wind energy investments under different support schemes
International Nuclear Information System (INIS)
Kitzing, Lena; Juul, Nina; Drud, Michael; Boomsma, Trine Krogh
2017-01-01
Highlights: • Real options model for wind projects considering investment timing and sizing. • Introducing a capacity constraint in the optimisation. • Addressing several uncertainty factors while still providing analytical solution. • Comparative policy analysis of investment incentives from different support schemes. • Improved quantification of trade-off between fast deployment and large projects. - Abstract: A real options model is developed to evaluate wind energy investments in a realistic and easily applicable way. Considering optimal investment timing and sizing (capacity choice), the model introduces a capacity constraint as part of the optimisation. Several correlated uncertainty factors are combined into a single stochastic process, which allows for analytical (closed-form) solutions. The approach is well suited for quantitative policy analysis, such as the comparison of different support schemes. A case study for offshore wind in the Baltic Sea quantifies differences in investment incentives under feed-in tariffs, feed-in premiums and tradable green certificates. Investors can under certificate schemes require up to 3% higher profit margins than under tariffs due to higher variance in profits. Feed-in tariffs may lead to 15% smaller project sizes. This trade-off between faster deployment of smaller projects and slower deployment of larger projects is neglected using traditional net present value approaches. In the analysis of such trade-off, previous real options studies did not consider a capacity constraint, which is here shown to decrease the significance of the effect. The impact on investment incentives also depends on correlations between the underlying stochastic factors. The results may help investors to make informed investment decisions and policy makers to strategically design renewable support and develop tailor-made incentive schemes.
Hannah, S. R.; Palazotto, A. N.
1978-01-01
A new trigonometric approach to the finite difference calculus was applied to the problem of beam buckling as represented by virtual work and equilibrium equations. The trigonometric functions were varied by adjusting a wavelength parameter in the approximating Fourier series. Values of the critical force obtained from the modified approach for beams with a variety of boundary conditions were compared to results using the conventional finite difference method. The trigonometric approach produced significantly more accurate approximations for the critical force than the conventional approach for a relatively wide range in values of the wavelength parameter; and the optimizing value of the wavelength parameter corresponded to the half-wavelength of the buckled mode shape. It was found from a modal analysis that the most accurate solutions are obtained when the approximating function closely represents the actual displacement function and matches the actual boundary conditions.
Symmetries of the second-difference matrix and the finite Fourier transform
International Nuclear Information System (INIS)
Aguilar, A.; Wolf, K.B.
1979-01-01
The finite Fourier transformation is well known to diagonalize the second-difference matrix and has been thus applied extensively to describe finite crystal lattices and electric networks. In setting out to find all transformations having this property, we obtain a multiparameter class of them. While permutations and unitary scaling of the eigenvectors constitute the trivial freedom of choice common to all diagonalization processes, the second-difference matrix has a larger symmetry group among whose elements we find the dihedral manifest symmetry transformations of the lattice. The latter are nevertheless sufficient for the unique specification of eigenvectors in various symmetry-adapted bases for the constrained lattice. The free symmetry parameters are shown to lead to a complete set of conserved quantities for the physical lattice motion. (author)
Accuracy of finite-difference harmonic frequencies in density functional theory.
Liu, Kuan-Yu; Liu, Jie; Herbert, John M
2017-07-15
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 numbers. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
Numerical study of water diffusion in biological tissues using an improved finite difference method
International Nuclear Information System (INIS)
Xu Junzhong; Does, Mark D; Gore, John C
2007-01-01
An improved finite difference (FD) method has been developed in order to calculate the behaviour of the nuclear magnetic resonance signal variations caused by water diffusion in biological tissues more accurately and efficiently. The algorithm converts the conventional image-based finite difference method into a convenient matrix-based approach and includes a revised periodic boundary condition which eliminates the edge effects caused by artificial boundaries in conventional FD methods. Simulated results for some modelled tissues are consistent with analytical solutions for commonly used diffusion-weighted pulse sequences, whereas the improved FD method shows improved efficiency and accuracy. A tightly coupled parallel computing approach was also developed to implement the FD methods to enable large-scale simulations of realistic biological tissues. The potential applications of the improved FD method for understanding diffusion in tissues are also discussed. (note)
A novel strong tracking finite-difference extended Kalman filter for nonlinear eye tracking
Institute of Scientific and Technical Information of China (English)
ZHANG ZuTao; ZHANG JiaShu
2009-01-01
Non-Intrusive methods for eye tracking are Important for many applications of vision-based human computer interaction. However, due to the high nonlinearity of eye motion, how to ensure the robust-ness of external interference and accuracy of eye tracking poses the primary obstacle to the integration of eye movements into today's interfaces. In this paper, we present a strong tracking finite-difference extended Kalman filter algorithm, aiming to overcome the difficulty In modeling nonlinear eye tracking. In filtering calculation, strong tracking factor is introduced to modify a priori covariance matrix and im-prove the accuracy of the filter. The filter uses finite-difference method to calculate partial derivatives of nonlinear functions for eye tracking. The latest experimental results show the validity of our method for eye tracking under realistic conditions.
Implementation of compact finite-difference method to parabolized Navier-Stokes equations
International Nuclear Information System (INIS)
Esfahanian, V.; Hejranfar, K.; Darian, H.M.
2005-01-01
The numerical simulation of the Parabolized Navier-Stokes (PNS) equations for supersonic/hypersonic flow field is obtained by using the fourth-order compact finite-difference method. The PNS equations in the general curvilinear coordinates are solved by using the implicit finite-difference algorithm of Beam and Warming. A shock fitting procedure is utilized to obtain the accurate solution in the vicinity of the shock. The computations are performed for hypersonic axisymmetric flow over a blunt cone. The present results for the flow field along with those of the second-order method are presented and accuracy analysis is performed to insure the fourth-order accuracy of the method. (author)
International Nuclear Information System (INIS)
Waligorski, M.P.R.; Urbanczyk, K.M.
1975-01-01
The basic principles of the finite-difference approximation applied to the solution of electrostatic field distributions in gaseous proportional counters are given. Using this method, complicated two-dimensional electrostatic problems may be solved, taking into account any number of anodes, each with its own radius, and any cathode shape. A general formula for introducing the anode radii into the calculations is derived and a method of obtaining extremely accurate (up to 0.1%) solutions is developed. Several examples of potential and absolute field distributions for single rectangular and multiwire proportional counters are calculated and compared with exact results according to Tomitani, in order to discuss in detail errors of the finite-difference approximation. (author)
Directory of Open Access Journals (Sweden)
Xinfeng Ruan
2013-01-01
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.
Research on GPU-accelerated algorithm in 3D finite difference neutron diffusion calculation method
International Nuclear Information System (INIS)
Xu Qi; Yu Ganglin; Wang Kan; Sun Jialong
2014-01-01
In this paper, the adaptability of the neutron diffusion numerical algorithm on GPUs was studied, and a GPU-accelerated multi-group 3D neutron diffusion code based on finite difference method was developed. The IAEA 3D PWR benchmark problem was calculated in the numerical test. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation for neutron diffusion equation. (authors)
Transport and dispersion of pollutants in surface impoundments: a finite difference model
Energy Technology Data Exchange (ETDEWEB)
Yeh, G.T.
1980-07-01
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.
Gabran, S R I; Saad, J H; Salama, M M A; Mansour, R R
2009-01-01
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.
TRUMP3-JR: a finite difference computer program for nonlinear heat conduction problems
International Nuclear Information System (INIS)
Ikushima, Takeshi
1984-02-01
Computer program TRUMP3-JR is a revised version of TRUMP3 which is a finite difference computer program used for the solution of multi-dimensional nonlinear heat conduction problems. Pre- and post-processings for input data generation and graphical representations of calculation results of TRUMP3 are avaiable in TRUMP3-JR. The calculation equations, program descriptions and user's instruction are presented. A sample problem is described to demonstrate the use of the program. (author)
Lei Wang; Hongjun Yin; Xiaoshuang Yang; Chuncheng Yang; Jing Fu
2015-01-01
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 wi...
Lansing, Faiza S.; Rascoe, Daniel L.
1993-01-01
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.
International Nuclear Information System (INIS)
Bensiali, Bouchra; Bodi, Kowsik; Ciraolo, Guido; Ghendrih, Philippe; Liandrat, Jacques
2013-01-01
In this work, we compare different interpolation operators in the context of particle tracking with an emphasis on situations involving velocity field with steep gradients. Since, in this case, most classical methods give rise to the Gibbs phenomenon (generation of oscillations near discontinuities), we present new methods for particle tracking based on subdivision schemes and especially on the Piecewise Parabolic Harmonic (PPH) scheme which has shown its advantage in image processing in presence of strong contrasts. First an analytic univariate case with a discontinuous velocity field is considered in order to highlight the effect of the Gibbs phenomenon on trajectory calculation. Theoretical results are provided. Then, we show, regardless of the interpolation method, the need to use a conservative approach when integrating a conservative problem with a velocity field deriving from a potential. Finally, the PPH scheme is applied in a more realistic case of a time-dependent potential encountered in the edge turbulence of magnetically confined plasmas, to compare the propagation of density structures (turbulence bursts) with the dynamics of test particles. This study highlights the difference between particle transport and density transport in turbulent fields
Linking renewable energy CDM projects and TGC schemes: An analysis of different options
Energy Technology Data Exchange (ETDEWEB)
Del Rio, Pablo [Department of Economics and Business, Facultad de Ciencias Juridicas y Sociales, Universidad de Castilla-La Mancha, C/ Cobertizo de S. Pedro Martir s/n., Toledo-45071 (Spain)]. E-mail: pablo.rio@uclm.es
2006-11-15
Renewable energy CDM (RE-CDM) projects encourage cost-effective GHG mitigation and enhanced sustainable development opportunities for the host countries. CERs from CDM projects include the value of the former benefits (i.e., 'climate change benefits'), whereas the second can be given value through the issuing and trading of tradable green certificates (TGCs). Countries could agree to trade these TGCs, leading to additional revenues for the investors in renewable energy projects and, therefore, further encouraging the deployment of CDM projects, currently facing significant barriers. However, the design of a combination of CDM projects and TGC schemes raises several conflicting issues and leads to trade-offs. This paper analyses these issues, identifies the alternatives that may exist to link TGC schemes with RE-CDM projects and analyses the impacts of those options on different variables and actors.
Linking renewable energy CDM projects and TGC schemes: An analysis of different options
International Nuclear Information System (INIS)
Del Rio, Pablo
2006-01-01
Renewable energy CDM (RE-CDM) projects encourage cost-effective GHG mitigation and enhanced sustainable development opportunities for the host countries. CERs from CDM projects include the value of the former benefits (i.e., 'climate change benefits'), whereas the second can be given value through the issuing and trading of tradable green certificates (TGCs). Countries could agree to trade these TGCs, leading to additional revenues for the investors in renewable energy projects and, therefore, further encouraging the deployment of CDM projects, currently facing significant barriers. However, the design of a combination of CDM projects and TGC schemes raises several conflicting issues and leads to trade-offs. This paper analyses these issues, identifies the alternatives that may exist to link TGC schemes with RE-CDM projects and analyses the impacts of those options on different variables and actors
Dynamic behaviour of nominal and PACMAN bunches for different LHC crossing schemes
Herr, Werner
2005-01-01
To avoid unwanted beam-beam interactions, the two LHC beams cross at an angle in all experimental interaction regions. The choice of the crossing plane in the different areas has fundamental consequences on the effects of the long range beam-beam interaction. An alternating crossing scheme, i.e. horizontal and vertical crossing planes in the two high luminosity experiments, is presently foreseen to partly compensate and minimize first order effects on PACMAN bunches. Recent studies with a simplified model of the machine suggested that an alternating crossing scheme may be less favourable due to a reduced dynamic aperture. In this report I investigate this assertion with a detailed tracking study. The head on and long range beam-beam effects are taken into account as well as machine imperfections. The effects on the dynamic aperture of nominal and PACMAN bunches are evaluated.
Institute of Scientific and Technical Information of China (English)
YUAN Dongfeng; WANG Chengxiang; YAO Qi; CAO Zhigang
2001-01-01
Based on "capacity rule", the perfor-mance of multilevel coding (MLC) schemes with dif-ferent set partitioning strategies and decoding meth-ods in AWGN and Rayleigh fading channels is investi-gated, in which BCH codes are chosen as componentcodes and 8ASK modulation is used. Numerical re-sults indicate that MLC scheme with UP strategy canobtain optimal performance in AWGN channels andBP is the best mapping strategy for Rayleigh fadingchannels. BP strategy is of good robustness in bothkinds of channels to realize an optimum MLC system.Multistage decoding (MSD) is a sub-optimal decodingmethod of MLC for both channels. For Ungerboeckpartitioning (UP) and mixed partitioning (MP) strat-egy, MSD is strongly recommended to use for MLCsystem, while for BP strategy, PDL is suggested to useas a simple decoding method compared with MSD.
Seismic wavefield modeling based on time-domain symplectic and Fourier finite-difference method
Fang, Gang; Ba, Jing; Liu, Xin-xin; Zhu, Kun; Liu, Guo-Chang
2017-06-01
Seismic wavefield modeling is important for improving seismic data processing and interpretation. Calculations of wavefield propagation are sometimes not stable when forward modeling of seismic wave uses large time steps for long times. Based on the Hamiltonian expression of the acoustic wave equation, we propose a structure-preserving method for seismic wavefield modeling by applying the symplectic finite-difference method on time grids and the Fourier finite-difference method on space grids to solve the acoustic wave equation. The proposed method is called the symplectic Fourier finite-difference (symplectic FFD) method, and offers high computational accuracy and improves the computational stability. Using acoustic approximation, we extend the method to anisotropic media. We discuss the calculations in the symplectic FFD method for seismic wavefield modeling of isotropic and anisotropic media, and use the BP salt model and BP TTI model to test the proposed method. The numerical examples suggest that the proposed method can be used in seismic modeling of strongly variable velocities, offering high computational accuracy and low numerical dispersion. The symplectic FFD method overcomes the residual qSV wave of seismic modeling in anisotropic media and maintains the stability of the wavefield propagation for large time steps.
Rotational degree-of-freedom synthesis: An optimised finite difference method for non-exact data
Gibbons, T. J.; Öztürk, E.; Sims, N. D.
2018-01-01
Measuring the rotational dynamic behaviour of a structure is important for many areas of dynamics such as passive vibration control, acoustics, and model updating. Specialist and dedicated equipment is often needed, unless the rotational degree-of-freedom is synthesised based upon translational data. However, this involves numerically differentiating the translational mode shapes to approximate the rotational modes, for example using a finite difference algorithm. A key challenge with this approach is choosing the measurement spacing between the data points, an issue which has often been overlooked in the published literature. The present contribution will for the first time prove that the use of a finite difference approach can be unstable when using non-exact measured data and a small measurement spacing, for beam-like structures. Then, a generalised analytical error analysis is used to propose an optimised measurement spacing, which balances the numerical error of the finite difference equation with the propagation error from the perturbed data. The approach is demonstrated using both numerical and experimental investigations. It is shown that by obtaining a small number of test measurements it is possible to optimise the measurement accuracy, without any further assumptions on the boundary conditions of the structure.
