WorldWideScience

Sample records for grid finite difference

  1. 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)

  2. 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.

  3. Energy stable and high-order-accurate finite difference methods on staggered grids

    Science.gov (United States)

    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.

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

    KAUST Repository

    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.

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

    KAUST Repository

    Gao, Longfei

    2018-02-16

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

  6. Slat Noise Predictions Using Higher-Order Finite-Difference Methods on Overset Grids

    Science.gov (United States)

    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.

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

    KAUST Repository

    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

  8. Double-grid finite-difference frequency-domain (DG-FDFD) method for scattering from chiral objects

    CERN Document Server

    Alkan, Erdogan; Elsherbeni, Atef

    2013-01-01

    This book presents the application of the overlapping grids approach to solve chiral material problems using the FDFD method. Due to the two grids being used in the technique, we will name this method as Double-Grid Finite Difference Frequency-Domain (DG-FDFD) method. As a result of this new approach the electric and magnetic field components are defined at every node in the computation space. Thus, there is no need to perform averaging during the calculations as in the aforementioned FDFD technique [16]. We formulate general 3D frequency-domain numerical methods based on double-grid

  9. A chimera grid scheme. [multiple overset body-conforming mesh system for finite difference adaptation to complex aircraft configurations

    Science.gov (United States)

    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.

  10. Solving the linearized forward-speed radiation problem using a high-order finite difference method on overlapping grids

    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...

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

    KAUST Repository

    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

  12. A non-conformal finite element/finite volume scheme for the non-structured grid-based approximation of low Mach number flows

    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)

  13. New 2D adaptive mesh refinement algorithm based on conservative finite-differences with staggered grid

    Science.gov (United States)

    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

  14. A staggered-grid finite-difference scheme optimized in the time–space domain for modeling scalar-wave propagation in geophysical problems

    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

  15. Hybrid finite difference/finite element immersed boundary method.

    Science.gov (United States)

    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.

  16. 3D Staggered-Grid Finite-Difference Simulation of Acoustic Waves in Turbulent Moving Media

    Science.gov (United States)

    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

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

    KAUST Repository

    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.

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

    KAUST Repository

    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.

  19. 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

  20. A finite difference method for free boundary problems

    KAUST Repository

    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

  1. Adaptive Finite Volume Method for the Shallow Water Equations on Triangular Grids

    Directory of Open Access Journals (Sweden)

    Sudi Mungkasi

    2016-01-01

    Full Text Available This paper presents a numerical entropy production (NEP scheme for two-dimensional shallow water equations on unstructured triangular grids. We implement NEP as the error indicator for adaptive mesh refinement or coarsening in solving the shallow water equations using a finite volume method. Numerical simulations show that NEP is successful to be a refinement/coarsening indicator in the adaptive mesh finite volume method, as the method refines the mesh or grids around nonsmooth regions and coarsens them around smooth regions.

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

    KAUST Repository

    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.

  3. On long-time instabilities in staggered finite difference simulations of the seismic acoustic wave equations on discontinuous grids

    Science.gov (United States)

    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.

  4. Implicit finite-difference simulations of seismic wave propagation

    KAUST Repository

    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.

  5. Implicit finite-difference simulations of seismic wave propagation

    KAUST Repository

    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.

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

    KAUST Repository

    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.

  7. 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

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

    KAUST Repository

    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.

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

    KAUST Repository

    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.

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2005-05-01

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

  11. GRIZ: Visualization of finite element analysis results on unstructured grids

    International Nuclear Information System (INIS)

    Dovey, D.; Loomis, M.D.

    1994-01-01

    GRIZ is a general-purpose post-processing application that supports interactive visualization of finite element analysis results on three-dimensional unstructured grids. GRIZ includes direct-to-videodisc animation capabilities and is being used as a production tool for creating engineering animations

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

    Science.gov (United States)

    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.

  13. A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

    Energy Technology Data Exchange (ETDEWEB)

    Bailey, T S; Adams, M L [Texas A M Univ., Dept. of Nuclear Engineering, College Station, TX (United States); Yang, B; Zika, M R [Lawrence Livermore National Lab., Livermore, CA (United States)

    2005-07-01

    We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2-dimensional) or polyhedral (3-dimensional) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids. (authors)

  14. 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...

  15. A Family of Multipoint Flux Mixed Finite Element Methods for Elliptic Problems on General Grids

    KAUST Repository

    Wheeler, Mary F.

    2011-01-01

    In this paper, we discuss a family of multipoint flux mixed finite element (MFMFE) methods on simplicial, quadrilateral, hexahedral, and triangular-prismatic grids. The MFMFE methods are locally conservative with continuous normal fluxes, since they are developed within a variational framework as mixed finite element methods with special approximating spaces and quadrature rules. The latter allows for local flux elimination giving a cell-centered system for the scalar variable. We study two versions of the method: with a symmetric quadrature rule on smooth grids and a non-symmetric quadrature rule on rough grids. Theoretical and numerical results demonstrate first order convergence for problems with full-tensor coefficients. Second order superconvergence is observed on smooth grids. © 2011 Published by Elsevier Ltd.

  16. A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

    Energy Technology Data Exchange (ETDEWEB)

    Bailey, T.S.; Adams, M.L. [Texas A M Univ., Dept. of Nuclear Engineering, College Station, TX (United States); Yang, B.; Zika, M.R. [Lawrence Livermore National Lab., Livermore, CA (United States)

    2005-07-01

    We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2-dimensional) or polyhedral (3-dimensional) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids. (authors)

  17. New ghost-node method for linking different models with varied grid refinement

    Science.gov (United States)

    James, S.C.; Dickinson, J.E.; Mehl, S.W.; Hill, M.C.; Leake, S.A.; Zyvoloski, G.A.; Eddebbarh, A.-A.

    2006-01-01

    A flexible, robust method for linking grids of locally refined ground-water flow models constructed with different numerical methods is needed to address a variety of hydrologic problems. This work outlines and tests a new ghost-node model-linking method for a refined "child" model that is contained within a larger and coarser "parent" model that is based on the iterative method of Steffen W. Mehl and Mary C. Hill (2002, Advances in Water Res., 25, p. 497-511; 2004, Advances in Water Res., 27, p. 899-912). The method is applicable to steady-state solutions for ground-water flow. Tests are presented for a homogeneous two-dimensional system that has matching grids (parent cells border an integer number of child cells) or nonmatching grids. The coupled grids are simulated by using the finite-difference and finite-element models MODFLOW and FEHM, respectively. The simulations require no alteration of the MODFLOW or FEHM models and are executed using a batch file on Windows operating systems. Results indicate that when the grids are matched spatially so that nodes and child-cell boundaries are aligned, the new coupling technique has error nearly equal to that when coupling two MODFLOW models. When the grids are nonmatching, model accuracy is slightly increased compared to that for matching-grid cases. Overall, results indicate that the ghost-node technique is a viable means to couple distinct models because the overall head and flow errors relative to the analytical solution are less than if only the regional coarse-grid model was used to simulate flow in the child model's domain.

  18. A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

    Energy Technology Data Exchange (ETDEWEB)

    Bailey, Teresa S. [Texas A and M University, Department of Nuclear Engineering, College Station, TX 77843-3133 (United States)], E-mail: baileyte@tamu.edu; Adams, Marvin L. [Texas A and M University, Department of Nuclear Engineering, College Station, TX 77843-3133 (United States)], E-mail: mladams@tamu.edu; Yang, Brian [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States); Zika, Michael R. [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States)], E-mail: zika@llnl.gov

    2008-04-01

    We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses recently introduced piecewise linear weight and basis functions in the finite element approximation and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We first demonstrate some analytical properties of the PWL method and perform a simple mode analysis to compare the PWL method with Palmer's vertex-centered finite-volume method and with a bilinear continuous finite element method. We then show that this new PWL method gives solutions comparable to those from Palmer's. However, since the PWL method produces a symmetric positive-definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids.

  19. A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

    International Nuclear Information System (INIS)

    Bailey, Teresa S.; Adams, Marvin L.; Yang, Brian; Zika, Michael R.

    2008-01-01

    We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses recently introduced piecewise linear weight and basis functions in the finite element approximation and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We first demonstrate some analytical properties of the PWL method and perform a simple mode analysis to compare the PWL method with Palmer's vertex-centered finite-volume method and with a bilinear continuous finite element method. We then show that this new PWL method gives solutions comparable to those from Palmer's. However, since the PWL method produces a symmetric positive-definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids

  20. A finite difference method for free boundary problems

    KAUST Repository

    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.

  1. New Ghost-node method for linking different models with varied grid refinement

    International Nuclear Information System (INIS)

    Mehl, Steffen W.; Hill, Mary Catherine; James, Scott Carlton; Leake, Stanley A.; Zyvoloski, George A.; Dickinson, Jesse E.; Eddebbarh, Al A.

    2006-01-01

    A flexible, robust method for linking grids of locally refined models constructed with different numerical methods is needed to address a variety of hydrologic problems. This work outlines and tests a new ghost-node model-linking method for a refined 'child' model that is contained within a larger and coarser 'parent' model that is based on the iterative method of Mehl and Hill (2002, 2004). The method is applicable to steady-state solutions for ground-water flow. Tests are presented for a homogeneous two-dimensional system that has either matching grids (parent cells border an integer number of child cells; Figure 2a) or non-matching grids (parent cells border a non-integer number of child cells; Figure 2b). The coupled grids are simulated using the finite-difference and finite-element models MODFLOW and FEHM, respectively. The simulations require no alteration of the MODFLOW or FEHM models and are executed using a batch file on Windows operating systems. Results indicate that when the grids are matched spatially so that nodes and child cell boundaries are aligned, the new coupling technique has error nearly equal to that when coupling two MODFLOW models (Mehl and Hill, 2002). When the grids are non-matching, model accuracy is slightly increased over matching-grid cases. Overall, results indicate that the ghost-node technique is a viable means to accurately couple distinct models because the overall error is less than if only the regional model was used to simulate flow in the child model's domain

  2. 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)

  3. 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.

  4. 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.

  5. Study of grid independence of finite element method on MHD free convective casson fluid flow with slip effect

    Science.gov (United States)

    Raju, R. Srinivasa; Ramesh, K.

    2018-05-01

    The purpose of this work is to study the grid independence of finite element method on MHD Casson fluid flow past a vertically inclined plate filled in a porous medium in presence of chemical reaction, heat absorption, an external magnetic field and slip effect has been investigated. For this study of grid independence, a mathematical model is developed and analyzed by using appropriate mathematical technique, called finite element method. Grid study discussed with the help of numerical values of velocity, temperature and concentration profiles in tabular form. avourable comparisons with previously published work on various special cases of the problem are obtained.

  6. 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...

  7. Seismic wavefield modeling based on time-domain symplectic and Fourier finite-difference method

    Science.gov (United States)

    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.

  8. Dual-mixed finite elements for the three-field Stokes model as a finite volume method on staggered grids

    KAUST Repository

    Kou, Jisheng

    2017-06-09

    In this paper, a new three-field weak formulation for Stokes problems is developed, and from this, a dual-mixed finite element method is proposed on a rectangular mesh. In the proposed mixed methods, the components of stress tensor are approximated by piecewise constant functions or Q1 functions, while the velocity and pressure are discretized by the lowest-order Raviart-Thomas element and the piecewise constant functions, respectively. Using quadrature rules, we demonstrate that this scheme can be reduced into a finite volume method on staggered grid, which is extensively used in computational fluid mechanics and engineering.

  9. A spatially adaptive grid-refinement approach for the finite element solution of the even-parity Boltzmann transport equation

    International Nuclear Information System (INIS)

    Mirza, Anwar M.; Iqbal, Shaukat; Rahman, Faizur

    2007-01-01

    A spatially adaptive grid-refinement approach has been investigated to solve the even-parity Boltzmann transport equation. A residual based a posteriori error estimation scheme has been utilized for checking the approximate solutions for various finite element grids. The local particle balance has been considered as an error assessment criterion. To implement the adaptive approach, a computer program ADAFENT (adaptive finite elements for neutron transport) has been developed to solve the second order even-parity Boltzmann transport equation using K + variational principle for slab geometry. The program has a core K + module which employs Lagrange polynomials as spatial basis functions for the finite element formulation and Legendre polynomials for the directional dependence of the solution. The core module is called in by the adaptive grid generator to determine local gradients and residuals to explore the possibility of grid refinements in appropriate regions of the problem. The a posteriori error estimation scheme has been implemented in the outer grid refining iteration module. Numerical experiments indicate that local errors are large in regions where the flux gradients are large. A comparison of the spatially adaptive grid-refinement approach with that of uniform meshing approach for various benchmark cases confirms its superiority in greatly enhancing the accuracy of the solution without increasing the number of unknown coefficients. A reduction in the local errors of the order of 10 2 has been achieved using the new approach in some cases

  10. A spatially adaptive grid-refinement approach for the finite element solution of the even-parity Boltzmann transport equation

    Energy Technology Data Exchange (ETDEWEB)

    Mirza, Anwar M. [Department of Computer Science, National University of Computer and Emerging Sciences, NUCES-FAST, A.K. Brohi Road, H-11, Islamabad (Pakistan)], E-mail: anwar.m.mirza@gmail.com; Iqbal, Shaukat [Faculty of Computer Science and Engineering, Ghulam Ishaq Khan (GIK) Institute of Engineering Science and Technology, Topi-23460, Swabi (Pakistan)], E-mail: shaukat@giki.edu.pk; Rahman, Faizur [Department of Physics, Allama Iqbal Open University, H-8 Islamabad (Pakistan)

    2007-07-15

    A spatially adaptive grid-refinement approach has been investigated to solve the even-parity Boltzmann transport equation. A residual based a posteriori error estimation scheme has been utilized for checking the approximate solutions for various finite element grids. The local particle balance has been considered as an error assessment criterion. To implement the adaptive approach, a computer program ADAFENT (adaptive finite elements for neutron transport) has been developed to solve the second order even-parity Boltzmann transport equation using K{sup +} variational principle for slab geometry. The program has a core K{sup +} module which employs Lagrange polynomials as spatial basis functions for the finite element formulation and Legendre polynomials for the directional dependence of the solution. The core module is called in by the adaptive grid generator to determine local gradients and residuals to explore the possibility of grid refinements in appropriate regions of the problem. The a posteriori error estimation scheme has been implemented in the outer grid refining iteration module. Numerical experiments indicate that local errors are large in regions where the flux gradients are large. A comparison of the spatially adaptive grid-refinement approach with that of uniform meshing approach for various benchmark cases confirms its superiority in greatly enhancing the accuracy of the solution without increasing the number of unknown coefficients. A reduction in the local errors of the order of 10{sup 2} has been achieved using the new approach in some cases.

  11. Dynamic visual cryptography on deformable finite element grids

    Science.gov (United States)

    Aleksiene, S.; Vaidelys, M.; Aleksa, A.; Ragulskis, M.

    2017-07-01

    Dynamic visual cryptography scheme based on time averaged moiré fringes on deformable finite element grids is introduced in this paper. A predefined Eigenshape function is used for the selection of the pitch of the moiré grating. The relationship between the pitch of moiré grating, the roots of the zero order Bessel function of the first kind and the amplitude of harmonic oscillations is derived and validated by computational experiments. Phase regularization algorithm is used in the entire area of the cover image in order to embed the secret image and to avoid large fluctuations of the moiré grating. Computational simulations are used to demonstrate the efficiency and the applicability of the proposed image hiding technique.