Wang, Yi
2016-07-21
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.
International Nuclear Information System (INIS)
Su Xiaoxing; Zhang Chuanzeng; Ma Tianxue; Wang Yuesheng
2012-01-01
When three-dimensional (3D) phononic band structures are calculated by using the finite difference time domain (FDTD) method with a relatively small number of iterations, the results can be effectively improved by post-processing the FDTD time series (FDTD-TS) based on the filter diagonalization method (FDM), instead of the classical fast Fourier transform. In this paper, we propose a way to further improve the performance of the FDM-based post-processing method by introducing a relatively large number of observing points to record the FDTD-TS. To this end, the existing scheme of FDTD-TS preprocessing is modified. With the new preprocessing scheme, the processing efficiency of a single FDTD-TS can be improved significantly, and thus the entire post-processing method can have sufficiently high efficiency even when a relatively large number of observing points are used. The feasibility of the proposed method for improvement is verified by the numerical results.
Turovets, Sergei; Volkov, Vasily; Zherdetsky, Aleksej; Prakonina, Alena; Malony, Allen D
2014-01-01
The Electrical Impedance Tomography (EIT) and electroencephalography (EEG) forward problems in anisotropic inhomogeneous media like the human head belongs to the class of the three-dimensional boundary value problems for elliptic equations with mixed derivatives. We introduce and explore the performance of several new promising numerical techniques, which seem to be more suitable for solving these problems. The proposed numerical schemes combine the fictitious domain approach together with the finite-difference method and the optimally preconditioned Conjugate Gradient- (CG-) type iterative method for treatment of the discrete model. The numerical scheme includes the standard operations of summation and multiplication of sparse matrices and vector, as well as FFT, making it easy to implement and eligible for the effective parallel implementation. Some typical use cases for the EIT/EEG problems are considered demonstrating high efficiency of the proposed numerical technique.
Modelling migration in multilayer systems by a finite difference method: the spherical symmetry case
International Nuclear Information System (INIS)
Hojbota, C I; Toşa, V; Mercea, P V
2013-01-01
We present a numerical model based on finite differences to solve the problem of chemical impurity migration within a multilayer spherical system. Migration here means diffusion of chemical species in conditions of concentration partitioning at layer interfaces due to different solubilities of the migrant in different layers. We detail here the numerical model and discuss the results of its implementation. To validate the method we compare it with cases where an analytic solution exists. We also present an application of our model to a practical problem in which we compute the migration of caprolactam from the packaging multilayer foil into the food
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
2009-01-01
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.
International Nuclear Information System (INIS)
Ibral, Asmaa; Zouitine, Asmaa; Assaid, El Mahdi
2015-01-01
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
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: eassaid@yahoo.fr [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
2015-02-01
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.
Numerically stable finite difference simulation for ultrasonic NDE in anisotropic composites
Leckey, Cara A. C.; Quintanilla, Francisco Hernando; Cole, Christina M.
2018-04-01
Simulation tools can enable optimized inspection of advanced materials and complex geometry structures. Recent work at NASA Langley is focused on the development of custom simulation tools for modeling ultrasonic wave behavior in composite materials. Prior work focused on the use of a standard staggered grid finite difference type of mathematical approach, by implementing a three-dimensional (3D) anisotropic Elastodynamic Finite Integration Technique (EFIT) code. However, observations showed that the anisotropic EFIT method displays numerically unstable behavior at the locations of stress-free boundaries for some cases of anisotropic materials. This paper gives examples of the numerical instabilities observed for EFIT and discusses the source of instability. As an alternative to EFIT, the 3D Lebedev Finite Difference (LFD) method has been implemented. The paper briefly describes the LFD approach and shows examples of stable behavior in the presence of stress-free boundaries for a monoclinic anisotropy case. The LFD results are also compared to experimental results and dispersion curves.
Analysis of adaptive walks on NK fitness landscapes with different interaction schemes
International Nuclear Information System (INIS)
Nowak, Stefan; Krug, Joachim
2015-01-01
Fitness landscapes are genotype to fitness mappings commonly used in evolutionary biology and computer science which are closely related to spin glass models. In this paper, we study the NK model for fitness landscapes where the interaction scheme between genes can be explicitly defined. The focus is on how this scheme influences the overall shape of the landscape. Our main tool for the analysis are adaptive walks, an idealized dynamics by which the population moves uphill in fitness and terminates at a local fitness maximum. We use three different types of walks and investigate how their length (the number of steps required to reach a local peak) and height (the fitness at the endpoint of the walk) depend on the dimensionality and structure of the landscape. We find that the distribution of local maxima over the landscape is particularly sensitive to the choice of interaction pattern. Most quantities that we measure are simply correlated to the rank of the scheme, which is equal to the number of nonzero coefficients in the expansion of the fitness landscape in terms of Walsh functions
Investment barriers under a renewable-electricity support scheme: Differences across investor types
International Nuclear Information System (INIS)
Linnerud, Kristin; Holden, Erling
2015-01-01
In 2012, Norway and Sweden implemented a common market for tradable green certificates to achieve each country's renewable-energy target. This is the first example of a cooperation mechanism that the EU has suggested to improve the cost efficiency of its renewable-energy policies. We asked investors in 446 planned hydropower projects in Norway what type of barriers may prevent their project from being realized under this scheme, and how likely it is that their project will be realized. Based on a regression analysis we find that the responses to these questions vary systematically with investor, project and process characteristics. We find that investors are concerned with capacity barriers imposed on the market because of the short duration and abrupt termination of the subsidy scheme at the end of 2020. Consequently, the cost efficiency of this and similar schemes can be improved by choosing a better design. Moreover, experienced investors and local landowners without previous experience in the energy sector responded differently to these questions. Local landowners were more optimistic, less concerned with capacity barriers and more concerned with economic barriers than experienced investors were. These observations are interesting given the recent emergence of new investors in the renewable energy sector. - Highlights: • Norway and Sweden have implemented a common market for tradable green certificates. • We asked questions on barriers and potential to investors in 446 hydropower projects. • Capacity barriers imposed on the market by the support scheme design are important. • Local landowners are more optimistic than experienced investors are, all else equal. • They focus relatively more on economic barriers and risk and less on capacity barriers
Moriyama, Eduardo H.; Zangaro, Renato A.; Lobo, Paulo D. d. C.; Villaverde, Antonio G. J. B.; Watanabe-Sei, Ii; Pacheco, Marcos T. T.; Otsuka, Daniel K.
2002-06-01
Thermal damage in dental pulp during Nd:YAG laser irradiation have been studied by several researchers; but due to dentin inhomogeneous structure, laser interaction with dentin in the hypersensitivity treatment are not fully understood. In this work, heat distribution profile on human dentine samples irradiated with Nd:YAG laser was simulated at surface and subjacent layers. Calculations were carried out using the Crank-Nicolson's finite difference method. Sixteen dentin samples with 1,5 mm of thickness were evenly distributed into four groups and irradiated with Nd:YAG laser pulses, according to the following scheme: (I) 1 pulse of 900 mJ, (II) 2 pulses of 450 mJ, (III) 3 pulses of 300 mJ, (IV) 6 pulses of 150 mJ; corresponding to a total laser energy of 900 mJ. The pulse interval was 300ms, the pulse duration of 900 ms and irradiated surface area of 0,005 mm2. Laser induced morphological changes in dentin were observed for all the irradiated samples. The heat distribution throughout the dentin layer, from the external dentin surface to the pulpal chamber wall, was calculated for each case, in order to obtain further information about the pulsed Nd:YAG laser-oral hard tissue interaction. The simulation showed significant differences in the final temperature at the pulpal chamber, depending on the exposition time and the energy contained in the laser pulse.
Zhu, D.; Zhu, H.; Luo, Y.; Chen, X.
2008-12-01
We use a new finite difference method (FDM) and the slip-weakening law to model the rupture dynamics of a non-planar fault embedded in a 3-D elastic media with free surface. The new FDM, based on boundary- conforming grid, sets up the mapping equations between the curvilinear coordinate and the Cartesian coordinate and transforms irregular physical space to regular computational space; it also employs a higher- order non-staggered DRP/opt MacCormack scheme which is of low dispersion and low dissipation so that the high accuracy and stability of our rupture modeling are guaranteed. Compared with the previous methods, not only we can compute the spontaneous rupture of an arbitrarily shaped fault, but also can model the influence of the surface topography on the rupture process of earthquake. In order to verify the feasibility of this method, we compared our results and other previous results, and found out they matched perfectly. Thanks to the boundary-conforming FDM, problems such as dynamic rupture with arbitrary dip, strike and rake over an arbitrary curved plane can be handled; and supershear or subshear rupture can be simulated with different parameters such as the initial stresses and the critical slip displacement Dc. Besides, our rupture modeling is economical to be implemented owing to its high efficiency and does not suffer from displacement leakage. With the help of inversion data of rupture by field observations, this method is convenient to model rupture processes and seismograms of natural earthquakes.
Siripatana, Chairat; Thongpan, Hathaikarn; Promraksa, Arwut
2017-03-01
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.
Ghil, M.; Balgovind, R.
1979-01-01
The inhomogeneous Cauchy-Riemann equations in a rectangle are discretized by a finite difference approximation. Several different boundary conditions are treated explicitly, leading to algorithms which have overall second-order accuracy. All boundary conditions with either u or v prescribed along a side of the rectangle can be treated by similar methods. The algorithms presented here have nearly minimal time and storage requirements and seem suitable for development into a general-purpose direct Cauchy-Riemann solver for arbitrary boundary conditions.
Computing with high-resolution upwind schemes for hyperbolic equations
International Nuclear Information System (INIS)
Chakravarthy, S.R.; Osher, S.; California Univ., Los Angeles)
1985-01-01
Computational aspects of modern high-resolution upwind finite-difference schemes for hyperbolic systems of conservation laws are examined. An operational unification is demonstrated for constructing a wide class of flux-difference-split and flux-split schemes based on the design principles underlying total variation diminishing (TVD) schemes. Consideration is also given to TVD scheme design by preprocessing, the extension of preprocessing and postprocessing approaches to general control volumes, the removal of expansion shocks and glitches, relaxation methods for implicit TVD schemes, and a new family of high-accuracy TVD schemes. 21 references
Environmental impact assessment of different design schemes of an industrial ecosystem
International Nuclear Information System (INIS)
Singh, Aditi; Lou, Helen H.; Yaws, Carl L.; Hopper, Jack R.; Pike, Ralph W.
2007-01-01
Industrial ecosystem is an important approach for sustainable development. In an industrial ecosystem, a group of industries are inter-connected through mass and energy exchanges for mutual benefits. However, some mass and energy exchange activities may cause unexpected environmental impacts. Therefore, it is vital to evaluate the environmental impacts of the symbiosis in order to provide a clear guidance for the decision-makers and stakeholders. The agro-chemical complex in the Lower Mississippi River Corridor with thirteen chemical and petrochemical industries emits huge amount of carbon dioxide. A bi-level design methodology is used to reconfigure this complex for utilizing surplus carbon dioxide. By using a superstructure-based approach, a new design scheme for this industrial ecosystem is proposed. In this paper, an LCA-type environmental impact assessment of different design schemes for this complex is conducted using the software TRACI, a tool developed by the United States Environmental Protection Agency (USEPA). This analysis compares various environmental impacts of different designs and identifies the potential trade-offs in different environmental impact categories. This information provides deep insight about the environmental sustainability of industrial ecosystems and facilitates the development of the most eco-effective symbiosis for recycle, reuse and resource conservation. (author)
Romanova, Vanya; Hense, Andreas; Wahl, Sabrina; Brune, Sebastian; Baehr, Johanna
2016-04-01
The decadal variability and its predictability of the surface net freshwater fluxes is compared in a set of retrospective predictions, all using the same model setup, and only differing in the implemented ocean initialisation method and ensemble generation method. The basic aim is to deduce the differences between the initialization/ensemble generation methods in view of the uncertainty of the verifying observational data sets. The analysis will give an approximation of the uncertainties of the net freshwater fluxes, which up to now appear to be one of the most uncertain products in observational data and model outputs. All ensemble generation methods are implemented into the MPI-ESM earth system model in the framework of the ongoing MiKlip project (www.fona-miklip.de). Hindcast experiments are initialised annually between 2000-2004, and from each start year 10 ensemble members are initialized for 5 years each. Four different ensemble generation methods are compared: (i) a method based on the Anomaly Transform method (Romanova and Hense, 2015) in which the initial oceanic perturbations represent orthogonal and balanced anomaly structures in space and time and between the variables taken from a control run, (ii) one-day-lagged ocean states from the MPI-ESM-LR baseline system (iii) one-day-lagged of ocean and atmospheric states with preceding full-field nudging to re-analysis in both the atmospheric and the oceanic component of the system - the baseline one MPI-ESM-LR system, (iv) an Ensemble Kalman Filter (EnKF) implemented into oceanic part of MPI-ESM (Brune et al. 2015), assimilating monthly subsurface oceanic temperature and salinity (EN3) using the Parallel Data Assimilation Framework (PDAF). The hindcasts are evaluated probabilistically using fresh water flux data sets from four different reanalysis data sets: MERRA, NCEP-R1, GFDL ocean reanalysis and GECCO2. The assessments show no clear differences in the evaluations scores on regional scales. However, on the
Jiang, Yu-ting; Mo, Zhi-wen
2017-10-01
Control power is used to discuss about the controller's measurable authority. It's a new index to describe the controlled teleportation schemes from the point of view of the controller. In this paper, we introduce two perfect controlled teleportation schemes and calculate the control power under different control particles. In scheme 1, the controller just controls one particle, which is particle 2. And in scheme 2, the controller controls the particles 2 and 3. They both use the cluster state |ψ > _{1234}={1/2}(|0000> +|0011> +|1100> -|1111> )_{1234} as communication channel. By calculating the control power between two schemes, the control power of scheme 1 is 1/3, which is the minimal value of control power. On the contrary, the control power of scheme 2 is maximal, 1/2. Scheme 2 which controls two particles successfully promotes the control power comparing with scheme 1. It's evidently that controlling particle 2 is a necessary condition. And controlling particle 3 can gain the control power but the controller cannot control it solely.