  12. Finite Volume Methods for Incompressible Navier-Stokes Equations on Collocated Grids with Nonconformal Interfaces

    DEFF Research Database (Denmark)

    Kolmogorov, Dmitry

    turbine computations, collocated grid-based SIMPLE-like algorithms are developed for computations on block-structured grids with nonconformal interfaces. A technique to enhance both the convergence speed and the solution accuracy of the SIMPLE-like algorithms is presented. The erroneous behavior, which...... versions of the SIMPLE algorithm. The new technique is implemented in an existing conservative 2nd order finite-volume scheme flow solver (EllipSys), which is extended to cope with grids with nonconformal interfaces. The behavior of the discrete Navier-Stokes equations is discussed in detail...... Block LU relaxation scheme is shown to possess several optimal conditions, which enables to preserve high efficiency of the multigrid solver on both conformal and nonconformal grids. The developments are done using a parallel MPI algorithm, which can handle multiple numbers of interfaces with multiple...

  13. Relative and Absolute Error Control in a Finite-Difference Method Solution of Poisson's Equation

    Science.gov (United States)

    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,…

  14. A non-conformal finite element/finite volume scheme for the non-structured grid-based approximation of low Mach number flows; Un schema elements finis non-conformes/volumes finis pour l'approximation en maillages non-structures des ecoulements a faible nombre de Mach

    Energy Technology Data Exchange (ETDEWEB)

    Ansanay-Alex, G.

    2009-06-17

    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)

  15. A Family of Multipoint Flux Mixed Finite Element Methods for Elliptic Problems on General Grids

    KAUST Repository

    Wheeler, Mary F.; Xue, Guangri; Yotov, Ivan

    2011-01-01

    In this paper, we discuss a family of multipoint flux mixed finite element (MFMFE) methods on simplicial, quadrilateral, hexahedral, and triangular-prismatic grids. The MFMFE methods are locally conservative with continuous normal fluxes, since

  16. Numerically stable finite difference simulation for ultrasonic NDE in anisotropic composites

    Science.gov (United States)

    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.

  17. Parameterized Finite Element Modeling and Buckling Analysis of Six Typical Composite Grid Cylindrical Shells

    Science.gov (United States)

    Lai, Changliang; Wang, Junbiao; Liu, Chuang

    2014-10-01

    Six typical composite grid cylindrical shells are constructed by superimposing three basic types of ribs. Then buckling behavior and structural efficiency of these shells are analyzed under axial compression, pure bending, torsion and transverse bending by finite element (FE) models. The FE models are created by a parametrical FE modeling approach that defines FE models with original natural twisted geometry and orients cross-sections of beam elements exactly. And the approach is parameterized and coded by Patran Command Language (PCL). The demonstrations of FE modeling indicate the program enables efficient generation of FE models and facilitates parametric studies and design of grid shells. Using the program, the effects of helical angles on the buckling behavior of six typical grid cylindrical shells are determined. The results of these studies indicate that the triangle grid and rotated triangle grid cylindrical shell are more efficient than others under axial compression and pure bending, whereas under torsion and transverse bending, the hexagon grid cylindrical shell is most efficient. Additionally, buckling mode shapes are compared and provide an understanding of composite grid cylindrical shells that is useful in preliminary design of such structures.

  18. Domain of composition and finite volume schemes on non-matching grids; Decomposition de domaine et schemas volumes finis sur maillages non-conformes

    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)

  19. 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

  20. Finite element analysis of optimized H shape spring in a nuclear fuel spacer grid by using contact definition

    International Nuclear Information System (INIS)

    Kim, Jae-Yong; Yoon, Kyung-Ho

    2007-01-01

    The primary role of the grid springs in spacer grid is to hold the fuel rods in an appropriate position using friction force and to prevent the fuel rods dropping during reactor operation. The spring force decreases as the fuel burn-up increases since the spring stiffness is degraded due to the high temperature and the irradiation effect in the reactor core. So this phenomenon has to be considered when the initial spring force of grid spring is designed. To check whether the spring have suitable spring force, the characterization test of spring is conducted. In this paper, finite element analysis using contact definition is established for prediction the spring stiffness without test. The test and analysis results are compared to check the availability of finite element model for investing the spring characteristics in assembly condition. (author)

  1. Optimal implicit 2-D finite differences to model wave propagation in poroelastic media

    Science.gov (United States)

    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.

  2. A finite-difference method for the variable coefficient Poisson equation on hierarchical Cartesian meshes

    Science.gov (United States)

    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.

  3. A unidirectional approach for d-dimensional finite element methods for higher order on sparse grids

    Energy Technology Data Exchange (ETDEWEB)

    Bungartz, H.J. [Technische Universitaet Muenchen (Germany)

    1996-12-31

    In the last years, sparse grids have turned out to be a very interesting approach for the efficient iterative numerical solution of elliptic boundary value problems. In comparison to standard (full grid) discretization schemes, the number of grid points can be reduced significantly from O(N{sup d}) to O(N(log{sub 2}(N)){sup d-1}) in the d-dimensional case, whereas the accuracy of the approximation to the finite element solution is only slightly deteriorated: For piecewise d-linear basis functions, e. g., an accuracy of the order O(N{sup - 2}(log{sub 2}(N)){sup d-1}) with respect to the L{sub 2}-norm and of the order O(N{sup -1}) with respect to the energy norm has been shown. Furthermore, regular sparse grids can be extended in a very simple and natural manner to adaptive ones, which makes the hierarchical sparse grid concept applicable to problems that require adaptive grid refinement, too. An approach is presented for the Laplacian on a uinit domain in this paper.

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

    CERN Document Server

    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

  5. Discretization of convection-diffusion equations with finite-difference scheme derived from simplified analytical solutions

    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

  6. Analysis of Grid-Scored Sandwich Structures of Different Curvatures and Grid Sizes For Wind Turbine Blades

    DEFF Research Database (Denmark)

    Laustsen, Steffen; Thomsen, Ole Thybo; Lund, Erik

    2012-01-01

    The stress and strain field developed locally in-situ the core of grid-scored sandwich structures in wind turbine blades is investigated. Due to the many singularities occurring from the “tri-material corners”, a full 3D analysis of the sandwich structure in terms of the Finite Element Method is ...

  7. 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

  8. 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

  9. A new ghost-node method for linking different models and initial investigations of heterogeneity and nonmatching grids

    Science.gov (United States)

    Dickinson, J.E.; James, S.C.; Mehl, S.; Hill, M.C.; Leake, S.A.; Zyvoloski, G.A.; Faunt, C.C.; Eddebbarh, A.-A.

    2007-01-01

    A flexible, robust method for linking parent (regional-scale) and child (local-scale) grids of locally refined models that use different numerical methods is developed based on a new, iterative ghost-node method. Tests are presented for two-dimensional and three-dimensional pumped systems that are homogeneous or that have simple heterogeneity. The parent and child grids are simulated using the block-centered finite-difference MODFLOW and control-volume finite-element FEHM models, respectively. The models are solved iteratively through head-dependent (child model) and specified-flow (parent model) boundary conditions. Boundary conditions for models with nonmatching grids or zones of different hydraulic conductivity are derived and tested against heads and flows from analytical or globally-refined models. Results indicate that for homogeneous two- and three-dimensional models with matched grids (integer number of child cells per parent cell), the new method is nearly as accurate as the coupling of two MODFLOW models using the shared-node method and, surprisingly, errors are slightly lower for nonmatching grids (noninteger number of child cells per parent cell). For heterogeneous three-dimensional systems, this paper compares two methods for each of the two sets of boundary conditions: external heads at head-dependent boundary conditions for the child model are calculated using bilinear interpolation or a Darcy-weighted interpolation; specified-flow boundary conditions for the parent model are calculated using model-grid or hydrogeologic-unit hydraulic conductivities. Results suggest that significantly more accurate heads and flows are produced when both Darcy-weighted interpolation and hydrogeologic-unit hydraulic conductivities are used, while the other methods produce larger errors at the boundary between the regional and local models. The tests suggest that, if posed correctly, the ghost-node method performs well. Additional testing is needed for highly

  10. Grid Generating Automatically Method of Finite Element Analysis for Rotator Structure%旋转体结构有限元网格自动划分法

    Institute of Scientific and Technical Information of China (English)

    许贤泽

    2000-01-01

    The finite element analysis is applied to structure and freedom-system analysis. Its grid generating method is important to the finite element modeling,which generates the grid automatically by the sectional division method and gets the finite element grid model, thus accomplishing the pre-work of the finite element analysis.%用有限元法对进行结构和自由度体系进行分析,其网格的生成是建立有限元模型的重要技术,利用分块分割法对网格自动划分,从而形成有限元网格模型,完成有限元分析的前处理。

  11. On the numerical dispersion of electromagnetic particle-in-cell code: Finite grid instability

    International Nuclear Information System (INIS)

    Meyers, M.D.; Huang, C.-K.; Zeng, Y.; Yi, S.A.; Albright, B.J.

    2015-01-01

    The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the Electromagnetic PIC model. We rigorously derive the faithful 3-D numerical dispersion relation of the PIC model, for a simple, direct current deposition scheme, which does not conserve electric charge exactly. We then specialize to the Yee FDTD scheme. In particular, we clarify the presence of alias modes in an eigenmode analysis of the PIC model, which combines both discrete and continuous variables. The manner in which the PIC model updates and samples the fields and distribution function, together with the temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme, is explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1-D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical modes admitted in the system and their aliases. The most significant interaction is due critically to the correct representation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction, which is then verified by simulation. We demonstrate that our analysis is readily extendable to charge conserving models

  12. On the numerical dispersion of electromagnetic particle-in-cell code: Finite grid instability

    Science.gov (United States)

    Meyers, M. D.; Huang, C.-K.; Zeng, Y.; Yi, S. A.; Albright, B. J.

    2015-09-01

    The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the Electromagnetic PIC model. We rigorously derive the faithful 3-D numerical dispersion relation of the PIC model, for a simple, direct current deposition scheme, which does not conserve electric charge exactly. We then specialize to the Yee FDTD scheme. In particular, we clarify the presence of alias modes in an eigenmode analysis of the PIC model, which combines both discrete and continuous variables. The manner in which the PIC model updates and samples the fields and distribution function, together with the temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme, is explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1-D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical modes admitted in the system and their aliases. The most significant interaction is due critically to the correct representation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction, which is then verified by simulation. We demonstrate that our analysis is readily extendable to charge conserving models.

  13. Parallelized implicit propagators for the finite-difference Schrödinger equation

    Science.gov (United States)

    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.

  14. On the Derivation of Highest-Order Compact Finite Difference Schemes for the One- and Two-Dimensional Poisson Equation with Dirichlet Boundary Conditions

    KAUST Repository

    Settle, Sean O.

    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.

  15. Comparison of numerical dispersion for finite-difference algorithms in transversely isotropic media with a vertical symmetry axis

    International Nuclear Information System (INIS)

    Liang, Wen-Quan; Wang, Yan-Fei; Yang, Chang-Chun

    2015-01-01

    Numerical simulation of the wave equation is widely used to synthesize seismograms theoretically and is also the basis of the reverse time migration and full waveform inversion. For the finite difference methods, grid dispersion often exists because of the discretization of the time and the spatial derivatives in the wave equation. How to suppress the grid dispersion is therefore a key problem for finite difference (FD) approaches. The FD operators for the space derivatives are usually obtained in the space domain. However, the wave equations are discretized in the time and space directions simultaneously. So it would be better to design the FD operators in the time–space domain. We improved the time–space domain method for obtaining the FD operators in an acoustic vertically transversely isotropic (VTI) media so as to cover a much wider range of frequencies. Dispersion analysis and seismic numerical simulation demonstrate the effectiveness of the proposed method. (paper)

  16. Stability of finite difference numerical simulations of acoustic logging-while-drilling with different perfectly matched layer schemes

    Science.gov (United States)

    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

  17. Wavefront-ray grid FDTD algorithm

    OpenAIRE

    ÇİYDEM, MEHMET

    2016-01-01

    A finite difference time domain algorithm on a wavefront-ray grid (WRG-FDTD) is proposed in this study to reduce numerical dispersion of conventional FDTD methods. A FDTD algorithm conforming to a wavefront-ray grid can be useful to take into account anisotropy effects of numerical grids since it features directional energy flow along the rays. An explicit and second-order accurate WRG-FDTD algorithm is provided in generalized curvilinear coordinates for an inhomogeneous isotropic medium. Num...

  18. 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....

  19. A superlinearly convergent finite volume method for the incompressible Navier-Stokes equations on staggered unstructured grids

    International Nuclear Information System (INIS)

    Vidovic, D.; Segal, A.; Wesseling, P.

    2004-01-01

    A method for linear reconstruction of staggered vector fields with special treatment of the divergence is presented. An upwind-biased finite volume scheme for solving the unsteady incompressible Navier-Stokes equations on staggered unstructured triangular grids that uses this reconstruction is described. The scheme is applied to three benchmark problems and is found to be superlinearly convergent in space

  20. Integrating GRID tools to build a computing resource broker: activities of DataGrid WP1

    International Nuclear Information System (INIS)

    Anglano, C.; Barale, S.; Gaido, L.; Guarise, A.; Lusso, S.; Werbrouck, A.

    2001-01-01

    Resources on a computational Grid are geographically distributed, heterogeneous in nature, owned by different individuals or organizations with their own scheduling policies, have different access cost models with dynamically varying loads and availability conditions. This makes traditional approaches to workload management, load balancing and scheduling inappropriate. The first work package (WP1) of the EU-funded DataGrid project is addressing the issue of optimizing the distribution of jobs onto Grid resources based on a knowledge of the status and characteristics of these resources that is necessarily out-of-date (collected in a finite amount of time at a very loosely coupled site). The authors describe the DataGrid approach in integrating existing software components (from Condor, Globus, etc.) to build a Grid Resource Broker, and the early efforts to define a workable scheduling strategy

  1. An overset grid approach to linear wave-structure interaction

    DEFF Research Database (Denmark)

    Read, Robert; Bingham, Harry B.

    2012-01-01

    A finite-difference based approach to wave-structure interaction is reported that employs the overset approach to grid generation. A two-dimensional code that utilizes the Overture C++ library has been developed to solve the linear radiation problem for a floating body of arbitrary form. This sof......A finite-difference based approach to wave-structure interaction is reported that employs the overset approach to grid generation. A two-dimensional code that utilizes the Overture C++ library has been developed to solve the linear radiation problem for a floating body of arbitrary form...

  2. A multiscale mortar multipoint flux mixed finite element method

    KAUST Repository

    Wheeler, Mary Fanett

    2012-02-03

    In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite element method that reduces to cell-centered finite differences on irregular grids. The subdomain grids do not have to match across the interfaces. Continuity of flux between coarse elements is imposed via a mortar finite element space on a coarse grid scale. With an appropriate choice of polynomial degree of the mortar space, we derive optimal order convergence on the fine scale for both the multiscale pressure and velocity, as well as the coarse scale mortar pressure. Some superconvergence results are also derived. The algebraic system is reduced via a non-overlapping domain decomposition to a coarse scale mortar interface problem that is solved using a multiscale flux basis. Numerical experiments are presented to confirm the theory and illustrate the efficiency and flexibility of the method. © EDP Sciences, SMAI, 2012.

  3. Finite element analysis of the contact between fuel rod and spacer grid

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Hyung Kyu; Kim, Young Koon; Kang, Heung Seok; Yoon, Kyung Ho; Song, Kee Nam [Korea Atomic Energy Research Institute, Taejon (Korea)

    1999-01-01

    For the research on the fretting failure problem of nuclear fuel, the contact length and normal stress field are evaluated for the contact between fuel rod and spacer grid by using the Finite Element Method (FEM). An assumption of semi-infiniteness is necessary for applying the Contact Mechanics which is based on the classical theory of elasticity to the present problem. For the contact problem of fuel fretting, the contact mechanical solutions could be utilized well with sufficient accuracy if the contact bodies (i.e., the cladding tube and the spacer grid) can be assumed as semi-infinite bodies. To this end, the contact length evaluated by FEM is discussed together with the relevant research which concerned the effect of dimension for the validity of the assumption of semi-infiniteness. Normal stress profile on the contact is also studied through comparing the theoretical and the FE results. For the analysis of contact problem by FEM, ANSYS code (Version 5.3) is utilized and the geometry is chosen to be the Hertzian (cylinder-to-cylinder), the strip-to-cylinder and the fuel rod/spacer grid contact (strip-to-tube). Present research will be utilized for accessing the fuel fretting problem by FEM together with the theoretical (i.e., contact mechanical) analysis which has been published as KAERI/TR-1113/98. (author). 15 refs., 44 figs., 4 tabs.

  4. Nonlinear Conservation Laws and Finite Volume Methods

    Science.gov (United States)

    Leveque, Randall J.

    Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References

  5. Finite element and finite difference methods in electromagnetic scattering

    CERN Document Server

    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

  6. Anisotropic three-dimensional inversion of CSEM data using finite-element techniques on unstructured grids

    Science.gov (United States)

    Wang, Feiyan; Morten, Jan Petter; Spitzer, Klaus

    2018-05-01

    In this paper, we present a recently developed anisotropic 3-D inversion framework for interpreting controlled-source electromagnetic (CSEM) data in the frequency domain. The framework integrates a high-order finite-element forward operator and a Gauss-Newton inversion algorithm. Conductivity constraints are applied using a parameter transformation. We discretize the continuous forward and inverse problems on unstructured grids for a flexible treatment of arbitrarily complex geometries. Moreover, an unstructured mesh is more desirable in comparison to a single rectilinear mesh for multisource problems because local grid refinement will not significantly influence the mesh density outside the region of interest. The non-uniform spatial discretization facilitates parametrization of the inversion domain at a suitable scale. For a rapid simulation of multisource EM data, we opt to use a parallel direct solver. We further accelerate the inversion process by decomposing the entire data set into subsets with respect to frequencies (and transmitters if memory requirement is affordable). The computational tasks associated with each data subset are distributed to different processes and run in parallel. We validate the scheme using a synthetic marine CSEM model with rough bathymetry, and finally, apply it to an industrial-size 3-D data set from the Troll field oil province in the North Sea acquired in 2008 to examine its robustness and practical applicability.

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

    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.

  8. A direct solver with reutilization of LU factorizations for h-adaptive finite element grids with point singularities

    KAUST Repository

    Paszyński, Maciej R.

    2013-04-01

    This paper describes a direct solver algorithm for a sequence of finite element meshes that are h-refined towards one or several point singularities. For such a sequence of grids, the solver delivers linear computational cost O(N) in terms of CPU time and memory with respect to the number of unknowns N. The linear computational cost is achieved by utilizing the recursive structure provided by the sequence of h-adaptive grids with a special construction of the elimination tree that allows for reutilization of previously computed partial LU (or Cholesky) factorizations over the entire unrefined part of the computational mesh. The reutilization technique reduces the computational cost of the entire sequence of h-refined grids from O(N2) down to O(N). Theoretical estimates are illustrated with numerical results on two- and three-dimensional model problems exhibiting one or several point singularities. © 2013 Elsevier Ltd. All rights reserved.

  9. A direct solver with reutilization of LU factorizations for h-adaptive finite element grids with point singularities

    KAUST Repository

    Paszyński, Maciej R.; Calo, Victor M.; Pardo, David

    2013-01-01

    This paper describes a direct solver algorithm for a sequence of finite element meshes that are h-refined towards one or several point singularities. For such a sequence of grids, the solver delivers linear computational cost O(N) in terms of CPU time and memory with respect to the number of unknowns N. The linear computational cost is achieved by utilizing the recursive structure provided by the sequence of h-adaptive grids with a special construction of the elimination tree that allows for reutilization of previously computed partial LU (or Cholesky) factorizations over the entire unrefined part of the computational mesh. The reutilization technique reduces the computational cost of the entire sequence of h-refined grids from O(N2) down to O(N). Theoretical estimates are illustrated with numerical results on two- and three-dimensional model problems exhibiting one or several point singularities. © 2013 Elsevier Ltd. All rights reserved.

  10. High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains

    Science.gov (United States)

    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.

  11. 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

  12. Analysis of a finite-difference and a Galerkin technique applied to the simulation of advection and diffusion of air pollutants from a line source

    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

  13. Adaptive solution of the multigroup diffusion equation on irregular structured grids using a conforming finite element method formulation

    International Nuclear Information System (INIS)

    Ragusa, J. C.

    2004-01-01

    In this paper, a method for performing spatially adaptive computations in the framework of multigroup diffusion on 2-D and 3-D Cartesian grids is investigated. The numerical error, intrinsic to any computer simulation of physical phenomena, is monitored through an a posteriori error estimator. In a posteriori analysis, the computed solution itself is used to assess the accuracy. By efficiently estimating the spatial error, the entire computational process is controlled through successively adapted grids. Our analysis is based on a finite element solution of the diffusion equation. Bilinear test functions are used. The derived a posteriori error estimator is therefore based on the Hessian of the numerical solution. (authors)

  14. A consistent method for finite volume discretization of body forces on collocated grids applied to flow through an actuator disk

    DEFF Research Database (Denmark)

    Troldborg, Niels; Sørensen, Niels N.; Réthoré, Pierre-Elouan

    2015-01-01

    This paper describes a consistent algorithm for eliminating the numerical wiggles appearing when solving the finite volume discretized Navier-Stokes equations with discrete body forces in a collocated grid arrangement. The proposed method is a modification of the Rhie-Chow algorithm where the for...

  15. Finite grid radius and thickness effects on retarding potential analyzer measured suprathermal electron density and temperature

    International Nuclear Information System (INIS)

    Knudsen, W.C.

    1992-01-01

    The effect of finite grid radius and thickness on the electron current measured by planar retarding potential analyzers (RPAs) is analyzed numerically. Depending on the plasma environment, the current is significantly reduced below that which is calculated using a theoretical equation derived for an idealized RPA having grids with infinite radius and vanishingly small thickness. A correction factor to the idealized theoretical equation is derived for the Pioneer Venus (PV) orbiter RPA (ORPA) for electron gases consisting of one or more components obeying Maxwell statistics. The error in density and temperature of Maxwellian electron distributions previously derived from ORPA data using the theoretical expression for the idealized ORPA is evaluated by comparing the densities and temperatures derived from a sample of PV ORPA data using the theoretical expression with and without the correction factor

  16. A grid-doubling finite-element technique for calculating dynamic three-dimensional spontaneous rupture on an earthquake fault

    Science.gov (United States)

    Barall, Michael

    2009-01-01

    We present a new finite-element technique for calculating dynamic 3-D spontaneous rupture on an earthquake fault, which can reduce the required computational resources by a factor of six or more, without loss of accuracy. The grid-doubling technique employs small cells in a thin layer surrounding the fault. The remainder of the modelling volume is filled with larger cells, typically two or four times as large as the small cells. In the resulting non-conforming mesh, an interpolation method is used to join the thin layer of smaller cells to the volume of larger cells. Grid-doubling is effective because spontaneous rupture calculations typically require higher spatial resolution on and near the fault than elsewhere in the model volume. The technique can be applied to non-planar faults by morphing, or smoothly distorting, the entire mesh to produce the desired 3-D fault geometry. Using our FaultMod finite-element software, we have tested grid-doubling with both slip-weakening and rate-and-state friction laws, by running the SCEC/USGS 3-D dynamic rupture benchmark problems. We have also applied it to a model of the Hayward fault, Northern California, which uses realistic fault geometry and rock properties. FaultMod implements fault slip using common nodes, which represent motion common to both sides of the fault, and differential nodes, which represent motion of one side of the fault relative to the other side. We describe how to modify the traction-at-split-nodes method to work with common and differential nodes, using an implicit time stepping algorithm.

  17. 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)

  18. Electron-phonon coupling from finite differences

    Science.gov (United States)

    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.

  19. Grid sensitivity capability for large scale structures

    Science.gov (United States)

    Nagendra, Gopal K.; Wallerstein, David V.

    1989-01-01

    The considerations and the resultant approach used to implement design sensitivity capability for grids into a large scale, general purpose finite element system (MSC/NASTRAN) are presented. The design variables are grid perturbations with a rather general linking capability. Moreover, shape and sizing variables may be linked together. The design is general enough to facilitate geometric modeling techniques for generating design variable linking schemes in an easy and straightforward manner. Test cases have been run and validated by comparison with the overall finite difference method. The linking of a design sensitivity capability for shape variables in MSC/NASTRAN with an optimizer would give designers a powerful, automated tool to carry out practical optimization design of real life, complicated structures.

  20. An optimal implicit staggered-grid finite-difference scheme based on the modified Taylor-series expansion with minimax approximation method for elastic modeling

    Science.gov (United States)

    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.

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

    KAUST Repository

    Wheeler, Mary; Xue, Guangri; Yotov, Ivan

    2011-01-01

    In this paper, we develop a new mixed finite element method for elliptic problems on general quadrilateral and hexahedral grids that reduces to a cell-centered finite difference scheme. A special non-symmetric quadrature rule is employed that yields

  2. 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)

  3. Numerical comparison of robustness of some reduction methods in rough grids

    KAUST Repository

    Hou, Jiangyong

    2014-04-09

    In this article, we present three nonsymmetric mixed hybrid RT 1 2 methods and compare with some recently developed reduction methods which are suitable for the single-phase Darcy flow problem with full anisotropic and highly heterogeneous permeability on general quadrilateral grids. The methods reviewed are multipoint flux approximation (MPFA), multipoint flux mixed finite element method, mixed-finite element with broken RT 1 2 method, MPFA-type mimetic finite difference method, and symmetric mixed-hybrid finite element method. The numerical experiments of these methods on different distorted meshes are compared, as well as their differences in performance of fluxes are discussed. © 2014 Wiley Periodicals, Inc.

  4. Evaluation of a new welding process used to joint grids thimbles properly in 16 x 16 fuel assemblies, using the finite element method

    Energy Technology Data Exchange (ETDEWEB)

    Schettino, Carlos Frederico Mattos, E-mail: DPNcarlosschettino@inb.gov.b [Industrias Nucleares do Brasil S.A. (DPN/INB), Resende, RJ (Brazil). Diretoria de Producao Nuclear; Silva, Marcio Adriano Coelho da, E-mail: marcio.adriano@inb.gov.b [Industrias Nucleares do Brasil S.A. (GEACON/INB), Resende, RJ (Brazil). Gerencia de Analise Tecnica do Combustivel

    2011-07-01

    The present work aims to evaluate structurally the new welding process used to join the grids to the guide thimbles properly in 16 x 16 fuel assemblies. This new process is an increase of the number of welding points, 4 to 8, between grids and guide thimbles, giving more stiffness to the whole structure. A finite element model of the fuel assembly design was generated in the program ANSYS 12.1. To build this model were used elements BEAM-4 and several spring type elements. The analysis covered specific loads and displacements, simulating the boundaries conditions found during small deflection acting on the entire structure. The method used to development this analysis was the simulation of a finite element model performing a fuel assembly with four weld points on each grid cell containing the guide thimbles, and then the results of it was compare with another model, with eight weld points on each grid cell containing the guide thimbles. The behavior of the structure under the acting displacement and the related results of the analysis, mainly the stiffness, were satisfied. The results of this analysis were used to prove that the new grid to guide thimble welding process improve the dimensional stability when submitted to loads and displacements required on the fuel assembly design. The performed analysis provided INB to get more information of extreme importance, for the continuity of the development of new process of manufacturing and to improve the design of the current fuel assemblies used in reactors. (author)

  5. Evaluation of a new welding process used to joint grids thimbles properly in 16 x 16 fuel assemblies, using the finite element method

    International Nuclear Information System (INIS)

    Schettino, Carlos Frederico Mattos; Silva, Marcio Adriano Coelho da

    2011-01-01

    The present work aims to evaluate structurally the new welding process used to join the grids to the guide thimbles properly in 16 x 16 fuel assemblies. This new process is an increase of the number of welding points, 4 to 8, between grids and guide thimbles, giving more stiffness to the whole structure. A finite element model of the fuel assembly design was generated in the program ANSYS 12.1. To build this model were used elements BEAM-4 and several spring type elements. The analysis covered specific loads and displacements, simulating the boundaries conditions found during small deflection acting on the entire structure. The method used to development this analysis was the simulation of a finite element model performing a fuel assembly with four weld points on each grid cell containing the guide thimbles, and then the results of it was compare with another model, with eight weld points on each grid cell containing the guide thimbles. The behavior of the structure under the acting displacement and the related results of the analysis, mainly the stiffness, were satisfied. The results of this analysis were used to prove that the new grid to guide thimble welding process improve the dimensional stability when submitted to loads and displacements required on the fuel assembly design. The performed analysis provided INB to get more information of extreme importance, for the continuity of the development of new process of manufacturing and to improve the design of the current fuel assemblies used in reactors. (author)

  6. A Solution Adaptive Structured/Unstructured Overset Grid Flow Solver with Applications to Helicopter Rotor Flows

    Science.gov (United States)

    Duque, Earl P. N.; Biswas, Rupak; Strawn, Roger C.

    1995-01-01

    This paper summarizes a method that solves both the three dimensional thin-layer Navier-Stokes equations and the Euler equations using overset structured and solution adaptive unstructured grids with applications to helicopter rotor flowfields. The overset structured grids use an implicit finite-difference method to solve the thin-layer Navier-Stokes/Euler equations while the unstructured grid uses an explicit finite-volume method to solve the Euler equations. Solutions on a helicopter rotor in hover show the ability to accurately convect the rotor wake. However, isotropic subdivision of the tetrahedral mesh rapidly increases the overall problem size.

  7. Group foliation of finite difference equations

    Science.gov (United States)

    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.

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

    KAUST Repository

    Wheeler, Mary

    2011-11-06

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

  9. A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal–icosahedral and cubed-sphere grids

    Directory of Open Access Journals (Sweden)

    J. Thuburn

    2014-05-01

    Full Text Available A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank–Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV. The algorithm is implemented and tested on two families of grids: hexagonal–icosahedral Voronoi grids, and modified equiangular cubed-sphere grids. Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing ∇ × ∇, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1. In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed-sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.

  10. 3-D minimum-structure inversion of magnetotelluric data using the finite-element method and tetrahedral grids

    Science.gov (United States)

    Jahandari, H.; Farquharson, C. G.