Elastic frequency-domain finite-difference contrast source inversion method
International Nuclear Information System (INIS)
He, Qinglong; Chen, Yong; Han, Bo; Li, Yang
2016-01-01
In this work, we extend the finite-difference contrast source inversion (FD-CSI) method to the frequency-domain elastic wave equations, where the parameters describing the subsurface structure are simultaneously reconstructed. The FD-CSI method is an iterative nonlinear inversion method, which exhibits several strengths. First, the finite-difference operator only relies on the background media and the given angular frequency, both of which are unchanged during inversion. Therefore, the matrix decomposition is performed only once at the beginning of the iteration if a direct solver is employed. This makes the inversion process relatively efficient in terms of the computational cost. In addition, the FD-CSI method automatically normalizes different parameters, which could avoid the numerical problems arising from the difference of the parameter magnitude. We exploit a parallel implementation of the FD-CSI method based on the domain decomposition method, ensuring a satisfactory scalability for large-scale problems. A simple numerical example with a homogeneous background medium is used to investigate the convergence of the elastic FD-CSI method. Moreover, the Marmousi II model proposed as a benchmark for testing seismic imaging methods is presented to demonstrate the performance of the elastic FD-CSI method in an inhomogeneous background medium. (paper)
Finite difference applied to the reconstruction method of the nuclear power density distribution
International Nuclear Information System (INIS)
Pessoa, Paulo O.; Silva, Fernando C.; Martinez, Aquilino S.
2016-01-01
Highlights: • A method for reconstruction of the power density distribution is presented. • The method uses discretization by finite differences of 2D neutrons diffusion equation. • The discretization is performed homogeneous meshes with dimensions of a fuel cell. • The discretization is combined with flux distributions on the four node surfaces. • The maximum errors in reconstruction occur in the peripheral water region. - Abstract: In this reconstruction method the two-dimensional (2D) neutron diffusion equation is discretized by finite differences, employed to two energy groups (2G) and meshes with fuel-pin cell dimensions. The Nodal Expansion Method (NEM) makes use of surface discontinuity factors of the node and provides for reconstruction method the effective multiplication factor of the problem and the four surface average fluxes in homogeneous nodes with size of a fuel assembly (FA). The reconstruction process combines the discretized 2D diffusion equation by finite differences with fluxes distribution on four surfaces of the nodes. These distributions are obtained for each surfaces from a fourth order one-dimensional (1D) polynomial expansion with five coefficients to be determined. The conditions necessary for coefficients determination are three average fluxes on consecutive surfaces of the three nodes and two fluxes in corners between these three surface fluxes. Corner fluxes of the node are determined using a third order 1D polynomial expansion with four coefficients. This reconstruction method uses heterogeneous nuclear parameters directly providing the heterogeneous neutron flux distribution and the detailed nuclear power density distribution within the FAs. The results obtained with this method has good accuracy and efficiency when compared with reference values.
A study of unstable rock failures using finite difference and discrete element methods
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
International Nuclear Information System (INIS)
Li Bihong; Shuang Na; Liu Qingcheng
2006-01-01
The principle of finite difference method is introduced, and the radon field distribution over sandstone-type uranium deposit is narrated. The radon field distribution theory equation is established. To solve radon field distribution equation using finite difference algorithm is to provide the value computational method for forward calculation about radon field over sandstone-type uranium mine. Study on 2-D finite difference method on the center of either high anomaly radon fields in view of the character of radon field over sandstone-type uranium provide an algorithm for further research. (authors)
DEFF Research Database (Denmark)
Santillan, Arturo Orozco
2011-01-01
The aim of the work described in this paper has been to investigate the use of the finite-difference time-domain method to describe the interactions between a moving object and a sound field. The main objective was to simulate oscillational instabilities that appear in single-axis acoustic...... levitation devices and to describe their evolution in time to further understand the physical mechanism involved. The study shows that the method gives accurate results for steady state conditions, and that it is a promising tool for simulations with a moving object....
Slat Noise Predictions Using Higher-Order Finite-Difference Methods on Overset Grids
Housman, Jeffrey A.; Kiris, Cetin
2016-01-01
Computational aeroacoustic simulations using the structured overset grid approach and higher-order finite difference methods within the Launch Ascent and Vehicle Aerodynamics (LAVA) solver framework are presented for slat noise predictions. The simulations are part of a collaborative study comparing noise generation mechanisms between a conventional slat and a Krueger leading edge flap. Simulation results are compared with experimental data acquired during an aeroacoustic test in the NASA Langley Quiet Flow Facility. Details of the structured overset grid, numerical discretization, and turbulence model are provided.
COVE-1: a finite difference creep collapse code for oval fuel pin cladding material
International Nuclear Information System (INIS)
Mohr, C.L.
1975-03-01
COVE-1 is a time-dependent incremental creep collapse code that estimates the change in ovality of a fuel pin cladding tube. It uses a finite difference method of solving the differential equations which describe the deflection of the tube walls as a function of time. The physical problem is nonlinear, both with respect to geometry and material properties, which requires the use of an incremental, analytical, path-dependent solution. The application of this code is intended primarily for tubes manufactured from Zircaloy. Therefore, provision has been made to include some of the effects of anisotropy in the flow equations for inelastic incremental deformations. 10 references. (U.S.)
Directory of Open Access Journals (Sweden)
Yuan Zhang
2016-01-01
Full Text Available Based on finite difference method, a mathematical model and a numerical model written by Fortran language were established in the paper. Then a series of experiments were conducted to figure out the evolution law of temperature field in high geothermal roadway. Research results indicate that temperature disturbance range increases gradually as the unsteady heat conduction goes on and it presents power function relationship with dimensionless time. Based on the case analysis, there is no distinct expansion of temperature disturbance range after four years of ventilation, when the temperature disturbance range R=13.6.
Analysis of multi lobe journal bearings with surface roughness using finite difference method
PhaniRaja Kumar, K.; Bhaskar, SUdaya; Manzoor Hussain, M.
2018-04-01
Multi lobe journal bearings are used for high operating speeds and high loads in machines. In this paper symmetrical multi lobe journal bearings are analyzed to find out the effect of surface roughnessduring non linear loading. Using the fourth order RungeKutta method, time transient analysis was performed to calculate and plot the journal centre trajectories. Flow factor method is used to evaluate the roughness and the finite difference method (FDM) is used to predict the pressure distribution over the bearing surface. The Transient analysis is done on the multi lobe journal bearings for threedifferent surface roughness orientations. Longitudinal surface roughness is more effective when compared with isotopic and traverse surface roughness.
Agarwal, P.; El-Sayed, A. A.
2018-06-01
In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.
New way for determining electron energy levels in quantum dots arrays using finite difference method
Dujardin, F.; Assaid, E.; Feddi, E.
2018-06-01
Electronic states are investigated in quantum dots arrays, depending on the type of cubic Bravais lattice (primitive, body centered or face centered) according to which the dots are arranged, the size of the dots and the interdot distance. It is shown that the ground state energy level can undergo significant variations when these parameters are modified. The results were obtained by means of finite difference method which has proved to be easily adaptable, efficient and precise. The symmetry properties of the lattice have been used to reduce the size of the Hamiltonian matrix.
Calculating modes of quantum wire systems using a finite difference technique
Directory of Open Access Journals (Sweden)
T Mardani
2013-03-01
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.
Solving the Schroedinger equation using the finite difference time domain method
International Nuclear Information System (INIS)
Sudiarta, I Wayan; Geldart, D J Wallace
2007-01-01
In this paper, we solve the Schroedinger equation using the finite difference time domain (FDTD) method to determine energies and eigenfunctions. In order to apply the FDTD method, the Schroedinger equation is first transformed into a diffusion equation by the imaginary time transformation. The resulting time-domain diffusion equation is then solved numerically by the FDTD method. The theory and an algorithm are provided for the procedure. Numerical results are given for illustrative examples in one, two and three dimensions. It is shown that the FDTD method accurately determines eigenfunctions and energies of these systems
Scattering analysis of periodic structures using finite-difference time-domain
ElMahgoub, Khaled; Elsherbeni, Atef Z
2012-01-01
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
Double absorbing boundaries for finite-difference time-domain electromagnetics
Energy Technology Data Exchange (ETDEWEB)
LaGrone, John, E-mail: jlagrone@smu.edu; Hagstrom, Thomas, E-mail: thagstrom@smu.edu
2016-12-01
We describe the implementation of optimal local radiation boundary condition sequences for second order finite difference approximations to Maxwell's equations and the scalar wave equation using the double absorbing boundary formulation. Numerical experiments are presented which demonstrate that the design accuracy of the boundary conditions is achieved and, for comparable effort, exceeds that of a convolution perfectly matched layer with reasonably chosen parameters. An advantage of the proposed approach is that parameters can be chosen using an accurate a priori error bound.
Finite difference time domain modeling of light matter interaction in light-propelled microtools
DEFF Research Database (Denmark)
Bañas, Andrew Rafael; Palima, Darwin; Aabo, Thomas
2013-01-01
save time as it helps optimize the structures prior to fabrication and experiments. In addition to field distributions, optical forces can also be obtained using the Maxwell stress tensor formulation. By calculating the forces on bent waveguides subjected to tailored static light distributions, we...... may trigger highly localized non linear processes in the surface of a cell. Since these functionalities are strongly dependent on design, it is important to use models that can handle complexities and take in little simplifying assumptions about the system. Hence, we use the finite difference time...
Transient analysis of printed lines using finite-difference time-domain method
Energy Technology Data Exchange (ETDEWEB)
Ahmed, Shahid [Thomas Jefferson National Accelerator Facility, 12050 Jefferson Avenue, Suite 704, Newport News, VA, 23606, USA
2012-03-29
Comprehensive studies of ultra-wideband pulses and electromagnetic coupling on printed coupled lines have been performed using full-wave 3D finite-difference time-domain analysis. Effects of unequal phase velocities of coupled modes, coupling between line traces, and the frequency dispersion on the waveform fidelity and crosstalk have been investigated in detail. To discriminate the contributions of different mechanisms into pulse evolution, single and coupled microstrip lines without (ϵ_{r} = 1) and with (ϵ_{r} > 1) dielectric substrates have been examined. To consistently compare the performance of the coupled lines with substrates of different permittivities and transients of different characteristic times, a generic metric similar to the electrical wavelength has been introduced. The features of pulse propagation on coupled lines with layered and pedestal substrates and on the irregular traces have been explored. Finally, physical interpretations of the simulation results are discussed in the paper.
Directory of Open Access Journals (Sweden)
Richasanty Septima S
2017-03-01
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.
Soil quality under two different management schemes in coffee plantations of southern Colombia.
Directory of Open Access Journals (Sweden)
Oscar Eduardo Valbuena-Calderón
2016-12-01
Full Text Available The aim of this work was to develop an additive soil quality index (ASQI in agrofostery managements of coffee (Coffea arabica L.. The study took place under two intense and traditional management schemes, in nine farms (32 lots in the south of Colombia, during 2013. A separation of means analysis was held through the LSD Fisher test (P<0,05 to each of the physical and chemical variables of the soil. The variables that showed differences between the schemes were submitted to a main components analysis to select the minimum data set (MDS of the components that explained the most variability and the redundancy was veri ed within the indicators, based on the correlation. The ASQI was obtained from the total sum of soil quality index (SQI of all the indicators, taking into account that the higher the score of the ASQI, the higher the quality of the soil within the study system. The selected physical variables were the content of sand and clay; while the chemical variables were: organic carbon (OC, P, CA, Mg, total bases (TB and Ca/Mg. The best ASQI was obtained from traditional management, because the value of the selected variables matched in a bigger proportion with the quality objective identi ed for the ASQI quanti cation; in this case the crop yield, based on limit values for coffee plantations.
International Nuclear Information System (INIS)
Kaprealian, Tania; Weinberg, Vivian; Speight, Joycelyn L.; Gottschalk, Alexander R.; Roach, Mack; Shinohara, Katsuto; Hsu, I.-Chow
2012-01-01
Purpose: This is a retrospective study comparing our experience with high-dose-rate (HDR) brachytherapy boost for prostate cancer, using two different fractionation schemes, 600 cGy × 3 fractions (patient group 1) and 950 cGy × 2 fractions (patient group 2). Methods and Materials: A total of 165 patients were treated for prostate cancer using external beam radiation therapy up to a dose of 45 Gy, followed by an HDR brachytherapy prostate radiation boost. Between July 1997 and Nov 1999, 64 patients were treated with an HDR boost of 600 cGy × 3 fractions; and between June 2000 and Nov 2005, 101 patients were treated with an HDR boost of 950 cGy × 2 fractions. All but 9 patients had at least one of the following risk features: pretreatment prostate-specific antigen (PSA) level >10, a Gleason score ≥7, and/or clinical stage T3 disease. Results: Median follow-up was 105 months for group 1 and 43 months for group 2. Patients in group 2 had a greater number of high-risk features than group 1 (p = 0.02). Adjusted for comparable follow-up, there was no difference in biochemical no-evidence-of-disease (bNED) rate between the two fractionation scheme approaches, with 5-year Kaplan-Meier estimates of 93.5% in group 1 and 87.3% in group 2 (p = 0.19). The 5-year estimates of progression-free survival were 86% for group 1 and 83% for group 2 (p = 0.53). Among high-risk patients, there were no differences in bNED or PFS rate due to fractionation. Conclusions: Results were excellent for both groups. Adjusted for comparable follow-up, no differences were found between groups.
A moving mesh finite difference method for equilibrium radiation diffusion equations
Energy Technology Data Exchange (ETDEWEB)
Yang, Xiaobo, E-mail: xwindyb@126.com [Department of Mathematics, College of Science, China University of Mining and Technology, Xuzhou, Jiangsu 221116 (China); Huang, Weizhang, E-mail: whuang@ku.edu [Department of Mathematics, University of Kansas, Lawrence, KS 66045 (United States); Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn [School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University, Xiamen, Fujian 361005 (China)
2015-10-01
An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.
Evaluation of explicit finite-difference techniques for LMFBR safety analysis
International Nuclear Information System (INIS)
Bernstein, D.; Golden, R.D.; Gross, M.B.; Hofmann, R.
1976-01-01
In the past few years, the use of explicit finite-difference (EFD) and finite-element computer programs for reactor safety calculations has steadily increased. One of the major areas of application has been for the analysis of hypothetical core disruptive accidents in liquid metal fast breeder reactors. Most of these EFD codes were derived to varying degrees from the same roots, but the codes are large and have progressed rapidly, so there may be substantial differences among them in spite of a common ancestry. When this fact is coupled with the complexity of HCDA calculations, it is not possible to assure that independent calculations of an HCDA will produce substantially the same results. Given the extreme importance of nuclear safety, it is essential to be sure that HCDA analyses are correct, and additional code validation is therefore desirable. A comparative evaluation of HCDA computational techniques is being performed under an ERDA-sponsored program called APRICOT (Analysis of PRImary COntainment Transients). The philosophy, calculations, and preliminary results from this program are described in this paper
Parallelized implicit propagators for the finite-difference Schrödinger equation
Parker, Jonathan; Taylor, K. T.
1995-08-01
We describe the application of block Gauss-Seidel and block Jacobi iterative methods to the design of implicit propagators for finite-difference models of the time-dependent Schrödinger equation. The block-wise iterative methods discussed here are mixed direct-iterative methods for solving simultaneous equations, in the sense that direct methods (e.g. LU decomposition) are used to invert certain block sub-matrices, and iterative methods are used to complete the solution. We describe parallel variants of the basic algorithm that are well suited to the medium- to coarse-grained parallelism of work-station clusters, and MIMD supercomputers, and we show that under a wide range of conditions, fine-grained parallelism of the computation can be achieved. Numerical tests are conducted on a typical one-electron atom Hamiltonian. The methods converge robustly to machine precision (15 significant figures), in some cases in as few as 6 or 7 iterations. The rate of convergence is nearly independent of the finite-difference grid-point separations.
A Proposed Stochastic Finite Difference Approach Based on Homogenous Chaos Expansion
Directory of Open Access Journals (Sweden)
O. H. Galal
2013-01-01
Full Text Available This paper proposes a stochastic finite difference approach, based on homogenous chaos expansion (SFDHC. The said approach can handle time dependent nonlinear as well as linear systems with deterministic or stochastic initial and boundary conditions. In this approach, included stochastic parameters are modeled as second-order stochastic processes and are expanded using Karhunen-Loève expansion, while the response function is approximated using homogenous chaos expansion. Galerkin projection is used in converting the original stochastic partial differential equation (PDE into a set of coupled deterministic partial differential equations and then solved using finite difference method. Two well-known equations were used for efficiency validation of the method proposed. First one being the linear diffusion equation with stochastic parameter and the second is the nonlinear Burger's equation with stochastic parameter and stochastic initial and boundary conditions. In both of these examples, the probability distribution function of the response manifested close conformity to the results obtained from Monte Carlo simulation with optimized computational cost.
A moving mesh finite difference method for equilibrium radiation diffusion equations
International Nuclear Information System (INIS)
Yang, Xiaobo; Huang, Weizhang; Qiu, Jianxian
2015-01-01
An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation
Finite difference method calculations of X-ray absorption fine structure for copper
Energy Technology Data Exchange (ETDEWEB)
Bourke, J.D. [School of Physics, University of Melbourne, Parkville, Vic 3010 (Australia); Chantler, C.T. [School of Physics, University of Melbourne, Parkville, Vic 3010 (Australia)]. E-mail: chantler@physics.unimelb.edu.au; Witte, C. [School of Physics, University of Melbourne, Parkville, Vic 3010 (Australia)
2007-01-15
The finite difference method is extended to calculate X-ray absorption fine structure (XAFS) for solid state copper. These extensions include the incorporation of a Monte Carlo frozen phonon technique to simulate the effect of thermal vibrations under a correlated Debye-Waller model, and the inclusion of broadening effects from inelastic processes. Spectra are obtained over an energy range in excess of 300 eV above the K absorption edge-more than twice the greatest energy range previously reported for a solid state calculation using this method. We find this method is highly sensitive to values of the photoelectron inelastic mean free path, allowing us to probe the accuracy of current models of this parameter, particularly at low energies. We therefore find that experimental data for the photoelectron inelastic mean free path can be obtained by this method. Our results compare favourably with high precision measurements of the X-ray mass attenuation coefficient for copper, reaching agreement to within 3%, and improving previous results using the finite difference method by an order of magnitude.
Gao, Longfei; Ketcheson, David I.; Keyes, David E.
2017-01-01
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
International Nuclear Information System (INIS)
Deupree, R.G.
1977-01-01
Finite difference techniques were used to examine the coupling of radial pulsation and convection in stellar models having comparable time scales. Numerical procedures are emphasized, including diagnostics to help determine the range of free parameters
Mitiku, Fikadu; Mey, de Yann; Nyssen, Jan; Maertens, Miet
2017-01-01
Private sustainability standards are increasingly important in food trade with developing countries, but the implications for smallholder farmers are still poorly understood. We analyze the implications of different coffee certification schemes in Ethiopia using cross-sectional survey data, and
Armand J, K. M.
2017-12-01
In this study, version 4 of the regional climate model (RegCM4) is used to perform 6 years simulation including one year for spin-up (from January 2001 to December 2006) over Central Africa using four convective schemes: The Emmanuel scheme (MIT), the Grell scheme with Arakawa-Schulbert closure assumption (GAS), the Grell scheme with Fritsch-Chappell closure assumption (GFC) and the Anthes-Kuo scheme (Kuo). We have investigated the ability of the model to simulate precipitation, surface temperature, wind and aerosols optical depth. Emphasis in the model results were made in December-January-February (DJF) and July-August-September (JAS) periods. Two subregions have been identified for more specific analysis namely: zone 1 which corresponds to the sahel region mainly classified as desert and steppe and zone 2 which is a region spanning the tropical rain forest and is characterised by a bimodal rain regime. We found that regardless of periods or simulated parameters, MIT scheme generally has a tendency to overestimate. The GAS scheme is more suitable in simulating the aforementioned parameters, as well as the diurnal cycle of precipitations everywhere over the study domain irrespective of the season. In JAS, model results are similar in the representation of regional wind circulation. Apart from the MIT scheme, all the convective schemes give the same trends in aerosols optical depth simulations. Additional experiment reveals that the use of BATS instead of Zeng scheme to calculate ocean flux appears to improve the quality of the model simulations.
Investigation of thermalization in giant-spin models by different Lindblad schemes
Energy Technology Data Exchange (ETDEWEB)
Beckmann, Christian; Schnack, Jürgen, E-mail: jschnack@uni-bielefeld.de
2017-09-01
Highlights: • The non-equilibrium magnetization is investigated with quantum master equations that rest on Lindblad schemes. • It is studied how different couplings to the bath modify the magnetization. • Various field protocols are employed; relaxation times are deduced. • Result: the time evolution depends strongly on the details of the transition operator used in the Lindblad term. - Abstract: The theoretical understanding of time-dependence in magnetic quantum systems is of great importance in particular for cases where a unitary time evolution is accompanied by relaxation processes. A key example is given by the dynamics of single-molecule magnets where quantum tunneling of the magnetization competes with thermal relaxation over the anisotropy barrier. In this article we investigate how good a Lindblad approach describes the relaxation in giant spin models and how the result depends on the employed operator that transmits the action of the thermal bath.
An efficient numerical scheme for the simulation of parallel-plate active magnetic regenerators
DEFF Research Database (Denmark)
Torregrosa-Jaime, Bárbara; Corberán, José M.; Payá, Jorge
2015-01-01
A one-dimensional model of a parallel-plate active magnetic regenerator (AMR) is presented in this work. The model is based on an efficient numerical scheme which has been developed after analysing the heat transfer mechanisms in the regenerator bed. The new finite difference scheme optimally com...... to the fully implicit scheme, the proposed scheme achieves more accurate results, prevents numerical errors and requires less computational effort. In AMR simulations the new scheme can reduce the computational time by 88%....
Finite element modelling of Plantar Fascia response during running on different surface types
Razak, A. H. A.; Basaruddin, K. S.; Salleh, A. F.; Rusli, W. M. R.; Hashim, M. S. M.; Daud, R.
2017-10-01
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.
Contact Stress Analysis for Gears of Different Helix Angle Using Finite Element Method
Directory of Open Access Journals (Sweden)
Patil Santosh
2014-07-01
Full Text Available The gear contact stress problem has been a great point of interest for many years, but still an extensive research is required to understand the various parameters affecting this stress. Among such parameters, helix angle is one which has played a crucial role in variation of contact stress. Numerous studies have been carried out on spur gear for contact stress variation. Hence, the present work is an attempt to study the contact stresses among the helical gear pairs, under static conditions, by using a 3D finite element method. The helical gear pairs on which the analysis is carried are 0, 5, 15, 25 degree helical gear sets. The Lagrange multiplier algorithm has been used between the contacting pairs to determine the stresses. The helical gear contact stress is evaluated using FE model and results have also been found at different coefficient of friction, varying from 0.0 to 0.3. The FE results have been further compared with the analytical calculations. The analytical calculations are based upon Hertz and AGMA equations, which are modified to include helix angle. The commercial finite element software was used in the study and it was shown that this approach can be applied to gear design efficiently. The contact stress results have shown a decreasing trend, with increase in helix angle.
Finite element modelling of different CANDU fuel bundle types in various refuelling conditions
International Nuclear Information System (INIS)
Roman, M. R.; Ionescu, D. V.; Olteanu, G.; Florea, S.; Radut, A. C.
2016-01-01
The objective of this paper is to develop a finite element model for static strength analysis of the CANDU standard with 37 elements fuel bundle and the SEU43 with 43 elements fuel bundle design for various refuelling conditions. The computer code, ANSYS7.1, is used to simulate the axial compression in CANDU type fuel bundles subject to hydraulic drag loads, deflection of fuel elements, stresses and displacements in the end plates. Two possible situations for the fuelling machine side stops are considered in our analyses, as follows: the last fuel bundle is supported by the two side stops and a side stop can be blocked therefore, the last fuel bundle is supported by only one side stop. The results of the analyses performed are briefly presented and also illustrated in a graphical form. The finite element model developed in present study is verified against test results for endplate displacement and element bowing obtained from strength tests with fuel bundle string and fuelling machine side-stop simulators. Comparison of ANSYS model predictions with these experimental results led to a very good agreement. Despite the difference in hydraulic load between SEU43 and CANDU standard fuel bundles strings, the maximum stress in the SEU43 endplate is about the same with the maximum stress in the CANDU standard endplate. The comparative assessment reveals that SEU43 fuel bundle is able to withstand high flow rate without showing a significant geometric instability. (authors)
Jin, Long; Liao, Bolin; Liu, Mei; Xiao, Lin; Guo, Dongsheng; Yan, Xiaogang
2017-01-01
By incorporating the physical constraints in joint space, a different-level simultaneous minimization scheme, which takes both the robot kinematics and robot dynamics into account, is presented and investigated for fault-tolerant motion planning of redundant manipulator in this paper. The scheme is reformulated as a quadratic program (QP) with equality and bound constraints, which is then solved by a discrete-time recurrent neural network. Simulative verifications based on a six-link planar redundant robot manipulator substantiate the efficacy and accuracy of the presented acceleration fault-tolerant scheme, the resultant QP and the corresponding discrete-time recurrent neural network.
International Nuclear Information System (INIS)
Kraus, H.G.; Jones, J.L.
1986-01-01
The problem of non-linear superconducting magnet and electrical protection circuit system transients is formulated. To enable studying the effects of coil normalization transients, coil distortion (due to imbalanced magnetic forces), internal coil arcs and shorts, and other normal and off-normal circuit element responses, the following capabilities are included: temporal, voltage and current-dependent voltage sources, current sources, resistors, capacitors and inductors. The concept of self-mutual inductance, and the form of the associated inductance matrix, is discussed for internally shorted coils. This is a Kirchhoff's voltage loop law and Kirchhoff's current node law formulation. The non-linear integrodifferential equation set is solved via a unique hybrid finite difference/integral finite element technique. (author)
International Nuclear Information System (INIS)
Grant, C.R.
1996-01-01
The reactor code PUMA, developed in CNEA, simulates nuclear reactors discretizing space in finite difference elements. Core representation is performed by means a cylindrical mesh, but the reactor channels are arranged in an hexagonal lattice. That is why a mapping using volume intersections must be used. This spatial treatment is the reason of an overestimation of the control rod reactivity values, which must be adjusted modifying the incremental cross sections. Also, a not very good treatment of the continuity conditions between core and reflector leads to an overestimation of channel power of the peripherical fuel elements between 5 to 8 per cent. Another code, DELFIN, developed also in CNEA, treats the spatial discretization using heterogeneous finite elements, allowing a correct treatment of the continuity of fluxes and current among elements and a more realistic representation of the hexagonal lattice of the reactor. A comparison between results obtained using both methods in done in this paper. (author). 4 refs., 3 figs
Sohn, Kiho D.; Ip, Shek-Se P.
1988-01-01
Three-dimensional finite element models were generated and transferred into three-dimensional finite difference models to perform transient thermal analyses for the SSME high pressure fuel turbopump's first stage nozzles and rotor blades. STANCOOL was chosen to calculate the heat transfer characteristics (HTCs) around the airfoils, and endwall effects were included at the intersections of the airfoils and platforms for the steady-state boundary conditions. Free and forced convection due to rotation effects were also considered in hollow cores. Transient HTCs were calculated by taking ratios of the steady-state values based on the flow rates and fluid properties calculated at each time slice. Results are presented for both transient plots and three-dimensional color contour isotherm plots; they were also converted into universal files to be used for FEM stress analyses.
GPU-accelerated 3D neutron diffusion code based on finite difference method
Energy Technology Data Exchange (ETDEWEB)
Xu, Q.; Yu, G.; Wang, K. [Dept. of Engineering Physics, Tsinghua Univ. (China)
2012-07-01
Finite difference method, as a traditional numerical solution to neutron diffusion equation, although considered simpler and more precise than the coarse mesh nodal methods, has a bottle neck to be widely applied caused by the huge memory and unendurable computation time it requires. In recent years, the concept of General-Purpose computation on GPUs has provided us with a powerful computational engine for scientific research. In this study, a GPU-Accelerated multi-group 3D neutron diffusion code based on finite difference method was developed. First, a clean-sheet neutron diffusion code (3DFD-CPU) was written in C++ on the CPU architecture, and later ported to GPUs under NVIDIA's CUDA platform (3DFD-GPU). The IAEA 3D PWR benchmark problem was calculated in the numerical test, where three different codes, including the original CPU-based sequential code, the HYPRE (High Performance Pre-conditioners)-based diffusion code and CITATION, were used as counterpoints to test the efficiency and accuracy of the GPU-based program. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation for neutron diffusion equation. A speedup factor of about 46 times was obtained, using NVIDIA's Geforce GTX470 GPU card against a 2.50 GHz Intel Quad Q9300 CPU processor. Compared with the HYPRE-based code performing in parallel on an 8-core tower server, the speedup of about 2 still could be observed. More encouragingly, without any mathematical acceleration technology, the GPU implementation ran about 5 times faster than CITATION which was speeded up by using the SOR method and Chebyshev extrapolation technique. (authors)
GPU-accelerated 3D neutron diffusion code based on finite difference method
International Nuclear Information System (INIS)
Xu, Q.; Yu, G.; Wang, K.