    2017-11-01

    Unstructured grids enable representing arbitrary structures more accurately and with fewer cells compared to regular structured grids. These grids also allow more efficient refinements compared to rectilinear meshes. In this study, tetrahedral grids are used for the inversion of magnetotelluric (MT) data, which allows for the direct inclusion of topography in the model, for constraining an inversion using a wireframe-based geological model and for local refinement at the observation stations. A minimum-structure method with an iterative model-space Gauss-Newton algorithm for optimization is used. An iterative solver is employed for solving the normal system of equations at each Gauss-Newton step and the sensitivity matrix-vector products that are required by this solver are calculated using pseudo-forward problems. This method alleviates the need to explicitly form the Hessian or Jacobian matrices which significantly reduces the required computation memory. Forward problems are formulated using an edge-based finite-element approach and a sparse direct solver is used for the solutions. This solver allows saving and re-using the factorization of matrices for similar pseudo-forward problems within a Gauss-Newton iteration which greatly minimizes the computation time. Two examples are presented to show the capability of the algorithm: the first example uses a benchmark model while the second example represents a realistic geological setting with topography and a sulphide deposit. The data that are inverted are the full-tensor impedance and the magnetic transfer function vector. The inversions sufficiently recovered the models and reproduced the data, which shows the effectiveness of unstructured grids for complex and realistic MT inversion scenarios. The first example is also used to demonstrate the computational efficiency of the presented model-space method by comparison with its data-space counterpart.

  11. Analyses of the Collapse Behavior of a Spacer Grid

    International Nuclear Information System (INIS)

    Jang, Myung-Geun; Na, Geum Ju; Jag, Yeon-Hui; Kim, Hee Cheol; Kim, Jong-Bong; Kim, Jaeyoug

    2016-01-01

    In order to investigate the protection capability of a spacer grid assembly for impact load, a hammer impact test has been carried out. The crush strength is measured in the hammer impact test. Song et al. carried out the experiment and finite element analysis for the hammer impact test for various weld line depth. Park et al. designed the spacer grid shape to get required crush strength via finite element analysis. Song et al. also optimized the spacer grid shape to maximize the crush strength, and carried out the finite element analysis for the hammer impact test considering the weld properties. Kim et al. carried out finite element analysis for various guide tube hole shape and compared the crush shape and crush strength. In this study, the effect of shape defect on the crush behavior in the hammer impact test is investigated. The spacer grid cannot be exactly the square. Therefore a lateral displacement (imperfection) is imposed to square spacer grid and then hammer impact is carried out. The effect of the lateral imperfection on the crush strength is investigated. The effect of the shape defect on the crushing behavior in the hammer impact test is investigated by finite element analysis. It is shown that the collapse become severe as the lateral imperfection displacement increases, especially when the imperfection is greater than or equal to 0.7 mm

  12. Solution of free-boundary problems using finite-element/Newton methods and locally refined grids - Application to analysis of solidification microstructure

    Science.gov (United States)

    Tsiveriotis, K.; Brown, R. A.

    1993-01-01

    A new method is presented for the solution of free-boundary problems using Lagrangian finite element approximations defined on locally refined grids. The formulation allows for direct transition from coarse to fine grids without introducing non-conforming basis functions. The calculation of elemental stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of elemental data to the global stiffness matrix and residual vector. This technique for local mesh refinement is combined with recently developed mapping methods and Newton's method to form an efficient algorithm for the solution of free-boundary problems, as demonstrated here by sample calculations of cellular interfacial microstructure during directional solidification of a binary alloy.

  13. Three-dimensional body-wave model of Nepal using finite difference tomography

    Science.gov (United States)

    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.

  14. Parallel iterative procedures for approximate solutions of wave propagation by finite element and finite difference methods

    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.

  15. 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

  16. Simulation of tandem hydrofoils by finite volume method with moving grid system; Henkei koshi wo tsukatta yugen taisekiho ni yoru tandem suichuyoku no simulation

    Energy Technology Data Exchange (ETDEWEB)

    Kawashima, H. [Ship Research Inst., Tokyo (Japan); Miyata, H. [The University of Tokyo, Tokyo (Japan). Faculty of Engineering

    1996-12-31

    With an objective to clarify possibility of application of time-advancing calculated fluid dynamic (CFD) simulation by using a finite volume method with moving grid system, a simulation was performed on motion of a ship with hydrofoils including the control system therein. The simulation consists of a method that couples a moving grid system technology, an equation of motion, and the control system. Complex interactions between wings and with free surface may be considered automatically by directly deriving fluid force from a flow field by using the CFD. In addition, two-dimensional flows around tandem hydrofoils were calculated to solve the motion problem within a vertical plane. As a result, the following results were obtained: a finite volume method using a dynamic moving grid system method was applied to problems in non-steady tandem hydrofoils to show its usefulness; a method that couples the CFD with the equation of motion was applied to the control problems in the tandem hydrofoils to show possibility of a new technology for simulating motions; and a simulation that considers such wing interference as wave creation, discharged vortices, and associated flows was shown useful to understand characteristics of the tandem hydrofoils. 13 refs., 14 figs.

  17. A hybrid finite-volume and finite difference scheme for depth-integrated non-hydrostatic model

    Science.gov (United States)

    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.

  18. Domain decomposition method for nonconforming finite element approximations of anisotropic elliptic problems on nonmatching grids

    Energy Technology Data Exchange (ETDEWEB)

    Maliassov, S.Y. [Texas A& M Univ., College Station, TX (United States)

    1996-12-31

    An approach to the construction of an iterative method for solving systems of linear algebraic equations arising from nonconforming finite element discretizations with nonmatching grids for second order elliptic boundary value problems with anisotropic coefficients is considered. The technique suggested is based on decomposition of the original domain into nonoverlapping subdomains. The elliptic problem is presented in the macro-hybrid form with Lagrange multipliers at the interfaces between subdomains. A block diagonal preconditioner is proposed which is spectrally equivalent to the original saddle point matrix and has the optimal order of arithmetical complexity. The preconditioner includes blocks for preconditioning subdomain and interface problems. It is shown that constants of spectral equivalence axe independent of values of coefficients and mesh step size.

  19. Finite volume methods for the incompressible Navier-Stokes equations on unstructured grids

    Energy Technology Data Exchange (ETDEWEB)

    Meese, Ernst Arne

    1998-07-01

    Most solution methods of computational fluid dynamics (CFD) use structured grids based on curvilinear coordinates for compliance with complex geometries. In a typical industry application, about 80% of the time used to produce the results is spent constructing computational grids. Recently the use of unstructured grids has been strongly advocated. For unstructured grids there are methods for generating them automatically on quite complex domains. This thesis focuses on the design of Navier-Stokes solvers that can cope with unstructured grids and ''low quality grids'', thus reducing the need for human intervention in the grid generation.

  20. 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.

  1. Collocated electrodynamic FDTD schemes using overlapping Yee grids and higher-order Hodge duals

    Science.gov (United States)

    Deimert, C.; Potter, M. E.; Okoniewski, M.

    2016-12-01

    The collocated Lebedev grid has previously been proposed as an alternative to the Yee grid for electromagnetic finite-difference time-domain (FDTD) simulations. While it performs better in anisotropic media, it performs poorly in isotropic media because it is equivalent to four overlapping, uncoupled Yee grids. We propose to couple the four Yee grids and fix the Lebedev method using discrete exterior calculus (DEC) with higher-order Hodge duals. We find that higher-order Hodge duals do improve the performance of the Lebedev grid, but they also improve the Yee grid by a similar amount. The effectiveness of coupling overlapping Yee grids with a higher-order Hodge dual is thus questionable. However, the theoretical foundations developed to derive these methods may be of interest in other problems.

  2. Grid interoperability: joining grid information systems

    International Nuclear Information System (INIS)

    Flechl, M; Field, L

    2008-01-01

    A grid is defined as being 'coordinated resource sharing and problem solving in dynamic, multi-institutional virtual organizations'. Over recent years a number of grid projects, many of which have a strong regional presence, have emerged to help coordinate institutions and enable grids. Today, we face a situation where a number of grid projects exist, most of which are using slightly different middleware. Grid interoperation is trying to bridge these differences and enable Virtual Organizations to access resources at the institutions independent of their grid project affiliation. Grid interoperation is usually a bilateral activity between two grid infrastructures. Recently within the Open Grid Forum, the Grid Interoperability Now (GIN) Community Group is trying to build upon these bilateral activities. The GIN group is a focal point where all the infrastructures can come together to share ideas and experiences on grid interoperation. It is hoped that each bilateral activity will bring us one step closer to the overall goal of a uniform grid landscape. A fundamental aspect of a grid is the information system, which is used to find available grid services. As different grids use different information systems, interoperation between these systems is crucial for grid interoperability. This paper describes the work carried out to overcome these differences between a number of grid projects and the experiences gained. It focuses on the different techniques used and highlights the important areas for future standardization

  3. Finite Mathematics and Discrete Mathematics: Is There a Difference?

    Science.gov (United States)

    Johnson, Marvin L.

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

  4. The Development of a Finite Volume Method for Modeling Sound in Coastal Ocean Environment

    Energy Technology Data Exchange (ETDEWEB)

    Long, Wen; Yang, Zhaoqing; Copping, Andrea E.; Jung, Ki Won; Deng, Zhiqun

    2015-10-28

    : As the rapid growth of marine renewable energy and off-shore wind energy, there have been concerns that the noises generated from construction and operation of the devices may interfere marine animals’ communication. In this research, a underwater sound model is developed to simulate sound prorogation generated by marine-hydrokinetic energy (MHK) devices or offshore wind (OSW) energy platforms. Finite volume and finite difference methods are developed to solve the 3D Helmholtz equation of sound propagation in the coastal environment. For finite volume method, the grid system consists of triangular grids in horizontal plane and sigma-layers in vertical dimension. A 3D sparse matrix solver with complex coefficients is formed for solving the resulting acoustic pressure field. The Complex Shifted Laplacian Preconditioner (CSLP) method is applied to efficiently solve the matrix system iteratively with MPI parallelization using a high performance cluster. The sound model is then coupled with the Finite Volume Community Ocean Model (FVCOM) for simulating sound propagation generated by human activities in a range-dependent setting, such as offshore wind energy platform constructions and tidal stream turbines. As a proof of concept, initial validation of the finite difference solver is presented for two coastal wedge problems. Validation of finite volume method will be reported separately.

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

    Science.gov (United States)

    Sprague, Mark W; Luczkovich, Joseph J

    2016-01-01

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

  6. An Eulerian-Lagrangian finite-element method for modeling crack growth in creeping materials

    International Nuclear Information System (INIS)

    Lee Hae Sung.

    1991-01-01

    This study is concerned with the development of finite-element-solution methods for analysis of quasi-static, ductile crack growth in history-dependent materials. The mixed Eulerian-Langrangian description (ELD) kinematic model is shown to have several desirable properties for modeling inelastic crack growth. Accordingly, a variational statement based on the ELD for history-dependent materials is developed, and a new moving-grid finite-element method based on the variational statement is presented. The moving-grid finite-element method based on the variational statement is presented. The moving-grid finite-element method is applied to the analysis of transient, quasi-static, mode-III crack growth in creeping materials. A generalized Petrov-Galerkin method (GPG) is developed that simultaneously stabilizes the statement to admit L 2 basis functions for the nonlinear strain field. Quasi-static, model-III crack growth in creeping materials under small-scale-yielding (SSY) conditions is considered. The GPG/ELD moving-grid finite-element formulation is used to model a transient crack-growth problem. The GPG/ELD results compare favorably with previously-published numerical results and the asymptotic solutions

  7. A finite difference Hartree-Fock program for atoms and diatomic molecules

    Science.gov (United States)

    Kobus, Jacek

    2013-03-01

    The newest version of the two-dimensional finite difference Hartree-Fock program for atoms and diatomic molecules is presented. This is an updated and extended version of the program published in this journal in 1996. It can be used to obtain reference, Hartree-Fock limit values of total energies and multipole moments for a wide range of diatomic molecules and their ions in order to calibrate existing and develop new basis sets, calculate (hyper)polarizabilities (αzz, βzzz, γzzzz, Az,zz, Bzz,zz) of atoms, homonuclear and heteronuclear diatomic molecules and their ions via the finite field method, perform DFT-type calculations using LDA or B88 exchange functionals and LYP or VWN correlations ones or the self-consistent multiplicative constant method, perform one-particle calculations with (smooth) Coulomb and Krammers-Henneberger potentials and take account of finite nucleus models. The program is easy to install and compile (tarball+configure+make) and can be used to perform calculations within double- or quadruple-precision arithmetic. Catalogue identifier: ADEB_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADEB_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 2 No. of lines in distributed program, including test data, etc.: 171196 No. of bytes in distributed program, including test data, etc.: 9481802 Distribution format: tar.gz Programming language: Fortran 77, C. Computer: any 32- or 64-bit platform. Operating system: Unix/Linux. RAM: Case dependent, from few MB to many GB Classification: 16.1. Catalogue identifier of previous version: ADEB_v1_0 Journal reference of previous version: Comput. Phys. Comm. 98(1996)346 Does the new version supersede the previous version?: Yes Nature of problem: The program finds virtually exact solutions of the Hartree-Fock and density functional theory type equations for atoms, diatomic molecules and their ions

  8. Super-Grid Modeling of the Elastic Wave Equation in Semi-Bounded Domains

    Energy Technology Data Exchange (ETDEWEB)

    Petersson, N. Anders; Sjögreen, Björn

    2014-10-01

    Abstract

    We develop a super-grid modeling technique for solving the elastic wave equation in semi-bounded two- and three-dimensional spatial domains. In this method, waves are slowed down and dissipated in sponge layers near the far-field boundaries. Mathematically, this is equivalent to a coordinate mapping that transforms a very large physical domain to a significantly smaller computational domain, where the elastic wave equation is solved numerically on a regular grid. To damp out waves that become poorly resolved because of the coordinate mapping, a high order artificial dissipation operator is added in layers near the boundaries of the computational domain. We prove by energy estimates that the super-grid modeling leads to a stable numerical method with decreasing energy, which is valid for heterogeneous material properties and a free surface boundary condition on one side of the domain. Our spatial discretization is based on a fourth order accurate finite difference method, which satisfies the principle of summation by parts. We show that the discrete energy estimate holds also when a centered finite difference stencil is combined with homogeneous Dirichlet conditions at several ghost points outside of the far-field boundaries. Therefore, the coefficients in the finite difference stencils need only be boundary modified near the free surface. This allows for improved computational efficiency and significant simplifications of the implementation of the proposed method in multi-dimensional domains. Numerical experiments in three space dimensions show that the modeling error from truncating the domain can be made very small by choosing a sufficiently wide super-grid damping layer. The numerical accuracy is first evaluated against analytical solutions of Lamb’s problem, where fourth order accuracy is observed with a sixth order artificial dissipation. We then use successive grid refinements to study the numerical accuracy in the more

  9. 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

  10. Task oriented design of robot kinematics using grid method and its application to nuclear power plant

    International Nuclear Information System (INIS)

    Chang, Pyung-Hun; Park, Joon-Young

    2002-01-01

    This paper presents a Task Oriented Design method for robot kinematics based on grid method, widely used in finite difference method and heat transfer/fluid flow analyses. This approach drastically reduces complexities and computational burden due to previous approaches. More specifically, the grid method with a new formulation simplifies the design to a problem of three-design-variable unit grid, which does not require to solve inverse/forward kinematics. The effectiveness of the grid method has been confirmed through a kinematics design of a robot for nuclear power plants. (author)

  11. The Finite-Surface Method for incompressible flow: a step beyond staggered grid

    Science.gov (United States)

    Hokpunna, Arpiruk; Misaka, Takashi; Obayashi, Shigeru

    2017-11-01

    We present a newly developed higher-order finite surface method for the incompressible Navier-Stokes equations (NSE). This method defines the velocities as a surface-averaged value on the surfaces of the pressure cells. Consequently, the mass conservation on the pressure cells becomes an exact equation. The only things left to approximate is the momentum equation and the pressure at the new time step. At certain conditions, the exact mass conservation enables the explicit n-th order accurate NSE solver to be used with the pressure treatment that is two or four order less accurate without loosing the apparent convergence rate. This feature was not possible with finite volume of finite difference methods. We use Fourier analysis with a model spectrum to determine the condition and found that the range covers standard boundary layer flows. The formal convergence and the performance of the proposed scheme is compared with a sixth-order finite volume method. Finally, the accuracy and performance of the method is evaluated in turbulent channel flows. This work is partially funded by a research colloaboration from IFS, Tohoku university and ASEAN+3 funding scheme from CMUIC, Chiang Mai University.