2012-01-01
Finite difference method, as a traditional numerical solution to neutron diffusion equation, although considered simpler and more precise than the coarse mesh nodal methods, has a bottle neck to be widely applied caused by the huge memory and unendurable computation time it requires. In recent years, the concept of General-Purpose computation on GPUs has provided us with a powerful computational engine for scientific research. In this study, a GPU-Accelerated multi-group 3D neutron diffusion code based on finite difference method was developed. First, a clean-sheet neutron diffusion code (3DFD-CPU) was written in C++ on the CPU architecture, and later ported to GPUs under NVIDIA's CUDA platform (3DFD-GPU). The IAEA 3D PWR benchmark problem was calculated in the numerical test, where three different codes, including the original CPU-based sequential code, the HYPRE (High Performance Pre-conditioners)-based diffusion code and CITATION, were used as counterpoints to test the efficiency and accuracy of the GPU-based program. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation for neutron diffusion equation. A speedup factor of about 46 times was obtained, using NVIDIA's Geforce GTX470 GPU card against a 2.50 GHz Intel Quad Q9300 CPU processor. Compared with the HYPRE-based code performing in parallel on an 8-core tower server, the speedup of about 2 still could be observed. More encouragingly, without any mathematical acceleration technology, the GPU implementation ran about 5 times faster than CITATION which was speeded up by using the SOR method and Chebyshev extrapolation technique. (authors)
Shen, Yi; Li, Xiaomiao; Fu, Xiaodong; Wang, Weili
2015-11-01
Posterior tibial slope that is created during proximal tibial resection in total knee arthroplasty has emerged as an important factor in the mechanics of the knee joint and the surgical outcome. But the ideal degree of posterior tibial slope for recovery of the knee joint function and preventions of complications remains controversial and should vary in different racial groups. The objective of this paper is to investigate the effects of posterior tibial slope on contact stresses in the tibial polyethylene component of total knee prostheses. Three-dimensional finite element analysis was used to calculate contact stresses in tibial polyethylene component of total knee prostheses subjected to a compressive load. The 3D finite element model of total knee prosthesis was constructed from the images produced by 3D scanning technology. Stresses in tibial polyethylene component were calculated with four different posterior tibial slopes (0°, 3°, 6° and 9°). The 3D finite element model of total knee prosthesis we presented was well validated. We found that the stress distribution in the polythene as evaluated by the distributions of the von Mises stress, the maximum principle stress, the minimum principle stress and the Cpress were more uniform with 3° and 6° posterior tibial slopes than with 0° and 9° posterior tibial slopes. Moreover, the peaks of the above stresses and trends of changes with increasing degree of knee flexion were more ideal with 3° and 6° posterior slopes. The results suggested that the tibial component inclination might be favourable to 7°-10° so far as the stress distribution is concerned. The range of the tibial component inclination also can decrease the wear of polyethylene. Chinese posterior tibial slope is bigger than in the West, and the current domestic use of prostheses is imported from the West, so their demands to tilt back bone cutting can lead to shorten the service life of prostheses; this experiment result is of important
Castaldo, Raffaele; Tizzani, Pietro
2016-04-01
Many numerical models have been developed to simulate the deformation and stress changes associated to the faulting process. This aspect is an important topic in fracture mechanism. In the proposed study, we investigate the impact of the deep fault geometry and tectonic setting on the co-seismic ground deformation pattern associated to different earthquake phenomena. We exploit the impact of the structural-geological data in Finite Element environment through an optimization procedure. In this framework, we model the failure processes in a physical mechanical scenario to evaluate the kinematics associated to the Mw 6.1 L'Aquila 2009 earthquake (Italy), the Mw 5.9 Ferrara and Mw 5.8 Mirandola 2012 earthquake (Italy) and the Mw 8.3 Gorkha 2015 earthquake (Nepal). These seismic events are representative of different tectonic scenario: the normal, the reverse and thrust faulting processes, respectively. In order to simulate the kinematic of the analyzed natural phenomena, we assume, under the plane stress approximation (is defined to be a state of stress in which the normal stress, sz, and the shear stress sxz and syz, directed perpendicular to x-y plane are assumed to be zero), the linear elastic behavior of the involved media. The performed finite element procedure consist of through two stages: (i) compacting under the weight of the rock successions (gravity loading), the deformation model reaches a stable equilibrium; (ii) the co-seismic stage simulates, through a distributed slip along the active fault, the released stresses. To constrain the models solution, we exploit the DInSAR deformation velocity maps retrieved by satellite data acquired by old and new generation sensors, as ENVISAT, RADARSAT-2 and SENTINEL 1A, encompassing the studied earthquakes. More specifically, we first generate 2D several forward mechanical models, then, we compare these with the recorded ground deformation fields, in order to select the best boundaries setting and parameters. Finally
3D finite element analysis of tightening process of bolt and nut connections with pitch difference
Liu, X.; Noda, N.-A.; Sano, Y.; Huang, Y. T.; Takase, Y.
2018-06-01
In a wide industrial field, the bolt-nut joint is unitized as an important machine element and anti-loosening performance is always required. In this paper, the effect of a slight pitch difference between a bolt and nut is studied. Firstly, by varying the pitch difference, the prevailing torque required for the nut rotation, before the nut touches the clamped body, is measured experimentally. Secondly, the tightening torque is determined as a function of the axial force of the bolt after the nut touches the clamped body. The results show that a large value of pitch difference may provide large prevailing torque that causes an anti-loosening effect although a very large pitch difference may deteriorate the bolt axial force under a certain tightening torque. Thirdly, a suitable pitch difference is determined taking into account the anti-loosening and clamping abilities. Furthermore, the chamfered corners at nut ends are considered, and it is found that the 3D finite element analysis with considering the chamfered nut threads has a good agreement with the experimental observation. Finally, the most desirable pitch difference required for improving anti-loosening is proposed.
Zhao, Liang; Adhikari, Avishek; Sakurai, Kouichi
Watermarking is one of the most effective techniques for copyright protection and information hiding. It can be applied in many fields of our society. Nowadays, some image scrambling schemes are used as one part of the watermarking algorithm to enhance the security. Therefore, how to select an image scrambling scheme and what kind of the image scrambling scheme may be used for watermarking are the key problems. Evaluation method of the image scrambling schemes can be seen as a useful test tool for showing the property or flaw of the image scrambling method. In this paper, a new scrambling evaluation system based on spatial distribution entropy and centroid difference of bit-plane is presented to obtain the scrambling degree of image scrambling schemes. Our scheme is illustrated and justified through computer simulations. The experimental results show (in Figs. 6 and 7) that for the general gray-scale image, the evaluation degree of the corresponding cipher image for the first 4 significant bit-planes selection is nearly the same as that for the 8 bit-planes selection. That is why, instead of taking 8 bit-planes of a gray-scale image, it is sufficient to take only the first 4 significant bit-planes for the experiment to find the scrambling degree. This 50% reduction in the computational cost makes our scheme efficient.
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)
2016-01-15
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.
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
2004-12-01
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)
CASKETSS-HEAT: a finite difference computer program for nonlinear heat conduction problems
International Nuclear Information System (INIS)
Ikushima, Takeshi
1988-12-01
A heat conduction program CASKETSS-HEAT has been developed. CASKETSS-HEAT is a finite difference computer program used for the solution of multi-dimensional nonlinear heat conduction problems. Main features of CASKETSS-HEAT are as follows. (1) One, two and three-dimensional geometries for heat conduction calculation are available. (2) Convection and radiation heat transfer of boundry can be specified. (3) Phase change and chemical change can be treated. (4) Finned surface heat transfer can be treated easily. (5) Data memory allocation in the program is variable according to problem size. (6) The program is a compatible heat transfer analysis program to the stress analysis program SAP4 and SAP5. (7) Pre- and post-processing for input data generation and graphic representation of calculation results are available. In the paper, brief illustration of calculation method, input data and sample calculation are presented. (author)
The delay function in finite difference models for nuclear channels thermo-hydraulic transients
International Nuclear Information System (INIS)
Agazzi, A.
1977-01-01
The study of the thermo-hydraulic transients in a nuclear reactor core often requires a bi- or tri-dimensional mathematical simulation of a reactor channel. The equations involved are generally solved by means of finite-difference methods. The determination of the spatial mesh-width and the time interval is strongly conditioned by the necessity of a good accuracy in the description of the delay function which defines the transfer of thermal perturbations along the cooling channel. In this paper the effects of both space and time discretization on the delay function are considered and for the classical cases of inlet temperature step and ramp universal functions and diagrams are given in order to make possible the determination of optimal spatial mesh-width and time interval, once the requested accuracy of the model is fixed in advance
Directory of Open Access Journals (Sweden)
Beltrán-Prieto Juan Carlos
2016-01-01
Full Text Available The mathematical modelling of diffusion of a bleaching agent into a porous material is studied in the present paper. Law of mass conservation was applied to analize the mass transfer of a reactant from the bulk into the external surface of a solid geometrically described as a flat plate. After diffusion of the reactant, surface reaction following kinetics of first order was considered to take place. The solution of the differential equation that described the process leaded to an equation that represents the concentration profile in function of distance, porosity and Thiele modulus. The case of interfacial mass resistance is also discused. In this case, finite difference method was used for the solution of the differential equation taking into account the respective boundary conditions. The profile of concentration can be obtained after numerical especification of Thiele modulus and Biot number.
Finite difference time domain solution of electromagnetic scattering on the hypercube
International Nuclear Information System (INIS)
Calalo, R.H.; Lyons, J.R.; Imbriale, W.A.
1988-01-01
Electromagnetic fields interacting with a dielectric or conducting structure produce scattered electromagnetic fields. To model the fields produced by complicated, volumetric structures, the finite difference time domain (FDTD) method employs an iterative solution to Maxwell's time dependent curl equations. Implementations of the FDTD method intensively use memory and perform numerous calculations per time step iteration. The authors have implemented an FDTD code on the California Institute of Technology/Jet Propulsion Laboratory Mark III Hypercube. This code allows to solve problems requiring as many as 2,048,000 unit cells on a 32 node Hypercube. For smaller problems, the code produces solutions in a fraction of the time to solve the same problems on sequential computers
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)
2012-05-15
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.
Finite-difference time-domain simulation of thermal noise in open cavities
International Nuclear Information System (INIS)
Andreasen, Jonathan; Cao Hui; Taflove, Allen; Kumar, Prem; Cao Changqi
2008-01-01
A numerical model based on the finite-difference time-domain (FDTD) method is developed to simulate thermal noise in open cavities owing to output coupling. The absorbing boundary of the FDTD grid is treated as a blackbody, whose thermal radiation penetrates the cavity in the grid. The calculated amount of thermal noise in a one-dimensional dielectric cavity recovers the standard result of the quantum Langevin equation in the Markovian regime. Our FDTD simulation also demonstrates that in the non-Markovian regime the buildup of the intracavity noise field depends on the ratio of the cavity photon lifetime to the coherence time of thermal radiation. The advantage of our numerical method is that the thermal noise is introduced in the time domain without prior knowledge of cavity modes
Simulation of acoustic streaming by means of the finite-difference time-domain method
DEFF Research Database (Denmark)
Santillan, Arturo Orozco
2012-01-01
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...... directions of rotation that are opposite to those of the outer streaming vortices (Rayleigh streaming). The general objective of the work described in this paper has been to study the extent to which it is possible to simulate both the outer streaming vortices and the inner boundary layer vortices using...... 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...
International Nuclear Information System (INIS)
Paul, O.P.K.
1978-01-01
An approach to simulate the flux vanishing boundary condition in solving the two group coupled neutron diffusion equations in three dimensions (x, y, z) employed to calculate the flux distribution and keff of the reactor is summarised. This is of particular interest when the flux vanishing boundary in x, y, z directions is not an integral multiple of the mesh spacings in these directions. The method assumes the flux to be negative, hypothetically at the mesh points lying outside the boundary and thus the finite difference formalism for Laplacian operator, taking into account six neighbours of a mesh point in a square mesh arrangement, is expressed in a general form so as to account for the boundary mesh points of the system. This approach has been incorporated in a three dimensional diffusion code similar to TAPPS23 and has been used for IRT-2000 reactor and the results are quite satisfactory. (author)
Directory of Open Access Journals (Sweden)
Mohammad Hadi Jalali
2018-01-01
Full Text Available Elastic stress analysis of rotating variable thickness annular disk made of functionally graded material (FGM is presented. Elasticity modulus, density, and thickness of the disk are assumed to vary radially according to a power-law function. Radial stress, circumferential stress, and radial deformation of the rotating FG annular disk of variable thickness with clamped-clamped (C-C, clamped-free (C-F, and free-free (F-F boundary conditions are obtained using the numerical finite difference method, and the effects of the graded index, thickness variation, and rotating speed on the stresses and deformation are evaluated. It is shown that using FG material could decrease the value of radial stress and increase the radial displacement in a rotating thin disk. It is also demonstrated that increasing the rotating speed can strongly increase the stress in the FG annular disk.
A Comparison of Angular Difference Schemes for One-Dimensional Spherical Geometry SN Equations
International Nuclear Information System (INIS)
Lathrop, K.D.
2000-01-01
To investigate errors caused by angular differencing in approximating the streaming terms of the transport equation, five different approximations are evaluated for three test problems in one-dimensional spherical geometry. The following schemes are compared: diamond, special truncation error minimizing weighted diamond, linear continuous (the original S N scheme), linear discontinuous, and new quadratic continuous. To isolate errors caused by angular differencing, the approximations are derived from the transport equation without spatial differencing, and the resulting coupled ordinary differential equations (ODEs) are solved with an ODE solver. Results from the approximations are compared with analytic solutions derived for two-region purely absorbing spheres. Most of the approximations are derived by taking moments of the conservation form of the transport equation. The quadratic continuous approximation is derived taking the zeroth moment of both the transport equation and the first angular derivative of the transport equation. The advantages of this approach are described. In all of the approximations, the desirability is shown of using an initializing computation of the μ = -1 angular flux to correctly compute the central flux and of having a difference approximation that ensures this central flux is the same for all directions. The behavior of the standard discrete ordinates equations in the diffusion limit is reviewed, and the linear and quadratic continuous approximations are shown to have the correct diffusion limit if an equal interval discrete quadrature is used.In all three test problems, the weighted diamond difference approximation has smaller maximum and average relative flux errors than the diamond or the linear continuous difference approximations. The quadratic continuous approximation and the linear discontinuous approximation are both more accurate than the other approximations, and the quadratic continuous approximation has a decided edge
A comparison of angular difference schemes for one-dimensional spherical geometry SN equations
International Nuclear Information System (INIS)
Lathrop, K.D.
2000-01-01
To investigate errors caused by angular differencing in approximating the streaming terms of the transport equation, five different approximations are evaluated for three test problems in one-dimensional spherical geometry. The following schemes are compared: diamond, special truncation error minimizing weighted diamond, linear continuous (the original S N scheme), linear discontinuous, and new quadratic continuous. To isolate errors caused by angular differencing, the approximations are derived from the transport equation without spatial differencing, and the resulting coupled ordinary differential equations (ODEs) are solved with an ODE solver. Results from the approximations are compared with analytic solutions derived for two-region purely absorbing spheres. Most of the approximations are derived by taking moments of the conservation form of the transport equation. The quadratic continuous approximation is derived taking the zeroth moment of both the transport equation and the first angular derivative of the transport equation. The advantages of this approach are described, In all of the approximations, the desirability is shown of using an initializing computation of the μ = -1 angular flux to correctly compute the central flux and of having a difference approximation that ensures this central flux is the same for all directions. The behavior of the standard discrete ordinates equations in the diffusion limit is reviewed, and the linear and quadratic continuous approximations are shown to have the correct diffusion limit if an equal interval discrete quadrature is used. In all three test problems, the weighted diamond difference approximation has smaller maximum and average relative flux errors than the diamond or the linear continuous difference approximations. The quadratic continuous approximation and the linear discontinuous approximation are both more accurate than the other approximations, and the quadratic continuous approximation has a decided edge
Fazi, Giovanni; Tellini, Simone; Vangi, Dario; Branchi, Roberto
2011-01-01
The distribution of stresses in bone, implants, and prosthesis were analyzed via three-dimensional finite element modeling in different implant configurations for a fixed implant-supported prosthesis in an edentulous mandible. A finite element model was created with data obtained from computed tomographic scans of a human mandible. Anisotropic characteristics for cortical and cancellous bone were incorporated into the model. Six different configurations of intraforaminal implants were tested, with the number of implants varying from three to five and the distal implants inserted either parallel to the other implants or tilted distally by 17 or 34 degrees. A prosthetic structure connecting the implants was designed, with 20-mm posterior cantilevers for the parallel implant configurations, and a load of 200 N was applied to the distal portion of the cantilevers. Stresses were measured at the level of the implant, the prosthetic structure, and the bone. Bone-level stresses were analyzed at the implant-bone interface, at the external cortical bone surface, distal to the terminal implant, and in the cancellous bone along the implant body. A three-parallel-implant configuration resulted in higher stress in the implant and bone than configurations with four or five parallel implants. Configurations with the distal implants tilted resulted in a more favorable stress distribution at all levels. In parallel-implant configurations for fixed implant-supported mandibular prostheses, four and five implants resulted in similar stress distribution in the bone, framework, and implants. A distribution of four implants with the distal implants tilted 34 degrees (ie, the "All-on-Four" configuration) resulted in a favorable reduction of stresses in the bone, framework, and implants.
Coco, Armando; Russo, Giovanni
2018-05-01
In this paper we propose a second-order accurate numerical method to solve elliptic problems with discontinuous coefficients (with general non-homogeneous jumps in the solution and its gradient) in 2D and 3D. The method consists of a finite-difference method on a Cartesian grid in which complex geometries (boundaries and interfaces) are embedded, and is second order accurate in the solution and the gradient itself. In order to avoid the drop in accuracy caused by the discontinuity of the coefficients across the interface, two numerical values are assigned on grid points that are close to the interface: a real value, that represents the numerical solution on that grid point, and a ghost value, that represents the numerical solution extrapolated from the other side of the interface, obtained by enforcing the assigned non-homogeneous jump conditions on the solution and its flux. The method is also extended to the case of matrix coefficient. The linear system arising from the discretization is solved by an efficient multigrid approach. Unlike the 1D case, grid points are not necessarily aligned with the normal derivative and therefore suitable stencils must be chosen to discretize interface conditions in order to achieve second order accuracy in the solution and its gradient. A proper treatment of the interface conditions will allow the multigrid to attain the optimal convergence factor, comparable with the one obtained by Local Fourier Analysis for rectangular domains. The method is robust enough to handle large jump in the coefficients: order of accuracy, monotonicity of the errors and good convergence factor are maintained by the scheme.
Luo, Y.; Xia, J.; Xu, Y.; Zeng, C.; Liu, J.
2010-01-01
Love-wave propagation has been a topic of interest to crustal, earthquake, and engineering seismologists for many years because it is independent of Poisson's ratio and more sensitive to shear (S)-wave velocity changes and layer thickness changes than are Rayleigh waves. It is well known that Love-wave generation requires the existence of a low S-wave velocity layer in a multilayered earth model. In order to study numerically the propagation of Love waves in a layered earth model and dispersion characteristics for near-surface applications, we simulate high-frequency (>5 Hz) Love waves by the staggered-grid finite-difference (FD) method. The air-earth boundary (the shear stress above the free surface) is treated using the stress-imaging technique. We use a two-layer model to demonstrate the accuracy of the staggered-grid modeling scheme. We also simulate four-layer models including a low-velocity layer (LVL) or a high-velocity layer (HVL) to analyze dispersive energy characteristics for near-surface applications. Results demonstrate that: (1) the staggered-grid FD code and stress-imaging technique are suitable for treating the free-surface boundary conditions for Love-wave modeling, (2) Love-wave inversion should be treated with extra care when a LVL exists because of a lack of LVL information in dispersions aggravating uncertainties in the inversion procedure, and (3) energy of high modes in a low-frequency range is very weak, so that it is difficult to estimate the cutoff frequency accurately, and "mode-crossing" occurs between the second higher and third higher modes when a HVL exists. ?? 2010 Birkh??user / Springer Basel AG.
DETERMINATION OF MOISTURE DIFFUSION COEFFICIENT OF LARCH BOARD WITH FINITE DIFFERENCE METHOD
Directory of Open Access Journals (Sweden)
Qiaofang Zhou
2011-04-01
Full Text Available This paper deals with the moisture diffusion coefficient of Dahurian Larch (Larix gmelinii Rupr. by use of the Finite Difference Method (FDM. To obtain moisture distributions the dimensional boards of Dahurian Larch were dried, from which test samples were cut and sliced evenly into 9 pieces in different drying periods, so that moisture distributions at different locations and times across the thickness of Dahurian Larch were obtained with a weighing method. With these experimental data, FDM was used to solve Fick’s one-dimensional unsteady-state diffusion equation, and the moisture diffusion coefficient across the thickness at specified time was obtained. Results indicated that the moisture diffusion coefficient decreased from the surface to the center of the Dahurian Larch wood, and it decreased with decreasing moisture content at constant wood temperature; as the wood temperature increased, the moisture diffusion coefficient increased, and the effect of the wood temperature on the moisture diffusion coefficient was more significant than that of moisture content. Moisture diffusion coefficients were different for the two experiments due to differing diffusivity of the specimens.
A finite difference method for off-fault plasticity throughout the earthquake cycle
Erickson, Brittany A.; Dunham, Eric M.; Khosravifar, Arash
2017-12-01
We have developed an efficient computational framework for simulating multiple earthquake cycles with off-fault plasticity. The method is developed for the classical antiplane problem of a vertical strike-slip fault governed by rate-and-state friction, with inertial effects captured through the radiation-damping approximation. Both rate-independent plasticity and viscoplasticity are considered, where stresses are constrained by a Drucker-Prager yield condition. The off-fault volume is discretized using finite differences and tectonic loading is imposed by displacing the remote side boundaries at a constant rate. Time-stepping combines an adaptive Runge-Kutta method with an incremental solution process which makes use of an elastoplastic tangent stiffness tensor and the return-mapping algorithm. Solutions are verified by convergence tests and comparison to a finite element solution. We quantify how viscosity, isotropic hardening, and cohesion affect the magnitude and off-fault extent of plastic strain that develops over many ruptures. If hardening is included, plastic strain saturates after the first event and the response during subsequent ruptures is effectively elastic. For viscoplasticity without hardening, however, successive ruptures continue to generate additional plastic strain. In all cases, coseismic slip in the shallow sub-surface is diminished compared to slip accumulated at depth during interseismic loading. The evolution of this slip deficit with each subsequent event, however, is dictated by the plasticity model. Integration of the off-fault plastic strain from the viscoplastic model reveals that a significant amount of tectonic offset is accommodated by inelastic deformation ( ∼ 0.1 m per rupture, or ∼ 10% of the tectonic deformation budget).
DQE of wireless digital detectors: Comparative performance with differing filtration schemes
International Nuclear Information System (INIS)
Samei, Ehsan; Murphy, Simon; Christianson, Olav
2013-01-01
Purpose: Wireless flat panel detectors are gaining increased usage in portable medical imaging. Two such detectors were evaluated and compared with a conventional flat-panel detector using the formalism of the International Electrotechnical Commission (IEC 62220-1) for measuring modulation transfer function (MTF), normalized noise power spectrum (NNPS), and detective quantum efficiency (DQE) using two different filtration schemes.Methods: Raw images were acquired for three image receptors (DRX-1C and DRX-1, Carestream Health; Inc., Pixium 4600, Trixell) using a radiographic system with a well-characterized output (Philips Super80 CP, Philips Healthcare). Free in-air exposures were measured using a calibrated radiation meter (Unfors Mult-O-Meter Type 407, Unfors Instruments AB). Additional aluminum filtration and a new alternative combined copper-aluminum filtration were used to conform the x ray output to IEC-specified beam quality definitions RQA5 and RQA9. Using the IEC 62220-1 formalism, each detector was evaluated at X N /2, X N , and 2X N , where the normal exposure level to the detector surface (X N ) was set to 8.73 μGy (1.0 mR). The prescribed edge test device was used to evaluate the MTF, while the NNPS was measured using uniform images. The DQE was then calculated from the MTF and NNPS and compared across detectors, exposures, and filtration schemes.Results: The three DR systems had largely comparable MTFs with DRX-1 demonstrating lower values above 1.0 cycles/mm. At each exposure, DRX-1C and Pixium detectors demonstrated better noise performance than that of DRX-1. Zero-frequency DQEs for DRX-1C, Pixium, and DRX-1 detectors were approximately 74%, 63%, and 38% for RQA5 and 50%, 42%, and 28% for RQA9, respectively.Conclusions: DRX-1C detector exhibited superior DQE performance compared to Pixium and DRX-1. In terms of filtration, the alternative filtration was found to provide comparable performance in terms of rank ordering of different detectors with
DQE of wireless digital detectors: Comparative performance with differing filtration schemes
Energy Technology Data Exchange (ETDEWEB)
Samei, Ehsan [Carl E. Ravin Advanced Imaging Laboratories, Departments of Radiology, Biomedical Engineering, Physics, and Electrical and Computer Engineering, Medical Physics Graduate Program, Duke University Medical Center, Durham, North Carolina 27705 (United States); Murphy, Simon; Christianson, Olav [Medical Physics Graduate Program, Duke University, Durham, North Carolina 27705 (United States)
2013-08-15
Purpose: Wireless flat panel detectors are gaining increased usage in portable medical imaging. Two such detectors were evaluated and compared with a conventional flat-panel detector using the formalism of the International Electrotechnical Commission (IEC 62220-1) for measuring modulation transfer function (MTF), normalized noise power spectrum (NNPS), and detective quantum efficiency (DQE) using two different filtration schemes.Methods: Raw images were acquired for three image receptors (DRX-1C and DRX-1, Carestream Health; Inc., Pixium 4600, Trixell) using a radiographic system with a well-characterized output (Philips Super80 CP, Philips Healthcare). Free in-air exposures were measured using a calibrated radiation meter (Unfors Mult-O-Meter Type 407, Unfors Instruments AB). Additional aluminum filtration and a new alternative combined copper-aluminum filtration were used to conform the x ray output to IEC-specified beam quality definitions RQA5 and RQA9. Using the IEC 62220-1 formalism, each detector was evaluated at X{sub N}/2, X{sub N}, and 2X{sub N}, where the normal exposure level to the detector surface (X{sub N}) was set to 8.73 μGy (1.0 mR). The prescribed edge test device was used to evaluate the MTF, while the NNPS was measured using uniform images. The DQE was then calculated from the MTF and NNPS and compared across detectors, exposures, and filtration schemes.Results: The three DR systems had largely comparable MTFs with DRX-1 demonstrating lower values above 1.0 cycles/mm. At each exposure, DRX-1C and Pixium detectors demonstrated better noise performance than that of DRX-1. Zero-frequency DQEs for DRX-1C, Pixium, and DRX-1 detectors were approximately 74%, 63%, and 38% for RQA5 and 50%, 42%, and 28% for RQA9, respectively.Conclusions: DRX-1C detector exhibited superior DQE performance compared to Pixium and DRX-1. In terms of filtration, the alternative filtration was found to provide comparable performance in terms of rank ordering of different
A Coupled Finite Difference and Moving Least Squares Simulation of Violent Breaking Wave Impact
DEFF Research Database (Denmark)
Lindberg, Ole; Bingham, Harry B.; Engsig-Karup, Allan Peter
2012-01-01
feature of this model is a generalized finite point set method which is applied to the solution of the Poisson equation on an unstructured point distribution. The presented finite point set method is generalized to arbitrary order of approximation. The two models are applied to simulation of steep...
On the accuracy and efficiency of finite difference solutions for nonlinear waves
DEFF Research Database (Denmark)
Bingham, Harry B.
2006-01-01
-uniform grid. Time-integration is performed using a fourth-order Runge-Kutta scheme. The linear accuracy, stability and convergence properties of the method are analyzed in two-dimensions, and high-order schemes with a stretched vertical grid are found to be advantageous relative to second-order schemes...... on an even grid. Comparison with highly accurate periodic solutions shows that these conclusions carry over to nonlinear problems. The combination of non-uniform grid spacing in the vertical and fourth-order schemes is suggested as providing an optimal balance between accuracy and complexity for practical...
Acceleration of Linear Finite-Difference Poisson-Boltzmann Methods on Graphics Processing Units.
Qi, Ruxi; Botello-Smith, Wesley M; Luo, Ray
2017-07-11
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.
Directory of Open Access Journals (Sweden)
Tsugio Fukuchi
2014-06-01
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.
Comparison of SAR calculation algorithms for the finite-difference time-domain method
International Nuclear Information System (INIS)
Laakso, Ilkka; Uusitupa, Tero; Ilvonen, Sami
2010-01-01
Finite-difference time-domain (FDTD) simulations of specific-absorption rate (SAR) have several uncertainty factors. For example, significantly varying SAR values may result from the use of different algorithms for determining the SAR from the FDTD electric field. The objective of this paper is to rigorously study the divergence of SAR values due to different SAR calculation algorithms and to examine if some SAR calculation algorithm should be preferred over others. For this purpose, numerical FDTD results are compared to analytical solutions in a one-dimensional layered model and a three-dimensional spherical object. Additionally, the implications of SAR calculation algorithms for dosimetry of anatomically realistic whole-body models are studied. The results show that the trapezium algorithm-based on the trapezium integration rule-is always conservative compared to the analytic solution, making it a good choice for worst-case exposure assessment. In contrast, the mid-ordinate algorithm-named after the mid-ordinate integration rule-usually underestimates the analytic SAR. The linear algorithm-which is approximately a weighted average of the two-seems to be the most accurate choice overall, typically giving the best fit with the shape of the analytic SAR distribution. For anatomically realistic models, the whole-body SAR difference between different algorithms is relatively independent of the used body model, incident direction and polarization of the plane wave. The main factors affecting the difference are cell size and frequency. The choice of the SAR calculation algorithm is an important simulation parameter in high-frequency FDTD SAR calculations, and it should be explained to allow intercomparison of the results between different studies. (note)
Velivelli, A. C.; Bryden, K. M.