  12. A high-order finite-volume method for hyperbolic conservation laws on locally-refined grids

    Energy Technology Data Exchange (ETDEWEB)

    McCorquodale, Peter; Colella, Phillip

    2011-01-28

    We present a fourth-order accurate finite-volume method for solving time-dependent hyperbolic systems of conservation laws on Cartesian grids with multiple levels of refinement. The underlying method is a generalization of that in [5] to nonlinear systems, and is based on using fourth-order accurate quadratures for computing fluxes on faces, combined with fourth-order accurate Runge?Kutta discretization in time. To interpolate boundary conditions at refinement boundaries, we interpolate in time in a manner consistent with the individual stages of the Runge-Kutta method, and interpolate in space by solving a least-squares problem over a neighborhood of each target cell for the coefficients of a cubic polynomial. The method also uses a variation on the extremum-preserving limiter in [8], as well as slope flattening and a fourth-order accurate artificial viscosity for strong shocks. We show that the resulting method is fourth-order accurate for smooth solutions, and is robust in the presence of complex combinations of shocks and smooth flows.

  13. The effect of finite-difference time-domain resolution and power-loss computation method on SAR values in plane-wave exposure of Zubal phantom

    International Nuclear Information System (INIS)

    Uusitupa, T M; Ilvonen, S A; Laakso, I M; Nikoskinen, K I

    2008-01-01

    In this paper, the anatomically realistic body model Zubal is exposed to a plane wave. A finite-difference time-domain (FDTD) method is used to obtain field data for specific-absorption-rate (SAR) computation. It is investigated how the FDTD resolution, power-loss computation method and positioning of the material voxels in the FDTD grid affect the SAR results. The results enable one to estimate the effects due to certain fundamental choices made in the SAR simulation

  14. Optimized Finite-Difference Coefficients for Hydroacoustic Modeling

    Science.gov (United States)

    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.

  15. A Pseudo-Temporal Multi-Grid Relaxation Scheme for Solving the Parabolized Navier-Stokes Equations

    Science.gov (United States)

    White, J. A.; Morrison, J. H.

    1999-01-01

    A multi-grid, flux-difference-split, finite-volume code, VULCAN, is presented for solving the elliptic and parabolized form of the equations governing three-dimensional, turbulent, calorically perfect and non-equilibrium chemically reacting flows. The space marching algorithms developed to improve convergence rate and or reduce computational cost are emphasized. The algorithms presented are extensions to the class of implicit pseudo-time iterative, upwind space-marching schemes. A full approximate storage, full multi-grid scheme is also described which is used to accelerate the convergence of a Gauss-Seidel relaxation method. The multi-grid algorithm is shown to significantly improve convergence on high aspect ratio grids.

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

    NARCIS (Netherlands)

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

    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

  17. Global Time Tomography of Finite Frequency Waves with Optimized Tetrahedral Grids.

    Science.gov (United States)

    Montelli, R.; Montelli, R.; Nolet, G.; Dahlen, F. A.; Masters, G.; Hung, S.

    2001-12-01

    Besides true velocity heterogeneities, tomographic images reflect the effect of data errors, model parametrization, linearization, uncertainties involved with the solution of the forward problem and the greatly inadequate sampling of the earth by seismic rays. These influences cannot be easily separated and often produce artefacts in the final image with amplitudes comparable to those of the velocity heterogeneities. In practice, the tomographer uses some form of damping of the ill-resolved aspects of the model to get a unique solution and reduce the influence of the errors. However damping is not fully adequate, and may reveal a strong influence of the ray path coverage in tomographic images. If some cells are ill determinated regularization techniques may lead to heterogeneity because these cells are damped towards zero. Thus we want a uniform resolution of the parameters in our model. This can be obtained by using an irregular grid with variable length scales. We have introduced an irregular parametrization of the velocity structure by using a Delaunay triangulation. Extensively work on error analysis of tomographic images together with mesh optimization has shown that both resolution and ray density can provide the critical informations needed to re-design grids. However, criteria based on resolution are preferred in the presence of narrow ray beams coming from the same direction. This can be understood if we realise that resolution is not only determined by the number of rays crossing a region, but also by their azimutal coverage. We shall discuss various strategies for grid optimization. In general the computation of the travel times is restricted to ray theory, the infinite frequency approximation of the elastodynamic equation of motion. This simplifies the mathematic and is therefore widely applied in seismic tomography. But ray theory does not account for scattering, wavefront healing and other diffraction effects that render the traveltime of a finite

  18. 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...

  19. A least squares principle unifying finite element, finite difference and nodal methods for diffusion theory

    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)

  20. 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.)

  1. Acceleration of Linear Finite-Difference Poisson-Boltzmann Methods on Graphics Processing Units.

    Science.gov (United States)

    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.

  2. Measuring device and method for dimples height differences of 17 x 17 grid

    International Nuclear Information System (INIS)

    Xu Yilan; Zheng Zhihui; Yan Liwei; Wang Xihe

    2001-01-01

    There are 264 cell for fastening fuel rods in the grid of 17 x 17 fuel assembly of PWR. The height differences of top and bottom dimples in a grid is an important quality characteristic of the grid. The report deals with measuring machine and method for dimples height differences of the grid. The device has two measuring probes. The Parallel Leaf Spring is used for transmitting the little displacement between two probes. The uncertainty of the device is σ≤4 μm. The measuring method is shown to be practicable

  3. Optimal moving grids for time-dependent partial differential equations

    Science.gov (United States)

    Wathen, A. J.

    1992-01-01

    Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.

  4. The Laguerre finite difference one-way equation solver

    Science.gov (United States)

    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.

  5. Geodynamo and mantle convection simulations on the Earth Simulator using the Yin-Yang grid

    International Nuclear Information System (INIS)

    Kageyama, Akira; Yoshida, Masaki

    2005-01-01

    We have developed finite difference codes based on the Yin-Yang grid for the geodynamo simulation and the mantle convection simulation. The Yin-Yang grid is a kind of spherical overset grid that is composed of two identical component grids. The intrinsic simplicity of the mesh configuration of the Yin-Yang grid enables us to develop highly optimized simulation codes on massively parallel supercomputers. The Yin-Yang geodynamo code has achieved 15.2 Tflops with 4096 processors on the Earth Simulator. This represents 46% of the theoretical peak performance. The Yin-Yang mantle code has enabled us to carry out mantle convection simulations in realistic regimes with a Rayleigh number of 10 7 including strongly temperature dependent viscosity with spatial contrast up to 10 6

  6. A multiscale mortar multipoint flux mixed finite element method

    KAUST Repository

    Wheeler, Mary Fanett; Xue, Guangri; Yotov, Ivan

    2012-01-01

    In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite

  7. Wavelet-based adaptation methodology combined with finite difference WENO to solve ideal magnetohydrodynamics

    Science.gov (United States)

    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.

  8. Flow Applications of the Least Squares Finite Element Method

    Science.gov (United States)

    Jiang, Bo-Nan

    1998-01-01

    The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.

  9. Methods for compressible fluid simulation on GPUs using high-order finite differences

    Science.gov (United States)

    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.

  10. 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.

  11. Computing the demagnetizing tensor for finite difference micromagnetic simulations via numerical integration

    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

  12. 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

  13. 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.

  14. Wind turbine aerodynamics using an incompressible overset grid method

    DEFF Research Database (Denmark)

    Zahle, Frederik; Johansen, Jeppe; Sørensen, Niels N.

    2007-01-01

    In this paper 3D Navier-Stokes simulations of the unsteady flow over the NREL Phase VI turbine are presented. The computations are carried out using the structured grid, incompressible, finite volume flow solver EllipSys3D, which has been extended to include the use of overset grids. Computations...

  15. Finite-difference modeling and dispersion analysis of high-frequency love waves for near-surface applications

    Science.gov (United States)

    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.

  16. Dispersion analysis of the Pn -Pn-1DG mixed finite element pair for atmospheric modelling

    Science.gov (United States)

    Melvin, Thomas

    2018-02-01

    Mixed finite element methods provide a generalisation of staggered grid finite difference methods with a framework to extend the method to high orders. The ability to generate a high order method is appealing for applications on the kind of quasi-uniform grids that are popular for atmospheric modelling, so that the method retains an acceptable level of accuracy even around special points in the grid. The dispersion properties of such schemes are important to study as they provide insight into the numerical adjustment to imbalance that is an important component in atmospheric modelling. This paper extends the recent analysis of the P2 - P1DG pair, that is a quadratic continuous and linear discontinuous finite element pair, to higher polynomial orders and also spectral element type pairs. In common with the previously studied element pair, and also with other schemes such as the spectral element and discontinuous Galerkin methods, increasing the polynomial order is found to provide a more accurate dispersion relation for the well resolved part of the spectrum but at the cost of a number of unphysical spectral gaps. The effects of these spectral gaps are investigated and shown to have a varying impact depending upon the width of the gap. Finally, the tensor product nature of the finite element spaces is exploited to extend the dispersion analysis into two-dimensions.

  17. A finite integration method for conformal, structured-grid, electromagnetic simulation

    International Nuclear Information System (INIS)

    Cooke, S.J.; Shtokhamer, R.; Mondelli, A.A.; Levush, B.

    2006-01-01

    We describe a numerical scheme for solving Maxwell's equations in the frequency domain on a conformal, structured, non-orthogonal, multi-block mesh. By considering Maxwell's equations in a volume parameterized by dimensionless curvilinear coordinates, we obtain a set of tensor equations that are a continuum analogue of common circuit equations, and that separate the metrical and metric-free parts of Maxwell's equations and the material constitutive relations. We discretize these equations using a new formulation that treats the electric field and magnetic induction using simple basis-function representations to obtain a discrete form of Faraday's law of induction, but that uses finite integral representations for the displacement current and magnetic field to obtain a discrete form of Ampere's law, as in the finite integration technique [T. Weiland, A discretization method for the solution of Maxwell's equations for six-component fields, Electron. Commun. (AE U) 31 (1977) 116; T. Weiland, Time domain electromagnetic field computation with finite difference methods, Int. J. Numer. Model: Electron. Netw. Dev. Field 9 (1996) 295-319]. We thereby derive new projection operators for the discrete tensor material equations and obtain a compact numerical scheme for the discrete differential operators. This scheme is shown to exhibit significantly reduced numerical dispersion when compared to the standard linear finite element method. We take advantage of the mesh structure on a block-by-block basis to implement these numerical operators efficiently, and achieve computational speed with modest memory requirements when compared to explicit sparse matrix storage. Using the Jacobi-Davidson [G.L.G. Sleijpen, H.A. van der Vorst, A Jacobi-Davidson iteration method for linear eigenvalue problems, SIAM J. Matrix Anal. Appl. 17 (2) (1996) 401-425; S.J. Cooke, B. Levush, Eigenmode solution of 2-D and 3-D electromagnetic cavities containing absorbing materials using the Jacobi

  18. A staggered-grid convolutional differentiator for elastic wave modelling

    Science.gov (United States)

    Sun, Weijia; Zhou, Binzhong; Fu, Li-Yun

    2015-11-01

    The computation of derivatives in governing partial differential equations is one of the most investigated subjects in the numerical simulation of physical wave propagation. An analytical staggered-grid convolutional differentiator (CD) for first-order velocity-stress elastic wave equations is derived in this paper by inverse Fourier transformation of the band-limited spectrum of a first derivative operator. A taper window function is used to truncate the infinite staggered-grid CD stencil. The truncated CD operator is almost as accurate as the analytical solution, and as efficient as the finite-difference (FD) method. The selection of window functions will influence the accuracy of the CD operator in wave simulation. We search for the optimal Gaussian windows for different order CDs by minimizing the spectral error of the derivative and comparing the windows with the normal Hanning window function for tapering the CD operators. It is found that the optimal Gaussian window appears to be similar to the Hanning window function for tapering the same CD operator. We investigate the accuracy of the windowed CD operator and the staggered-grid FD method with different orders. Compared to the conventional staggered-grid FD method, a short staggered-grid CD operator achieves an accuracy equivalent to that of a long FD operator, with lower computational costs. For example, an 8th order staggered-grid CD operator can achieve the same accuracy of a 16th order staggered-grid FD algorithm but with half of the computational resources and time required. Numerical examples from a homogeneous model and a crustal waveguide model are used to illustrate the superiority of the CD operators over the conventional staggered-grid FD operators for the simulation of wave propagations.

  19. A fast Poisson solver for unsteady incompressible Navier-Stokes equations on the half-staggered grid

    Science.gov (United States)

    Golub, G. H.; Huang, L. C.; Simon, H.; Tang, W. -P.

    1995-01-01

    In this paper, a fast Poisson solver for unsteady, incompressible Navier-Stokes equations with finite difference methods on the non-uniform, half-staggered grid is presented. To achieve this, new algorithms for diagonalizing a semi-definite pair are developed. Our fast solver can also be extended to the three dimensional case. The motivation and related issues in using this second kind of staggered grid are also discussed. Numerical testing has indicated the effectiveness of this algorithm.

  20. Finite difference computing with PDEs a modern software approach

    CERN Document Server

    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.

  1. Bending Moment Calculations for Piles Based on the Finite Element Method

    Directory of Open Access Journals (Sweden)

    Yu-xin Jie

    2013-01-01

    Full Text Available Using the finite element analysis program ABAQUS, a series of calculations on a cantilever beam, pile, and sheet pile wall were made to investigate the bending moment computational methods. The analyses demonstrated that the shear locking is not significant for the passive pile embedded in soil. Therefore, higher-order elements are not always necessary in the computation. The number of grids across the pile section is important for bending moment calculated with stress and less significant for that calculated with displacement. Although computing bending moment with displacement requires fewer grid numbers across the pile section, it sometimes results in variation of the results. For displacement calculation, a pile row can be suitably represented by an equivalent sheet pile wall, whereas the resulting bending moments may be different. Calculated results of bending moment may differ greatly with different grid partitions and computational methods. Therefore, a comparison of results is necessary when performing the analysis.

  2. Mixed isogeometric finite cell methods for the stokes problem

    NARCIS (Netherlands)

    Hoang, T.; Verhoosel, C.V.; Auricchio, F.; van Brummelen, E.H.; Reali, A.

    2017-01-01

    We study the application of the Isogeometric Finite Cell Method (IGA-FCM) to mixed formulations in the context of the Stokes problem. We investigate the performance of the IGA-FCM when utilizing some isogeometric mixed finite elements, namely: Taylor-Hood, Sub-grid, Raviart-Thomas, and Nédélec

  3. Second order finite-difference ghost-point multigrid methods for elliptic problems with discontinuous coefficients on an arbitrary interface

    Science.gov (United States)

    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.