2006-03-01
Lattice Boltzmann methods are gaining recognition in the field of computational fluid dynamics due to their computational efficiency. In order to quantify the computational efficiency and accuracy of the lattice Boltzmann method, it is compared with efficient traditional finite difference methods such as the alternating direction implicit scheme. The lattice Boltzmann algorithm implemented in previous studies does not approach peak performance for simulations where the data involved in computation per time step is more than the cache size. Due to this, data is obtained from the main memory and this access is much slower than access to cache memory. Using a cache-optimized lattice Boltzmann algorithm, this paper takes into account the full computational strength of the lattice Boltzmann method. The com parison is performed on both a single processor and multiple processors.
The discount framing in different pricing schemes: Combined versus partitioned pricing
Matthew Lee; Dr. Frankie Law
2015-01-01
Pricing is one of the most sophisticated and critical issues which managers have to face. It is obvious that managers have been undervaluing the behavioural and psychological perspective of pricing for many years. With a clear understanding of behavioural pricing, managers are able to make extra profit for their firms. In the current study, it was interesting to investigating exactly how manipulation of discounts in the combined pricing scheme and partitioned pricing scheme affects the purcha...
Analysis of sensitivity to different parameterization schemes for a subtropical cyclone
Quitián-Hernández, L.; Fernández-González, S.; González-Alemán, J. J.; Valero, F.; Martín, M. L.
2018-05-01
A sensitivity analysis to diverse WRF model physical parameterization schemes is carried out during the lifecycle of a Subtropical cyclone (STC). STCs are low-pressure systems that share tropical and extratropical characteristics, with hybrid thermal structures. In October 2014, a STC made landfall in the Canary Islands, causing widespread damage from strong winds and precipitation there. The system began to develop on October 18 and its effects lasted until October 21. Accurate simulation of this type of cyclone continues to be a major challenge because of its rapid intensification and unique characteristics. In the present study, several numerical simulations were performed using the WRF model to do a sensitivity analysis of its various parameterization schemes for the development and intensification of the STC. The combination of parameterization schemes that best simulated this type of phenomenon was thereby determined. In particular, the parameterization combinations that included the Tiedtke cumulus schemes had the most positive effects on model results. Moreover, concerning STC track validation, optimal results were attained when the STC was fully formed and all convective processes stabilized. Furthermore, to obtain the parameterization schemes that optimally categorize STC structure, a verification using Cyclone Phase Space is assessed. Consequently, the combination of parameterizations including the Tiedtke cumulus schemes were again the best in categorizing the cyclone's subtropical structure. For strength validation, related atmospheric variables such as wind speed and precipitable water were analyzed. Finally, the effects of using a deterministic or probabilistic approach in simulating intense convective phenomena were evaluated.
Rößler, Thomas; Stein, Olaf; Heng, Yi; Baumeister, Paul; Hoffmann, Lars
2018-02-01
The accuracy of trajectory calculations performed by Lagrangian particle dispersion models (LPDMs) depends on various factors. The optimization of numerical integration schemes used to solve the trajectory equation helps to maximize the computational efficiency of large-scale LPDM simulations. We analyzed global truncation errors of six explicit integration schemes of the Runge-Kutta family, which we implemented in the Massive-Parallel Trajectory Calculations (MPTRAC) advection module. The simulations were driven by wind fields from operational analysis and forecasts of the European Centre for Medium-Range Weather Forecasts (ECMWF) at T1279L137 spatial resolution and 3 h temporal sampling. We defined separate test cases for 15 distinct regions of the atmosphere, covering the polar regions, the midlatitudes, and the tropics in the free troposphere, in the upper troposphere and lower stratosphere (UT/LS) region, and in the middle stratosphere. In total, more than 5000 different transport simulations were performed, covering the months of January, April, July, and October for the years 2014 and 2015. We quantified the accuracy of the trajectories by calculating transport deviations with respect to reference simulations using a fourth-order Runge-Kutta integration scheme with a sufficiently fine time step. Transport deviations were assessed with respect to error limits based on turbulent diffusion. Independent of the numerical scheme, the global truncation errors vary significantly between the different regions. Horizontal transport deviations in the stratosphere are typically an order of magnitude smaller compared with the free troposphere. We found that the truncation errors of the six numerical schemes fall into three distinct groups, which mostly depend on the numerical order of the scheme. Schemes of the same order differ little in accuracy, but some methods need less computational time, which gives them an advantage in efficiency. The selection of the integration
Xu, Zhenli; Ma, Manman; Liu, Pei
2014-07-01
We propose a modified Poisson-Nernst-Planck (PNP) model to investigate charge transport in electrolytes of inhomogeneous dielectric environment. The model includes the ionic polarization due to the dielectric inhomogeneity and the ion-ion correlation. This is achieved by the self energy of test ions through solving a generalized Debye-Hückel (DH) equation. We develop numerical methods for the system composed of the PNP and DH equations. Particularly, toward the numerical challenge of solving the high-dimensional DH equation, we developed an analytical WKB approximation and a numerical approach based on the selective inversion of sparse matrices. The model and numerical methods are validated by simulating the charge diffusion in electrolytes between two electrodes, for which effects of dielectrics and correlation are investigated by comparing the results with the prediction by the classical PNP theory. We find that, at the length scale of the interface separation comparable to the Bjerrum length, the results of the modified equations are significantly different from the classical PNP predictions mostly due to the dielectric effect. It is also shown that when the ion self energy is in weak or mediate strength, the WKB approximation presents a high accuracy, compared to precise finite-difference results.
International Nuclear Information System (INIS)
Thompson, S.L.; Herrmann, W.
1977-01-01
Calculations, using the two-dimensional Eulerian finite-difference code CSQ, were performed for the problem of a small spherical high-explosive charge detonated in a closed heavy-walled cylindrical container partially filled with water. Data from corresponding experiments, specifically performed to validate codes used for hypothetical core disruptive accidents of liquid metal fast breeder reactors, are available in the literature. The calculations were performed specifically to test whether Eulerian methods could handle this type of problem, to determine whether water cavitation, which plays a large role in the loadings on the roof of the containment vessel, could be described adequately by an equilibrium liquid-vapor mixed phase model, and to investigate the trade-off between accuracy and cost of the calculations by using different sizes of computational meshes. Comparison of the experimental and computational data shows that the Eulerian method can handle the problem with ease, giving good predictions of wall and floor loadings. While roof loadings are qualitatively correct, peak impulse appears to be affected by numerical resolution and is underestimated somewhat
Finite-difference time-domain simulation of electromagnetic bandgap and bi-anisotropic metamaterials
Bray, Matthew G.
The term "Metamaterial" has been introduced into the electromagnetic lexicon in recent years to describe new artificial materials with electromagnetic properties that are not found in naturally occurring materials. Metamaterials exhibit electromagnetic properties that are not observed in its constituent materials, and/or not observed in nature. This thesis will analyze two different classes of metamaterials through the use of the finite-difference time-domain (FDTD) technique. The first class of metamaterials are artificial magnetic conductors (AMC) which approximate the behavior of a perfect magnetic conductor (PMC) over a finite frequency range. The AMC metamaterials are created through the use of an electromagnetic bandgap (EBG) structure. A periodic FDTD code is used to simulate a full-wave model of the metallodielectric EBG structures. The AMCs developed with the aid of the FDTD tool are then used to create low-profile antenna systems consisting of a dipole antenna in close proximity to an AMC surface. Through the use of this FDTD tool, several original contributions were made to the electromagnetic community. These include the first dual-band independently tunable EBG AMC ground plane and the first linearly polarized single-band and dual-band tunable antenna/EBG systems. The second class of materials analyzed are bi-anisotropic metamaterials. Bi-anisotropic media are the largest class of linear media which is able to describe the macroscopic material properties of artificial dielectrics, artificial magnetics, artificial chiral materials, left-handed materials, and other composite materials. The dispersive properties of these materials can be approximated by the oscillator model. This model assumes a Lorentzian frequency profile for the permittivity and permeability and a Condon model for chirality. A new FDTD formulation is introduced which can simulate this type of bi-anisotropic media. This FDTD method incorporates the dispersive material properties through
International Nuclear Information System (INIS)
Schickert, Martin
2015-01-01
Ultrasonic testing systems using transducer arrays and the SAFT (Synthetic Aperture Focusing Technique) reconstruction allow for imaging the internal structure of concrete elements. At one-sided access, three-dimensional representations of the concrete volume can be reconstructed in relatively great detail, permitting to detect and localize objects such as construction elements, built-in components, and flaws. Different SAFT data acquisition and processing schemes can be utilized which differ in terms of the measuring and computational effort and the reconstruction result. In this contribution, two methods are compared with respect to their principle of operation and their imaging characteristics. The first method is the conventional single-channel SAFT algorithm which is implemented using a virtual transducer that is moved within a transducer array by electronic switching. The second method is the Combinational SAFT algorithm (C-SAFT), also named Sampling Phased Array (SPA) or Full Matrix Capture/Total Focusing Method (TFM/FMC), which is realized using a combination of virtual transducers within a transducer array. Five variants of these two methods are compared by means of measurements obtained at test specimens containing objects typical of concrete elements. The automated SAFT imaging system FLEXUS is used for the measurements which includes a three-axis scanner with a 1.0 m × 0.8 m scan range and an electronically switched ultrasonic array consisting of 48 transducers in 16 groups. On the basis of two-dimensional and three-dimensional reconstructed images, qualitative and some quantitative results of the parameters image resolution, signal-to-noise ratio, measurement time, and computational effort are discussed in view of application characteristics of the SAFT variants
DEFF Research Database (Denmark)
Amini Afshar, Mostafa; Bingham, Harry B.
2017-01-01
. Frequency-domain results are then obtained from a Fourier transform of the force and motion signals. In order to make a robust Fourier transform, and capture the response around the critical frequency, the tail of the force signal is asymptotically extrapolated assuming a linear decay rate. Fourth......The linearized potential flow approximation for the forward speed radiation problem is solved in the time domain using a high-order finite difference method. The finite-difference discretization is developed on overlapping, curvilinear body-fitted grids. To ensure numerical stability...
Directory of Open Access Journals (Sweden)
Mohammed Hussein
2007-01-01
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.
Directory of Open Access Journals (Sweden)
Yanxue Yu
2017-01-01
Full Text Available As a basic building block in power systems, the three-phase voltage-source inverter (VSI connects the distributed energy to the grid. For the inductor-capacitor-inductor (LCL-filter three-phase VSI, according to different current sampling position and different reference frame, there mainly exist four control schemes. Different control schemes present different impedance characteristics in their corresponding determined frequency range. To analyze the existing resonance phenomena due to the variation of grid impedances, the sequence impedance models of LCL-type grid-connected three-phase inverters under different control schemes are presented using the harmonic linearization method. The impedance-based stability analysis approach is then applied to compare the relative stability issues due to the impedance differences at some frequencies and to choose the best control scheme and the better controller parameters regulating method for the LCL-type three-phase VSI. The simulation and experiments both validate the resonance analysis results.
Modelling optimization involving different types of elements in finite element analysis
International Nuclear Information System (INIS)
Wai, C M; Rivai, Ahmad; Bapokutty, Omar
2013-01-01
Finite elements are used to express the mechanical behaviour of a structure in finite element analysis. Therefore, the selection of the elements determines the quality of the analysis. The aim of this paper is to compare and contrast 1D element, 2D element, and 3D element used in finite element analysis. A simple case study was carried out on a standard W460x74 I-beam. The I-beam was modelled and analyzed statically with 1D elements, 2D elements and 3D elements. The results for the three separate finite element models were compared in terms of stresses, deformation and displacement of the I-beam. All three finite element models yield satisfactory results with acceptable errors. The advantages and limitations of these elements are discussed. 1D elements offer simplicity although lacking in their ability to model complicated geometry. 2D elements and 3D elements provide more detail yet sophisticated results which require more time and computer memory in the modelling process. It is also found that the choice of element in finite element analysis is influence by a few factors such as the geometry of the structure, desired analysis results, and the capability of the computer
International Nuclear Information System (INIS)
Tokuda, Shinji; Watanabe, Tomoko.
1996-08-01
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)
Calculation of electrical potentials on the surface of a realistic head model by finite differences
International Nuclear Information System (INIS)
Lemieux, L.; McBride, A.; Hand, J.W.
1996-01-01
We present a method for the calculation of electrical potentials at the surface of realistic head models from a point dipole generator based on a 3D finite-difference algorithm. The model was validated by comparing calculated values with those obtained algebraically for a three-shell spherical model. For a 1.25 mm cubic grid size, the mean error was 4.9% for a superficial dipole (3.75 mm from the inner surface of the skull) pointing in the radial direction. The effect of generator discretization and node spacing on the accuracy of the model was studied. Three values of the node spacing were considered: 1, 1.25 and 1.5 mm. The mean relative errors were 4.2, 6.3 and 9.3%, respectively. The quality of the approximation of a point dipole by an array of nodes in a spherical neighbourhood did not depend significantly on the number of nodes used. The application of the method to a conduction model derived from MRI data is demonstrated. (author)
Ping, Jing
2017-05-19
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.
Barão, Valentim Adelino Ricardo; Assunção, Wirley Gonçalves; Tabata, Lucas Fernando; Delben, Juliana Aparecida; Gomes, Erica Alves; de Sousa, Edson Antonio Capello; Rocha, Eduardo Passos
2009-07-01
This finite element analysis compared stress distribution on complete dentures and implant-retained overdentures with different attachment systems. Four models of edentulous mandible were constructed: group A (control), complete denture; group B, overdenture retained by 2 splinted implants with bar-clip system; group C, overdenture retained by 2 unsplinted implants with o'ring system; and group D, overdenture retained by 2 splinted implants with bar-clip and 2 distally placed o'ring system. Evaluation was performed on Ansys software, with 100-N vertical load applied on central incisive teeth. The lowest maximum general stress value (in megapascal) was observed in group A (64.305) followed by groups C (119.006), D (258.650), and B (349.873). The same trend occurred in supporting tissues with the highest stress value for cortical bone. Unsplinted implants associated with the o'ring attachment system showed the lowest maximum stress values among all overdenture groups. Furthermore, o'ring system also improved stress distribution when associated with bar-clip system.
Accelerated cardiac cine MRI using locally low rank and finite difference constraints.
Miao, Xin; Lingala, Sajan Goud; Guo, Yi; Jao, Terrence; Usman, Muhammad; Prieto, Claudia; Nayak, Krishna S
2016-07-01
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.
Finite difference solution of the time dependent neutron group diffusion equations
International Nuclear Information System (INIS)
Hendricks, J.S.; Henry, A.F.