  4. Adaptive hierarchical grid model of water-borne pollutant dispersion

    Science.gov (United States)

    Borthwick, A. G. L.; Marchant, R. D.; Copeland, G. J. M.

    Water pollution by industrial and agricultural waste is an increasingly major public health issue. It is therefore important for water engineers and managers to be able to predict accurately the local behaviour of water-borne pollutants. This paper describes the novel and efficient coupling of dynamically adaptive hierarchical grids with standard solvers of the advection-diffusion equation. Adaptive quadtree grids are able to focus on regions of interest such as pollutant fronts, while retaining economy in the total number of grid elements through selective grid refinement. Advection is treated using Lagrangian particle tracking. Diffusion is solved separately using two grid-based methods; one is by explicit finite differences, the other a diffusion-velocity approach. Results are given in two dimensions for pure diffusion of an initially Gaussian plume, advection-diffusion of the Gaussian plume in the rotating flow field of a forced vortex, and the transport of species in a rectangular channel with side wall boundary layers. Close agreement is achieved with analytical solutions of the advection-diffusion equation and simulations from a Lagrangian random walk model. An application to Sepetiba Bay, Brazil is included to demonstrate the method with complex flows and topography.

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

    Directory of Open Access Journals (Sweden)

    Treena Basu

    2015-10-01

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

  6. Uniform stable conformal convolutional perfectly matched layer for enlarged cell technique conformal finite-difference time-domain method

    International Nuclear Information System (INIS)

    Wang Yue; Wang Jian-Guo; Chen Zai-Gao

    2015-01-01

    Based on conformal construction of physical model in a three-dimensional Cartesian grid, an integral-based conformal convolutional perfectly matched layer (CPML) is given for solving the truncation problem of the open port when the enlarged cell technique conformal finite-difference time-domain (ECT-CFDTD) method is used to simulate the wave propagation inside a perfect electric conductor (PEC) waveguide. The algorithm has the same numerical stability as the ECT-CFDTD method. For the long-time propagation problems of an evanescent wave in a waveguide, several numerical simulations are performed to analyze the reflection error by sweeping the constitutive parameters of the integral-based conformal CPML. Our numerical results show that the integral-based conformal CPML can be used to efficiently truncate the open port of the waveguide. (paper)

  7. A piecewise bi-linear discontinuous finite element spatial discretization of the Sn transport equation

    International Nuclear Information System (INIS)

    Bailey, Teresa S.; Warsa, James S.; Chang, Jae H.; Adams, Marvin L.

    2011-01-01

    We present a new spatial discretization of the discrete-ordinates transport equation in two dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretization that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems. (author)

  8. A Piecewise Bi-Linear Discontinuous Finite Element Spatial Discretization of the Sn Transport Equation

    International Nuclear Information System (INIS)

    Bailey, T.S.; Chang, J.H.; Warsa, J.S.; Adams, M.L.

    2010-01-01

    We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.

  9. A Piecewise Bi-Linear Discontinuous Finite Element Spatial Discretization of the Sn Transport Equation

    Energy Technology Data Exchange (ETDEWEB)

    Bailey, T S; Chang, J H; Warsa, J S; Adams, M L

    2010-12-22

    We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.

  10. 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.

  11. Valuing modular nuclear power plants in finite time decision horizon

    International Nuclear Information System (INIS)

    Jain, Shashi; Roelofs, Ferry; Oosterlee, Cornelis W.

    2013-01-01

    Small and medium sized reactors, SMRs, (according to IAEA, ‘small’ refers to reactors with power less than 300 MWe, and ‘medium’ with power less than 700 MWe) are considered as an attractive option for investment in nuclear power plants. SMRs may benefit from flexibility of investment, reduced upfront expenditure, enhanced safety, and easy integration with small sized grids. Large reactors on the other hand have been an attractive option due to the economy of scale. In this paper we focus on the economic impact of flexibility due to modular construction of SMRs. We demonstrate, using real option analysis, the value of sequential modular SMRs. Numerical results under different considerations of decision time, uncertainty in electricity prices, and constraints on the construction of units, are reported for a single large unit and for modular SMRs. - Highlights: ► Real option value of modular construction in finite time decision horizon. ► Stochastic grid method is used to value the real option. ► Decisions in finite time can differ significantly from infinite decision time. ► Decisions depend on length of decision horizon and price volatilities

  12. Thermo-mechanical design of the extraction grids for RF negative ion source at HUST

    Energy Technology Data Exchange (ETDEWEB)

    Zuo, Chen; Liu, Kaifeng, E-mail: kfliuhust@hust.edu.cn; Li, Dong; Mei, Zhiyuan; Zhang, Zhe; Chen, Dezhi

    2017-01-15

    Highlights: • An extraction system with cooling channels has been designed for HUST negative ion source. • Corresponding heat loads onto three grids has been used in thermo-mechanical analysis. • The analysis results could be very useful for driving the engineering design. - Abstract: Huazhong University of Science and Technology (HUST) is developing a small radio frequency negative ion source experimental setup to promote research on neutral beam injection ion sources. The extraction system for the negative ion source is the key component to obtain the negative ions. The extraction system is composed of three grids: the plasma grid, the extraction grid and the grounded grid. Each grid is impacted by different heat loads. As the grids have to fulfil specific requirements regarding ion extraction, beam optics, and thermo-mechanical issues, grid cooling systems have been included for ensuring reliable operation. This paper focuses on the thermo-hydraulic and thermo-mechanical design of the grids. Finite element calculations have been carried out to analyse the temperature and deformation of the grids under heat loads using the fluid dynamics code CFX. Based on these results, the cooling circuit design and cooling parameters are optimised to satisfy the grid requirements.

  13. Numerical analysis of the spacer grids' compression strength

    International Nuclear Information System (INIS)

    Schettino, C.F.M.; Gouvea, J.P.; Medeiros, N.

    2013-01-01

    Among the components of the fuel assembly, the spacer grids play an important structural role during the energy generation process, mainly for their requirement to have enough structural strength to withstand lateral impact loads, due to fuel assembly shipping/handling and due to forces outcome from postulated accidents (earthquake and LOCA). This requirement ensures a proper geometry for cooling and for guide thimble straightness in the fuel assembly. In this way, the understanding of the macroscopic mechanical behavior of this component becomes essential even to any subsequent geometrical modifications to optimize the flue assemblies' structural behavior. In the present work, three-dimensional finite element models destined to provide consistent predictions of 16X16-type spacer grids lateral strength were proposed. Firstly, buckling tests based on results available in the literature were performed to establish a methodology for spacer grid finite element-based modeling. The, by considering a spacer grid interesting geometry and some possible variations associated to its fabrication, tolerance, the proposed numerical models were submitted to compression conditions to calculate the buckling force. Also, these models were validated for comparison with experimental buckling load results. Comparison of buckling predictions combined to observations of actual and simulated deformed spacer grids geometries permitted to verify the consistency and applicability of the proposed models. Thus, these numerical results show a good agreement between the and the experimental results. (author)

  14. Finite Volume Method for Unstructured Grid

    International Nuclear Information System (INIS)

    Casmara; Kardana, N.D.

    1997-01-01

    The success of a computational method depends on the solution algorithm and mesh generation techniques. cell distributions are needed, which allow the solution to be calculated over the entire body surface with sufficient accuracy. to handle the mesh generation for multi-connected region such as multi-element bodies, the unstructured finite volume method will be applied. the advantages of the unstructured meshes are it provides a great deal more flexibility for generating meshes about complex geometries and provides a natural setting for the use of adaptive meshing. the governing equations to be discretized are inviscid and rotational euler equations. Applications of the method will be evaluated on flow around single and multi-component bodies

  15. Difference analysis for fluid-structure interaction

    International Nuclear Information System (INIS)

    Giencke, E.; Forkel, M.

    1979-01-01

    For solving fluid structure interaction problems it is possible to organize the compter programs for the difference method in the same way as for the finite element method by establishing the difference equations with the principial of virtual work. In the finite element method the individual localized functions for the approximation of the potential function PHI will be chosen also as virtual functions delta PHI. Deriving difference equations the virtual states are simple as possible and the approximation of the potential function may be linear or parabolic. The equations become symmetric both for points in the interiour and the boundaries and for grids with rectangular and triangular elements. The boundary and edge-conditions shall established for elastic walls and for the free surface. For regular rectangular and triangular grids it is possible to derive on the same way multipoint difference equations, which for the same numbers of unknowns are two orders better in accuracy as the usual difference or the finite element equations. Some examples for the pressure distribution in a BWR-steel-containment due to steam bubble collaps at the condenser pipes will be shown. (orig.)

  16. 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

  17. Finite-difference numerical simulations of underground explosion cavity decoupling

    Science.gov (United States)

    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

  18. Exact Finite-Difference Schemes for d-Dimensional Linear Stochastic Systems with Constant Coefficients

    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.

  19. The mimetic finite difference method for elliptic problems

    CERN Document Server

    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.

  20. The use of the spectral method within the fast adaptive composite grid method

    Energy Technology Data Exchange (ETDEWEB)

    McKay, S.M.

    1994-12-31

    The use of efficient algorithms for the solution of partial differential equations has been sought for many years. The fast adaptive composite grid (FAC) method combines an efficient algorithm with high accuracy to obtain low cost solutions to partial differential equations. The FAC method achieves fast solution by combining solutions on different grids with varying discretizations and using multigrid like techniques to find fast solution. Recently, the continuous FAC (CFAC) method has been developed which utilizes an analytic solution within a subdomain to iterate to a solution of the problem. This has been shown to achieve excellent results when the analytic solution can be found. The CFAC method will be extended to allow solvers which construct a function for the solution, e.g., spectral and finite element methods. In this discussion, the spectral methods will be used to provide a fast, accurate solution to the partial differential equation. As spectral methods are more accurate than finite difference methods, the ensuing accuracy from this hybrid method outside of the subdomain will be investigated.

  1. Evaluation of Callable Bonds: Finite Difference Methods, Stability and Accuracy.

    OpenAIRE

    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...

  2. Hybrid multicore/vectorisation technique applied to the elastic wave equation on a staggered grid

    Science.gov (United States)

    Titarenko, Sofya; Hildyard, Mark

    2017-07-01

    In modern physics it has become common to find the solution of a problem by solving numerically a set of PDEs. Whether solving them on a finite difference grid or by a finite element approach, the main calculations are often applied to a stencil structure. In the last decade it has become usual to work with so called big data problems where calculations are very heavy and accelerators and modern architectures are widely used. Although CPU and GPU clusters are often used to solve such problems, parallelisation of any calculation ideally starts from a single processor optimisation. Unfortunately, it is impossible to vectorise a stencil structured loop with high level instructions. In this paper we suggest a new approach to rearranging the data structure which makes it possible to apply high level vectorisation instructions to a stencil loop and which results in significant acceleration. The suggested method allows further acceleration if shared memory APIs are used. We show the effectiveness of the method by applying it to an elastic wave propagation problem on a finite difference grid. We have chosen Intel architecture for the test problem and OpenMP (Open Multi-Processing) since they are extensively used in many applications.

  3. Generalized Multiscale Finite Element Methods for Wave Propagation in Heterogeneous Media

    KAUST Repository

    Chung, Eric T.

    2014-11-13

    Numerical modeling of wave propagation in heterogeneous media is important in many applications. Due to their complex nature, direct numerical simulations on the fine grid are prohibitively expensive. It is therefore important to develop efficient and accurate methods that allow the use of coarse grids. In this paper, we present a multiscale finite element method for wave propagation on a coarse grid. The proposed method is based on the generalized multiscale finite element method (GMsFEM) (see [Y. Efendiev, J. Galvis, and T. Hou, J. Comput. Phys., 251 (2012), pp. 116--135]). To construct multiscale basis functions, we start with two snapshot spaces in each coarse-grid block, where one represents the degrees of freedom on the boundary and the other represents the degrees of freedom in the interior. We use local spectral problems to identify important modes in each snapshot space. These local spectral problems are different from each other and their formulations are based on the analysis. To the best of knowledge, this is the first time that multiple snapshot spaces and multiple spectral problems are used and necessary for efficient computations. Using the dominant modes from local spectral problems, multiscale basis functions are constructed to represent the solution space locally within each coarse block. These multiscale basis functions are coupled via the symmetric interior penalty discontinuous Galerkin method which provides a block diagonal mass matrix and, consequently, results in fast computations in an explicit time discretization. Our methods\\' stability and spectral convergence are rigorously analyzed. Numerical examples are presented to show our methods\\' performance. We also test oversampling strategies. In particular, we discuss how the modes from different snapshot spaces can affect the proposed methods\\' accuracy.

  4. Finite-difference time-domain simulation of electromagnetic bandgap and bi-anisotropic metamaterials

    Science.gov (United States)

    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

  5. On the use of Schwarz-Christoffel conformal mappings to the grid generation for global ocean models

    Science.gov (United States)

    Xu, S.; Wang, B.; Liu, J.

    2015-10-01

    In this article we propose two grid generation methods for global ocean general circulation models. Contrary to conventional dipolar or tripolar grids, the proposed methods are based on Schwarz-Christoffel conformal mappings that map areas with user-prescribed, irregular boundaries to those with regular boundaries (i.e., disks, slits, etc.). The first method aims at improving existing dipolar grids. Compared with existing grids, the sample grid achieves a better trade-off between the enlargement of the latitudinal-longitudinal portion and the overall smooth grid cell size transition. The second method addresses more modern and advanced grid design requirements arising from high-resolution and multi-scale ocean modeling. The generated grids could potentially achieve the alignment of grid lines to the large-scale coastlines, enhanced spatial resolution in coastal regions, and easier computational load balance. Since the grids are orthogonal curvilinear, they can be easily utilized by the majority of ocean general circulation models that are based on finite difference and require grid orthogonality. The proposed grid generation algorithms can also be applied to the grid generation for regional ocean modeling where complex land-sea distribution is present.

  6. Wind turbine rotor-tower interaction using an incompressible overset grid method

    DEFF Research Database (Denmark)

    Zahle, Frederik; Johansen, Jeppe; Sørensen, Niels N.

    2007-01-01

    In this paper 3D Navier-Stokes simulations of the flow over the NREL Phase VI turbine are presented. The computations are carried out using the structured grid, incompressible, finite volume flow solver EllipSys3D, which has been extended to include the use of overset grids. Computations are pres...

  7. Accuracy of finite-difference modeling of seismic waves : Simulation versus laboratory measurements

    Science.gov (United States)

    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.

  8. Evaluation of finite difference and FFT-based solutions of the transport of intensity equation.

    Science.gov (United States)

    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.

  9. Implementation of grid-connected to/from off-grid transference for micro-grid inverters

    OpenAIRE

    Heredero Peris, Daniel; Chillón Antón, Cristian; Pages Gimenez, Marc; Gross, Gabriel Igor; Montesinos Miracle, Daniel

    2013-01-01

    This paper presents the transfer of a microgrid converter from/to on-grid to/from off-grid when the converter is working in two different modes. In the first transfer presented method, the converter operates as a Current Source Inverter (CSI) when on-grid and as a Voltage Source Inverter (VSI) when off-grid. In the second transfer method, the converter is operated as a VSI both, when operated on-grid and off-grid. The two methods are implemented successfully in a real pla...

  10. 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

  11. Adaptive Method Using Controlled Grid Deformation

    Directory of Open Access Journals (Sweden)

    Florin FRUNZULICA

    2011-09-01

    Full Text Available The paper presents an adaptive method using the controlled grid deformation over an elastic, isotropic and continuous domain. The adaptive process is controlled with the principal strains and principal strain directions and uses the finite elements method. Numerical results are presented for several test cases.

  12. Analysis of the nine-point finite difference approximation for the heat conduction equation in a nuclear fuel element

    International Nuclear Information System (INIS)

    Kadri, M.

    1983-01-01

    The time dependent heat conduction equation in the x-y Cartesian geometry is formulated in terms of a nine-point finite difference relation using a Taylor series expansion technique. The accuracy of the nine-point formulation over the five-point formulation has been tested and evaluated for various reactor fuel-cladding plate configurations using a computer program. The results have been checked against analytical solutions for various model problems. The following cases were considered in the steady-state condition: (a) The thermal conductivity and the heat generation were uniform. (b) The thermal conductivity was constant, the heat generation variable. (c) The thermal conductivity varied linearly with the temperature, the heat generation was uniform. (d) Both thermal conductivity and heat generation vary. In case (a), approximately, for the same accuracy, 85% fewer grid points were needed for the nine-point relation which has a 14% higher convergence rate as compared to the five-point relation. In case (b), on the average, 84% fewer grid points were needed for the nine-point relation which has a 65% higher convergence rate as compared to the five-point relation. In case (c) and (d), there is significant accuracy (91% higher than the five-point relation) for the nine-point relation when a worse grid was used. The numerical solution of the nine-point formula in the time dependent case was also more accurate and converges faster than the numerical solution of the five-point formula for all comparative tests related to heat conduction problems in a nuclear fuel element

  13. Numerical analysis of the spacer grids' compression strength

    Energy Technology Data Exchange (ETDEWEB)

    Schettino, C.F.M.; Gouvea, J.P.; Medeiros, N., E-mail: carlosschettino@inb.gov.br, E-mail: jpg@metal.eeimvr.uff.br [Universidade Federal Fluminense (UFF), Volta Redonda, RJ (Brazil). Programa de Engenharia Metalurgica

    2013-07-01

    Among the components of the fuel assembly, the spacer grids play an important structural role during the energy generation process, mainly for their requirement to have enough structural strength to withstand lateral impact loads, due to fuel assembly shipping/handling and due to forces outcome from postulated accidents (earthquake and LOCA). This requirement ensures a proper geometry for cooling and for guide thimble straightness in the fuel assembly. In this way, the understanding of the macroscopic mechanical behavior of this component becomes essential even to any subsequent geometrical modifications to optimize the flue assemblies' structural behavior. In the present work, three-dimensional finite element models destined to provide consistent predictions of 16X16-type spacer grids lateral strength were proposed. Firstly, buckling tests based on results available in the literature were performed to establish a methodology for spacer grid finite element-based modeling. The, by considering a spacer grid interesting geometry and some possible variations associated to its fabrication, tolerance, the proposed numerical models were submitted to compression conditions to calculate the buckling force. Also, these models were validated for comparison with experimental buckling load results. Comparison of buckling predictions combined to observations of actual and simulated deformed spacer grids geometries permitted to verify the consistency and applicability of the proposed models. Thus, these numerical results show a good agreement between the and the experimental results. (author)

  14. Research on Thermal-Field and Sound-Field Coupling Properties of Different Grid Forms

    Directory of Open Access Journals (Sweden)

    Enlai Zhang

    2016-01-01

    Full Text Available The inlet grid and exhaust grid are widely used in engineering machinery products. The process that airflow goes through grids is a complex turbulent flow and directly related to the heat dispersion and aerodynamic noise. The theoretical analysis result shows that the jet noise generated by airflow has a connection with the grid structure form, fluid flowing situation, and heat conduction. In addition, the influences of different grid structure forms (included the round hole, long hole, and square hole and porosity on the heat dissipation and aerodynamic noise were analyzed and presented based on the verified computational fluid dynamics (CFD model. Results show that the heat dispersion and aerodynamic noise of the round hole are most effective under the same porosity; as the porosity increases, the disturbance degree decreases and the noise reduction effect gets better. Finally, the research result provides the scientific basis for improving grid structure and achieving energy saving and noise reduction.

  15. Finite Difference Schemes as Algebraic Correspondences between Layers

    Science.gov (United States)

    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.

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

    KAUST Repository

    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.

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

    KAUST Repository

    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.

  18. 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...

  19. MICROARRAY IMAGE GRIDDING USING GRID LINE REFINEMENT TECHNIQUE

    Directory of Open Access Journals (Sweden)

    V.G. Biju

    2015-05-01

    Full Text Available An important stage in microarray image analysis is gridding. Microarray image gridding is done to locate sub arrays in a microarray image and find co-ordinates of spots within each sub array. For accurate identification of spots, most of the proposed gridding methods require human intervention. In this paper a fully automatic gridding method which enhances spot intensity in the preprocessing step as per a histogram based threshold method is used. The gridding step finds co-ordinates of spots from horizontal and vertical profile of the image. To correct errors due to the grid line placement, a grid line refinement technique is proposed. The algorithm is applied on different image databases and results are compared based on spot detection accuracy and time. An average spot detection accuracy of 95.06% depicts the proposed method’s flexibility and accuracy in finding the spot co-ordinates for different database images.

  20. Preconditioned finite-difference frequency-domain for modelling periodic dielectric structures - comparisons with FDTD

    NARCIS (Netherlands)

    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

  1. Preconditioned finite-difference frequency-domain for modelling periodic dielectric structures : comparisons with FDTD

    NARCIS (Netherlands)

    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

  2. A hybrid finite-difference and integral-equation method for modeling and inversion of marine controlled-source electromagnetic data

    DEFF Research Database (Denmark)

    Yoon, Daeung; Zhdanov, Michael; Mattsson, Johan

    2016-01-01

    One of the major problems in the modeling and inversion of marine controlled-source electromagnetic (CSEM) data is related to the need for accurate representation of very complex geoelectrical models typical for marine environment. At the same time, the corresponding forward-modeling algorithms...... should be powerful and fast enough to be suitable for repeated use in hundreds of iterations of the inversion and for multiple transmitter/receiver positions. To this end, we have developed a novel 3D modeling and inversion approach, which combines the advantages of the finite-difference (FD......) and integral-equation (IE) methods. In the framework of this approach, we have solved Maxwell’s equations for anomalous electric fields using the FD approximation on a staggered grid. Once the unknown electric fields in the computation domain of the FD method are computed, the electric and magnetic fields...

  3. Smart grid security

    Energy Technology Data Exchange (ETDEWEB)

    Cuellar, Jorge (ed.) [Siemens AG, Muenchen (Germany). Corporate Technology

    2013-11-01

    The engineering, deployment and security of the future smart grid will be an enormous project requiring the consensus of many stakeholders with different views on the security and privacy requirements, not to mention methods and solutions. The fragmentation of research agendas and proposed approaches or solutions for securing the future smart grid becomes apparent observing the results from different projects, standards, committees, etc, in different countries. The different approaches and views of the papers in this collection also witness this fragmentation. This book contains the following papers: 1. IT Security Architecture Approaches for Smart Metering and Smart Grid. 2. Smart Grid Information Exchange - Securing the Smart Grid from the Ground. 3. A Tool Set for the Evaluation of Security and Reliability in Smart Grids. 4. A Holistic View of Security and Privacy Issues in Smart Grids. 5. Hardware Security for Device Authentication in the Smart Grid. 6. Maintaining Privacy in Data Rich Demand Response Applications. 7. Data Protection in a Cloud-Enabled Smart Grid. 8. Formal Analysis of a Privacy-Preserving Billing Protocol. 9. Privacy in Smart Metering Ecosystems. 10. Energy rate at home Leveraging ZigBee to Enable Smart Grid in Residential Environment.

  4. Simulations of viscous and compressible gas-gas flows using high-order finite difference schemes

    Science.gov (United States)

    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.

  5. Solution of Poisson equations for 3-dimensional grid generations. [computations of a flow field over a thin delta wing

    Science.gov (United States)

    Fujii, K.

    1983-01-01

    A method for generating three dimensional, finite difference grids about complicated geometries by using Poisson equations is developed. The inhomogenous terms are automatically chosen such that orthogonality and spacing restrictions at the body surface are satisfied. Spherical variables are used to avoid the axis singularity, and an alternating-direction-implicit (ADI) solution scheme is used to accelerate the computations. Computed results are presented that show the capability of the method. Since most of the results presented have been used as grids for flow-field computations, this is indicative that the method is a useful tool for generating three-dimensional grids about complicated geometries.

  6. Integral equations with difference kernels on finite intervals

    CERN Document Server

    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...

  7. Black-hole excision with multiple grid patches

    Energy Technology Data Exchange (ETDEWEB)

    Thornburg, Jonathan [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, D-14476 Golm (Germany)

    2004-08-07

    When using black-hole excision to numerically evolve a black-hole spacetime with no continuous symmetries, most 3 + 1 finite differencing codes use a Cartesian grid. It is difficult to do excision on such a grid because the natural r = constant excision surface must be approximated either by a very different shape such as a contained cube, or by an irregular and non-smooth 'LEGO{sup 1} sphere' which may introduce numerical instabilities into the evolution. In this paper I describe an alternate scheme which uses multiple {l_brace}r x (angular coordinates){r_brace} grid patches, each patch using a different (nonsingular) choice of angular coordinates. This allows excision on a smooth r = constant 2-sphere. I discuss the key design choices in such a multiple-patch scheme, including the choice of ghost-zone versus internal-boundary treatment of the interpatch boundaries (I use a ghost-zone scheme), the number and shape of the patches (I use a 6-patch 'inflated-cube' scheme), the details of how the ghost zones are 'synchronized' by interpolation from neighbouring patches, the tensor basis for the Einstein equations in each patch, and the handling of non-tensor field variables such as the BSSN {gamma}-tilde{sup i} (I use a scheme which requires ghost zones which are twice as wide for the BSSN conformal factor {phi} as for {gamma}-tilde{sup i} and the other BSSN field variables). I present sample numerical results from a prototype implementation of this scheme. This code simulates the time evolution of the (asymptotically flat) spacetime around a single (excised) black hole, using fourth-order finite differencing in space and time. Using Kerr initial data with J/m{sup 2} = 0.6, I present evolutions to t {approx}> 1500m. The lifetime of these evolutions appears to be limited only by outer boundary instabilities, not by any excision instabilities or by any problems inherent to the multiple-patch scheme.

  8. Black-hole excision with multiple grid patches

    International Nuclear Information System (INIS)

    Thornburg, Jonathan

    2004-01-01

    When using black-hole excision to numerically evolve a black-hole spacetime with no continuous symmetries, most 3 + 1 finite differencing codes use a Cartesian grid. It is difficult to do excision on such a grid because the natural r = constant excision surface must be approximated either by a very different shape such as a contained cube, or by an irregular and non-smooth 'LEGO 1 sphere' which may introduce numerical instabilities into the evolution. In this paper I describe an alternate scheme which uses multiple {r x (angular coordinates)} grid patches, each patch using a different (nonsingular) choice of angular coordinates. This allows excision on a smooth r = constant 2-sphere. I discuss the key design choices in such a multiple-patch scheme, including the choice of ghost-zone versus internal-boundary treatment of the interpatch boundaries (I use a ghost-zone scheme), the number and shape of the patches (I use a 6-patch 'inflated-cube' scheme), the details of how the ghost zones are 'synchronized' by interpolation from neighbouring patches, the tensor basis for the Einstein equations in each patch, and the handling of non-tensor field variables such as the BSSN Γ-tilde i (I use a scheme which requires ghost zones which are twice as wide for the BSSN conformal factor φ as for Γ-tilde i and the other BSSN field variables). I present sample numerical results from a prototype implementation of this scheme. This code simulates the time evolution of the (asymptotically flat) spacetime around a single (excised) black hole, using fourth-order finite differencing in space and time. Using Kerr initial data with J/m 2 = 0.6, I present evolutions to t ∼> 1500m. The lifetime of these evolutions appears to be limited only by outer boundary instabilities, not by any excision instabilities or by any problems inherent to the multiple-patch scheme

  9. 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

  10. Generalized multiscale finite element methods for problems in perforated heterogeneous domains

    KAUST Repository

    Chung, Eric T.

    2015-06-08

    Complex processes in perforated domains occur in many real-world applications. These problems are typically characterized by physical processes in domains with multiple scales. Moreover, these problems are intrinsically multiscale and their discretizations can yield very large linear or nonlinear systems. In this paper, we investigate multiscale approaches that attempt to solve such problems on a coarse grid by constructing multiscale basis functions in each coarse grid, where the coarse grid can contain many perforations. In particular, we are interested in cases when there is no scale separation and the perforations can have different sizes. In this regard, we mention some earlier pioneering works, where the authors develop multiscale finite element methods. In our paper, we follow Generalized Multiscale Finite Element Method (GMsFEM) and develop a multiscale procedure where we identify multiscale basis functions in each coarse block using snapshot space and local spectral problems. We show that with a few basis functions in each coarse block, one can approximate the solution, where each coarse block can contain many small inclusions. We apply our general concept to (1) Laplace equation in perforated domains; (2) elasticity equation in perforated domains; and (3) Stokes equations in perforated domains. Numerical results are presented for these problems using two types of heterogeneous perforated domains. The analysis of the proposed methods will be presented elsewhere. © 2015 Taylor & Francis

  11. Improving the performance parameters of metal cylindrical grid shell ...

    African Journals Online (AJOL)

    Improving the performance parameters of metal cylindrical grid shell structures. ... Finite element models are designed taking into account minimization of production and ... The force factors and deformation parameters of the basic circuits of a ...

  12. 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)

  13. A simple finite-difference scheme for handling topography with the first-order wave equation

    NARCIS (Netherlands)

    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

  14. Geospatial Applications on Different Parallel and Distributed Systems in enviroGRIDS Project

    Science.gov (United States)

    Rodila, D.; Bacu, V.; Gorgan, D.

    2012-04-01

    The execution of Earth Science applications and services on parallel and distributed systems has become a necessity especially due to the large amounts of Geospatial data these applications require and the large geographical areas they cover. The parallelization of these applications comes to solve important performance issues and can spread from task parallelism to data parallelism as well. Parallel and distributed architectures such as Grid, Cloud, Multicore, etc. seem to offer the necessary functionalities to solve important problems in the Earth Science domain: storing, distribution, management, processing and security of Geospatial data, execution of complex processing through task and data parallelism, etc. A main goal of the FP7-funded project enviroGRIDS (Black Sea Catchment Observation and Assessment System supporting Sustainable Development) [1] is the development of a Spatial Data Infrastructure targeting this catchment region but also the development of standardized and specialized tools for storing, analyzing, processing and visualizing the Geospatial data concerning this area. For achieving these objectives, the enviroGRIDS deals with the execution of different Earth Science applications, such as hydrological models, Geospatial Web services standardized by the Open Geospatial Consortium (OGC) and others, on parallel and distributed architecture to maximize the obtained performance. This presentation analysis the integration and execution of Geospatial applications on different parallel and distributed architectures and the possibility of choosing among these architectures based on application characteristics and user requirements through a specialized component. Versions of the proposed platform have been used in enviroGRIDS project on different use cases such as: the execution of Geospatial Web services both on Web and Grid infrastructures [2] and the execution of SWAT hydrological models both on Grid and Multicore architectures [3]. The current

  15. 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)

  16. A multithreaded and GPU-optimized compact finite difference algorithm for turbulent mixing at high Schmidt number using petascale computing

    Science.gov (United States)

    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.