1975-08-01
In this thesis two unrelated topics of reactor physics are examined: the prompt jump approximation and alternating direction checkerboard methods. In the prompt jump approximation it is assumed that the prompt and delayed neutrons in a nuclear reactor may be described mathematically as being instantaneously in equilibrium with each other. This approximation is applied to the spatially dependent neutron diffusion theory reactor kinetics model. Alternating direction checkerboard methods are a family of finite difference alternating direction methods which may be used to solve the multigroup, multidimension, time-dependent neutron diffusion equations. The reactor mesh grid is not swept line by line or point by point as in implicit or explicit alternating direction methods; instead, the reactor mesh grid may be thought of as a checkerboard in which all the ''red squares'' and '' black squares'' are treated successively. Two members of this family of methods, the ADC and NSADC methods, are at least as good as other alternating direction methods. It has been found that the accuracy of implicit and explicit alternating direction methods can be greatly improved by the application of an exponential transformation. This transformation is incompatible with checkerboard methods. Therefore, a new formulation of the exponential transformation has been developed which is compatible with checkerboard methods and at least as good as the former transformation for other alternating direction methods
Methods for compressible fluid simulation on GPUs using high-order finite differences
Pekkilä, Johannes; Väisälä, Miikka S.; Käpylä, Maarit J.; Käpylä, Petri J.; Anjum, Omer
2017-08-01
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.
International Nuclear Information System (INIS)
Filio Lopez, Carlos.
1979-01-01
A calculation program (URA 6.F4) was elaborated on FORTRAN IV language, that through finite differences solves the unidimensional scalar Helmholtz equation, assuming only one energy group, in spherical cylindrical or plane geometry. The purpose is the determination of the flow distribution in a reactor of spherical cylindrical or plane geometry and the critical dimensions. Feeding as entrance datas to the program the geometry, diffusion coefficients and macroscopic transversals cross sections of absorption and fission for each region. The differential diffusion equation is converted with its boundary conditions, to one system of homogeneous algebraic linear equations using the box integration technique. The investigation on criticality is converted then in a succession of eigenvalue problems for the critical eigenvalue. In general, only is necessary to solve the first eigenvalue and its corresponding eigenvector, employing the power method. The obtained results by the program for the critical dimensions of the clean reactors are admissible, the existing error as respect to the analytic is less of 0.5%; by the analysed reactors of three regions, the relative error with respect to the semianalytic result is less of 0.2%. With this program is possible to obtain one quantitative description of one reactor if the transversal sections that appears in the monoenergetic model are adequatedly averaged by the energy group used. (author)
Chiranjeevi, C.; Srinivas, T.
2017-11-01
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.
Zhou, Min; Tan, Shukui; Zhang, Lu
2015-01-01
Land use planning is always officially implemented as an effective tool to control urban development and protect farmland. However, its impact on land use change remains untested in China. Using a case study of Hang-Jia-Hu region, the main objective of this paper was to investigate the influence of different land use spatial control schemes on farmland conversion and urban development. Comparisons of farmland conversion and urban development patterns between the urban planning area and the non-urban planning area were characterized by using remote sensing, geographical information systems, and landscape metrics. Results indicated that farmland conversion in the non-urban planning area was more intensive than that in the urban planning area, and that farmland patterns was more fragmented in the non-urban planning area. Built-up land patterns in the non-urban planning area showed a trend of aggregation, while those in the urban planning area had a dual trend of fragmentation and aggregation. Existing built-up areas had less influence on built-up land sprawl in the non-urban planning area than that in the urban planning area. Built-up land sprawl in the form of continuous development in the urban planning area led to farmland conversion; and in the non-urban planning area, built-up land sprawl in the form of leapfrogging development resulted in farmland areal declines and fragmentation. We argued that it is a basic requirement to integrate land use plans in urban and non-urban planning areas for land use planning and management. PMID:25915897
Zhou, Min; Tan, Shukui; Zhang, Lu
2015-01-01
Land use planning is always officially implemented as an effective tool to control urban development and protect farmland. However, its impact on land use change remains untested in China. Using a case study of Hang-Jia-Hu region, the main objective of this paper was to investigate the influence of different land use spatial control schemes on farmland conversion and urban development. Comparisons of farmland conversion and urban development patterns between the urban planning area and the non-urban planning area were characterized by using remote sensing, geographical information systems, and landscape metrics. Results indicated that farmland conversion in the non-urban planning area was more intensive than that in the urban planning area, and that farmland patterns was more fragmented in the non-urban planning area. Built-up land patterns in the non-urban planning area showed a trend of aggregation, while those in the urban planning area had a dual trend of fragmentation and aggregation. Existing built-up areas had less influence on built-up land sprawl in the non-urban planning area than that in the urban planning area. Built-up land sprawl in the form of continuous development in the urban planning area led to farmland conversion; and in the non-urban planning area, built-up land sprawl in the form of leapfrogging development resulted in farmland areal declines and fragmentation. We argued that it is a basic requirement to integrate land use plans in urban and non-urban planning areas for land use planning and management.
Finite difference modelling of the temperature rise in non-linear medical ultrasound fields.
Divall, S A; Humphrey, V F
2000-03-01
Non-linear propagation of ultrasound can lead to increased heat generation in medical diagnostic imaging due to the preferential absorption of harmonics of the original frequency. A numerical model has been developed and tested that is capable of predicting the temperature rise due to a high amplitude ultrasound field. The acoustic field is modelled using a numerical solution to the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, known as the Bergen Code, which is implemented in cylindrical symmetric form. A finite difference representation of the thermal equations is used to calculate the resulting temperature rises. The model allows for the inclusion of a number of layers of tissue with different acoustic and thermal properties and accounts for the effects of non-linear propagation, direct heating by the transducer, thermal diffusion and perfusion in different tissues. The effect of temperature-dependent skin perfusion and variation in background temperature between the skin and deeper layers of the body are included. The model has been tested against analytic solutions for simple configurations and then used to estimate temperature rises in realistic obstetric situations. A pulsed 3 MHz transducer operating with an average acoustic power of 200 mW leads to a maximum steady state temperature rise inside the foetus of 1.25 degrees C compared with a 0.6 degree C rise for the same transmitted power under linear propagation conditions. The largest temperature rise occurs at the skin surface, with the temperature rise at the foetus limited to less than 2 degrees C for the range of conditions considered.
Ishak, Muhammad Ikman; Shafi, Aisyah Ahmad; Rosli, M. U.; Khor, C. Y.; Zakaria, M. S.; Rahim, Wan Mohd Faizal Wan Abd; Jamalludin, Mohd Riduan
2017-09-01
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.
Use of the finite-difference time-domain method in electromagnetic dosimetry
International Nuclear Information System (INIS)
Sullivan, D.M.
1987-01-01
Although there are acceptable methods for calculating whole body electromagnetic absorption, no completely acceptable method for calculating the local specific absorption rate (SAR) at points within the body has been developed. Frequency domain methods, such as the method of moments (MoM) have achieved some success; however, the MoM requires computer storage on the order of (3N) 2 , and computation time on the order of (3N) 3 where N is the number of cells. The finite-difference time-domain (FDTD) method has been employed extensively in calculating the scattering from metallic objects, and recently is seeing some use in calculating the interaction of EM fields with complex, lossy dielectric bodies. Since the FDTD method has storage and time requirements proportional to N, it presents an attractive alternative to calculating SAR distribution in large bodies. This dissertation describes the FDTD method and evaluates it by comparing its results with analytic solutions in 2 and 3 dimensions. The results obtained demonstrate that the FDTD method is capable of calculating internal SAR distribution with acceptable accuracy. The construction of a data base to provide detailed, inhomogeneous man models for use with the FDTD method is described. Using this construction method, a model of 40,000 1.31 cm. cells is developed for use at 350 MHz, and another model consisting of 5000 2.62 cm. cells is developed for use at 100 MHz. To add more realism to the problem, a ground plane is added to the FDTD software. The needed changes to the software are described, along with a test which confirms its accuracy. Using the CRAY II supercomputer, SAR distributions in human models are calculated using incident frequencies of 100 MHz and 350 MHz for three different cases: (1) A homogeneous man model in free space, (2) an inhomogeneous man model in free space, and (3) an inhomogeneous man model standing on a ground plane
Tang, Hui-Yi; Wang, Jian-Hui; Ma, Yong-Li
2014-06-01
For a small system at a low temperature, thermal fluctuation and quantum effect play important roles in quantum thermodynamics. Starting from micro-canonical ensemble, we generalize the Boltzmann-Gibbs statistical factor from infinite to finite systems, no matter the interactions between particles are considered or not. This generalized factor, similar to Tsallis's q-form as a power-law distribution, has the restriction of finite energy spectrum and includes the nonextensivities of the small systems. We derive the exact expression for distribution of average particle numbers in the interacting classical and quantum nonextensive systems within a generalized canonical ensemble. This expression in the almost independent or elementary excitation quantum finite systems is similar to the corresponding ones obtained from the conventional grand-canonical ensemble. In the reconstruction for the statistical theory of the small systems, we present the entropy of the equilibrium systems and equation of total thermal energy. When we investigate the thermodynamics for the interacting nonextensive systems, we obtain the system-bath heat exchange and "uncompensated heat" which are in the thermodynamical level and independent on the detail of the system-bath coupling. For ideal finite systems, with different traps and boundary conditions, we calculate some thermodynamic quantities, such as the specific heat, entropy, and equation of state, etc. Particularly at low temperatures for the small systems, we predict some novel behaviors in the quantum thermodynamics, including internal entropy production, heat exchanges between the system and its surroundings and finite-size effects on the free energy.
Zhao, Yan; Belov, Pavel A.; Hao, Yang
2006-06-01
In this paper, a spatially dispersive finite-difference time-domain (FDTD) method to model wire media is developed and validated. Sub-wavelength imaging properties of the finite wire medium slabs are examined. It is demonstrated that the slab with its thickness equal to an integer number of half-wavelengths is capable of transporting images with sub-wavelength resolution from one interface of the slab to another. It is also shown that the operation of such transmission devices is not sensitive to their transverse dimensions, which can be made even comparable to the wavelength. In this case, the edge diffractions are negligible and do not disturb the image formation.
Anwar, Adeel; Lv, Decheng; Zhao, Zhi; Zhang, Zhen; Lu, Ming; Nazir, Muhammad Umar; Qasim, Wasim
2017-04-01
Appropriate fixation method for the posterior malleolar fractures (PMF) according to the fracture size is still not clear. Aim of this study was to evaluate the outcomes of the different fixation methods used for fixation of PMF by finite element analysis (FEA) and to compare the effect of fixation constructs on the size of the fracture computationally. Three dimensional model of the tibia was reconstructed from computed tomography (CT) images. PMF of 30%, 40% and 50% fragment sizes were simulated through computational processing. Two antero-posterior (AP) lag screws, two postero-anterior (PA) lag screws and posterior buttress plate were analysed for three different fracture volumes. The simulated loads of 350N and 700N were applied to the proximal tibial end. Models were fixed distally in all degrees of freedom. In single limb standing condition, the posterior plate group produced the lowest relative displacement (RD) among all the groups (0.01, 0.03 and 0.06mm). Further nodal analysis of the highest RD fracture group showed a higher mean displacement of 4.77mm and 4.23mm in AP and PA lag screws model (p=0.000). The amounts of stress subjected to these implants, 134.36MPa and 140.75MPa were also significantly lower (p=0.000). There was a negative correlation (p=0.021) between implant stress and the displacement which signifies a less stable fixation using AP and PA lag screws. Progressively increasing fracture size demands more stable fixation construct because RD increases significantly. Posterior buttress plate produces superior stability and lowest RD in PMF models irrespective of the fragment size. Copyright © 2017 Elsevier Ltd. All rights reserved.
DEFF Research Database (Denmark)
Kiel, Nikolaj; Andersen, Lars Vabbersgaard; Niu, Bin
2012-01-01
. With the number of modules in the three axial directions defined, wall and floor panels are constructed, placed and coupled in the global model. The core of this modular finite element model consists of connecting the different panels to each other in a rational manner, where the accuracy is as high as possible......, 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....... In this way a well-defined master geometry is present onto which all panels can be tied. But as the skeleton is an element itself, it will have a physical mass and a corresponding stiffness to be included in the linear system of equations. This means that the skeleton will influence the structure...
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
2016-01-01
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...
Kiessling, Jonas; Tempone, Raul
2014-01-01
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
Emoto, K.; Saito, T.; Shiomi, K.
2017-12-01
Short-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 leads the way to characterizing a wider wavenumber range of spectra, including the corner wavenumber.
Three-dimensional body-wave model of Nepal using finite difference tomography
Ho, T. M.; Priestley, K.; Roecker, S. W.
2017-12-01
The processes occurring during continent-continent collision are still poorly understood. Ascertaining the seismic properties of the crust and uppermost mantle in such settings provides insight into continental rheology and geodynamics. The most active present-day continent-continent collision is that of India with Eurasia which has created the Himalayas and the Tibetan Plateau. Nepal provides an ideal laboratory for imaging the crustal processes resulting from the Indo-Eurasia collision. We build body wave models using local body wave arrivals picked at stations in Nepal deployed by the Department of Mining and Geology of Nepal. We use the tomographic inversion method of Roecker et al. [2006], the key feature of which is that the travel times are generated using a finite difference solution to the eikonal equation. The advantage of this technique is increased accuracy in the highly heterogeneous medium expected for the Himalayas. Travel times are calculated on a 3D Cartesian grid with a grid spacing of 6 km and intragrid times are estimated by trilinear interpolation. The gridded area spans a region of 80-90o longitude and 25-30o latitude. For a starting velocity model, we use IASP91. Inversion is performed using the LSQR algorithm. Since the damping parameter can have a significant effect on the final solution, we tested a range of damping parameters to fully explore its effect. Much of the seismicity is clustered to the West of Kathmandu at depths Small areas of strong fast wavespeeds exist in the centre of the region in the upper 30 km of the crust. At depths of 40-50 km, large areas of slow wavespeeds are present which track along the plate boundary.
Ashyralyyeva, Maral; Ashyraliyev, Maksat
2016-08-01
In the present paper, a second order of accuracy difference scheme for the approximate solution of a source identification problem for hyperbolic-parabolic equations is constructed. Theorem on stability estimates for the solution of this difference scheme and their first and second order difference derivatives is presented. In applications, this abstract result permits us to obtain the stability estimates for the solutions of difference schemes for approximate solutions of two source identification problems for hyperbolic-parabolic equations.
DEFF Research Database (Denmark)
Rasmussen, Birgit
2012-01-01
having several similarities. In 2012, status is that number and denotations of classes for dwellings are identical in the Nordic countries, but the structures of the standards and several details are quite different. Also the issues dealt with are different. Examples of differences are sound insulation...... for classification of such buildings. This paper presents and compares the main class criteria for sound insulation of dwellings and summarizes differences and similarities in criteria and in structures of standards. Classification schemes for dwellings also exist in several other countries in Europe......In all five Nordic countries, sound classification schemes for dwellings have been published in national standards being implemented and revised gradually since the late 1990s. The national classification criteria for dwellings originate from a common Nordic INSTA-B proposal from the 1990s, thus...