  17. Adaptive moving grid methods for two-phase flow in porous media

    KAUST Repository

    Dong, Hao

    2014-08-01

    In this paper, we present an application of the moving mesh method for approximating numerical solutions of the two-phase flow model in porous media. The numerical schemes combine a mixed finite element method and a finite volume method, which can handle the nonlinearities of the governing equations in an efficient way. The adaptive moving grid method is then used to distribute more grid points near the sharp interfaces, which enables us to obtain accurate numerical solutions with fewer computational resources. The numerical experiments indicate that the proposed moving mesh strategy could be an effective way to approximate two-phase flows in porous media. © 2013 Elsevier B.V. All rights reserved.

  18. On applications of chimera grid schemes to store separation

    Science.gov (United States)

    Cougherty, F. C.; Benek, J. A.; Steger, J. L.

    1985-01-01

    A finite difference scheme which uses multiple overset meshes to simulate the aerodynamics of aircraft/store interaction and store separation is described. In this chimera, or multiple mesh, scheme, a complex configuration is mapped using a major grid about the main component of the configuration, and minor overset meshes are used to map each additional component such as a store. As a first step in modeling the aerodynamics of store separation, two dimensional inviscid flow calculations were carried out in which one of the minor meshes is allowed to move with respect to the major grid. Solutions of calibrated two dimensional problems indicate that allowing one mesh to move with respect to another does not adversely affect the time accuracy of an unsteady solution. Steady, inviscid three dimensional computations demonstrate the capability to simulate complex configurations, including closely packed multiple bodies.

  19. 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.

  20. Finite-Time Synchronization of Chaotic Systems with Different Dimension and Secure Communication

    Directory of Open Access Journals (Sweden)

    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.

  1. Acoustic wave simulation using an overset grid for the global monitoring system

    Science.gov (United States)

    Kushida, N.; Le Bras, R.

    2017-12-01

    The International Monitoring System of the Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO) has been monitoring hydro-acoustic and infrasound waves over the globe. Because of the complex natures of the oceans and the atmosphere, computer simulation can play an important role in understanding the observed signals. In this regard, methods which depend on partial differential equations and require minimum modelling, are preferable. So far, to our best knowledge, acoustic wave propagation simulations based on partial differential equations on such a large scale have not been performed (pp 147 - 161 of ref [1], [2]). The main difficulties in building such simulation codes are: (1) considering the inhomogeneity of medium including background flows, (2) high aspect ratio of computational domain, (3) stability during long time integration. To overcome these difficulties, we employ a two-dimensional finite different (FDM) scheme on spherical coordinates with the Yin-Yang overset grid[3] solving the governing equation of acoustic waves introduces by Ostashev et. al.[4]. The comparison with real recording examples in hydro-acoustic will be presented at the conference. [1] Paul C. Etter: Underwater Acoustic Modeling and Simulation, Fourth Edition, CRC Press, 2013. [2] LIAN WANG et. al.: REVIEW OF UNDERWATER ACOUSTIC PROPAGATION MODELS, NPL Report AC 12, 2014. [3] A. Kageyama and T. Sato: "Yin-Yang grid": An overset grid in spherical geometry, Geochem. Geophys. Geosyst., 5, Q09005, 2004. [4] Vladimir E. Ostashev et. al: Equations for finite-difference, time-domain simulation of sound propagation in moving inhomogeneous media and numerical implementation, Acoustical Society of America. DOI: 10.1121/1.1841531, 2005.

  2. High-order finite-difference methods for Poisson's equation

    NARCIS (Netherlands)

    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

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

    CERN Document Server

    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

  4. Integrating renewables in distribution grids. Storage, regulation and the interaction of different stakeholders in future grids

    Energy Technology Data Exchange (ETDEWEB)

    Nykamp, S.

    2013-10-18

    In recent years, the transition of the power supply chain towards a sustainable system based on 'green' electricity generation out of renewable energy sources (RES-E) has become a main challenge for grid operators and further stakeholders in the power system. To enable the evaluation of new concepts for the integration of RES-E, first the feed-in characteristics of photovoltaic, wind and biomass generators located in a distribution grid area and based on numerous measured feed-in data are studied in this thesis. The achieved insights from the feed-in profiles can be used for the dimensioning of grid assets. Furthermore, the results are useful for the evaluation of congestion management or for the dimensioning of storage assets in distribution grids. The latter aspect is analyzed in detail such that suitable storage characteristics for an introduction in the grid are determined. An economic approach is presented to derive break-even points for storage assets as a substitute to conventional reinforcements. For a case study from a real world low voltage grid with reinforcement needs, these break-even points are determined and the main influencing parameters are evaluated. A further important question in this context concerns the role DSOs (distribution system operators) may play with the operation of decentralized storage assets since several stakeholders may be interested in using the flexibility provided by these assets. This unclear responsibility also applies to the steering of adjustable consumption devices such as electric heat pumps or electric cars. For decentralized storage assets as well as heat pump appliances, optimal operation modes based on the optimization objectives for a DSO and a trader are derived. It is shown based on real world data that choosing a 'copperplate' scenario is not only technically insufficient for a global balance of the consumption and generation. It may even be harmful for the society from a welfare economic

  5. A study of infrasound propagation based on high-order finite difference solutions of the Navier-Stokes equations.

    Science.gov (United States)

    Marsden, O; Bogey, C; Bailly, C

    2014-03-01

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

  6. Smart Grid: Network simulator for smart grid test-bed

    International Nuclear Information System (INIS)

    Lai, L C; Ong, H S; Che, Y X; Do, N Q; Ong, X J

    2013-01-01

    Smart Grid become more popular, a smaller scale of smart grid test-bed is set up at UNITEN to investigate the performance and to find out future enhancement of smart grid in Malaysia. The fundamental requirement in this project is design a network with low delay, no packet drop and with high data rate. Different type of traffic has its own characteristic and is suitable for different type of network and requirement. However no one understands the natural of traffic in smart grid. This paper presents the comparison between different types of traffic to find out the most suitable traffic for the optimal network performance.

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

    KAUST Repository

    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.

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

    KAUST Repository

    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.

  9. Accuracy of finite-difference harmonic frequencies in density functional theory.

    Science.gov (United States)

    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.

  10. Enabling Campus Grids with Open Science Grid Technology

    International Nuclear Information System (INIS)

    Weitzel, Derek; Fraser, Dan; Pordes, Ruth; Bockelman, Brian; Swanson, David

    2011-01-01

    The Open Science Grid is a recognized key component of the US national cyber-infrastructure enabling scientific discovery through advanced high throughput computing. The principles and techniques that underlie the Open Science Grid can also be applied to Campus Grids since many of the requirements are the same, even if the implementation technologies differ. We find five requirements for a campus grid: trust relationships, job submission, resource independence, accounting, and data management. The Holland Computing Center's campus grid at the University of Nebraska-Lincoln was designed to fulfill the requirements of a campus grid. A bridging daemon was designed to bring non-Condor clusters into a grid managed by Condor. Condor features which make it possible to bridge Condor sites into a multi-campus grid have been exploited at the Holland Computing Center as well.

  11. 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)

  12. Direct solvers performance on h-adapted grids

    KAUST Repository

    Paszynski, Maciej; Pardo, David; Calo, Victor M.

    2015-01-01

    We analyse the performance of direct solvers when applied to a system of linear equations arising from an hh-adapted, C0C0 finite element space. Theoretical estimates are derived for typical hh-refinement patterns arising as a result of a point, edge, or face singularity as well as boundary layers. They are based on the elimination trees constructed specifically for the considered grids. Theoretical estimates are compared with experiments performed with MUMPS using the nested-dissection algorithm for construction of the elimination tree from METIS library. The numerical experiments provide the same performance for the cases where our trees are identical with those constructed by the nested-dissection algorithm, and worse performance for some cases where our trees are different. We also present numerical experiments for the cases with mixed singularities, where how to construct optimal elimination trees is unknown. In all analysed cases, the use of hh-adaptive grids significantly reduces the cost of the direct solver algorithm per unknown as compared to uniform grids. The theoretical estimates predict and the experimental data confirm that the computational complexity is linear for various refinement patterns. In most cases, the cost of the direct solver per unknown is lower when employing anisotropic refinements as opposed to isotropic ones.

  13. Direct solvers performance on h-adapted grids

    KAUST Repository

    Paszynski, Maciej

    2015-05-27

    We analyse the performance of direct solvers when applied to a system of linear equations arising from an hh-adapted, C0C0 finite element space. Theoretical estimates are derived for typical hh-refinement patterns arising as a result of a point, edge, or face singularity as well as boundary layers. They are based on the elimination trees constructed specifically for the considered grids. Theoretical estimates are compared with experiments performed with MUMPS using the nested-dissection algorithm for construction of the elimination tree from METIS library. The numerical experiments provide the same performance for the cases where our trees are identical with those constructed by the nested-dissection algorithm, and worse performance for some cases where our trees are different. We also present numerical experiments for the cases with mixed singularities, where how to construct optimal elimination trees is unknown. In all analysed cases, the use of hh-adaptive grids significantly reduces the cost of the direct solver algorithm per unknown as compared to uniform grids. The theoretical estimates predict and the experimental data confirm that the computational complexity is linear for various refinement patterns. In most cases, the cost of the direct solver per unknown is lower when employing anisotropic refinements as opposed to isotropic ones.

  14. 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

  15. Grid3: An Application Grid Laboratory for Science

    CERN Multimedia

    CERN. Geneva

    2004-01-01

    level services required by the participating experiments. The deployed infrastructure has been operating since November 2003 with 27 sites, a peak of 2800 processors, work loads from 10 different applications exceeding 1300 simultaneous jobs, and data transfers among sites of greater than 2 TB/day. The Grid3 infrastructure was deployed from grid level services provided by groups and applications within the collaboration. The services were organized into four distinct "grid level services" including: Grid3 Packaging, Monitoring and Information systems, User Authentication and the iGOC Grid Operatio...

  16. CFD analysis on mixing effects of spacer grids with different dimples and sizes for advanced fuel assemblies

    Energy Technology Data Exchange (ETDEWEB)

    Yang, B.W.; Zhang, H.; Han, B.; Zha, Y.D.; Shan, J.Q. [Xi' an Jiaotong Univ. (China). School of Nuclear Science and Technology

    2016-07-15

    The thermal hydraulic characteristics of a mixing vane grid are largely dependent on the structure of key components, such as strip, spring, dimple, weld nugget, as well as the mixing vane configuration. In this paper, several types of spacer grids with different dimple shapes are modeled under subcooled boiling conditions. Prior to the application of CFD on the dimple shape analysis, the mixing effects of spacer grids were studied. After the dimple shape analysis, the side channel effect is discussed by comparing the simulation results of a 3 x 3 and a 5 x 5 spacer grid. The two phase flow CFD models in this study are validated through simple geometry showing that the calculated void fraction is in good agreement with the experimental data. The dimple comparison result shows that varying dimple structures can result in different temperatures, lateral velocities and void fraction distributions downstream of the spacer grids. Comparison of two sizes of spacer grids demonstrate that the side channel generates different flow distribution pattern in the center channel.

  17. Enabling campus grids with open science grid technology

    Energy Technology Data Exchange (ETDEWEB)

    Weitzel, Derek [Nebraska U.; Bockelman, Brian [Nebraska U.; Swanson, David [Nebraska U.; Fraser, Dan [Argonne; Pordes, Ruth [Fermilab

    2011-01-01

    The Open Science Grid is a recognized key component of the US national cyber-infrastructure enabling scientific discovery through advanced high throughput computing. The principles and techniques that underlie the Open Science Grid can also be applied to Campus Grids since many of the requirements are the same, even if the implementation technologies differ. We find five requirements for a campus grid: trust relationships, job submission, resource independence, accounting, and data management. The Holland Computing Center's campus grid at the University of Nebraska-Lincoln was designed to fulfill the requirements of a campus grid. A bridging daemon was designed to bring non-Condor clusters into a grid managed by Condor. Condor features which make it possible to bridge Condor sites into a multi-campus grid have been exploited at the Holland Computing Center as well.

  18. Resilience of electricity grids against transmission line overloads under wind power injection at different nodes.

    Science.gov (United States)

    Schiel, Christoph; Lind, Pedro G; Maass, Philipp

    2017-09-14

    A steadily increasing fraction of renewable energy sources for electricity production requires a better understanding of how stochastic power generation affects the stability of electricity grids. Here, we assess the resilience of an IEEE test grid against single transmission line overloads under wind power injection based on the dc power flow equations and a quasi-static grid response to wind fluctuations. Thereby we focus on the mutual influence of wind power generation at different nodes. We find that overload probabilities vary strongly between different pairs of nodes and become highly affected by spatial correlations of wind fluctuations. An unexpected behaviour is uncovered: for a large number of node pairs, increasing wind power injection at one node can increase the power threshold at the other node with respect to line overloads in the grid. We find that this seemingly paradoxical behaviour is related to the topological distance of the overloaded line from the shortest path connecting the wind nodes. In the considered test grid, it occurs for all node pairs, where the overloaded line belongs to the shortest path.

  19. 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)

  20. The Dirac Equation in the algebraic approximation. VII. A comparison of molecular finite difference and finite basis set calculations using distributed Gaussian basis sets

    NARCIS (Netherlands)

    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

  1. Hierarchical multiscale modeling for flows in fractured media using generalized multiscale finite element method

    KAUST Repository

    Efendiev, Yalchin R.

    2015-06-05

    In this paper, we develop a multiscale finite element method for solving flows in fractured media. Our approach is based on generalized multiscale finite element method (GMsFEM), where we represent the fracture effects on a coarse grid via multiscale basis functions. These multiscale basis functions are constructed in the offline stage via local spectral problems following GMsFEM. To represent the fractures on the fine grid, we consider two approaches (1) discrete fracture model (DFM) (2) embedded fracture model (EFM) and their combination. In DFM, the fractures are resolved via the fine grid, while in EFM the fracture and the fine grid block interaction is represented as a source term. In the proposed multiscale method, additional multiscale basis functions are used to represent the long fractures, while short-size fractures are collectively represented by a single basis functions. The procedure is automatically done via local spectral problems. In this regard, our approach shares common concepts with several approaches proposed in the literature as we discuss. We would like to emphasize that our goal is not to compare DFM with EFM, but rather to develop GMsFEM framework which uses these (DFM or EFM) fine-grid discretization techniques. Numerical results are presented, where we demonstrate how one can adaptively add basis functions in the regions of interest based on error indicators. We also discuss the use of randomized snapshots (Calo et al. Randomized oversampling for generalized multiscale finite element methods, 2014), which reduces the offline computational cost.

  2. Optical strain measurements and its finite element analysis of cold ...

    African Journals Online (AJOL)

    International Journal of Engineering, Science and Technology ... Online video images of square grid were recorded during the deformation ... Finite element software ANSYS has been applied for the analysis of the upset forming process.

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

    NARCIS (Netherlands)

    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

  4. Modeling and Analysis of Resonance in LCL-Type Grid-Connected Inverters under Different Control Schemes

    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.

  5. Grid-generated He II turbulence in a finite channel - experiment

    International Nuclear Information System (INIS)

    Niemela, J.J.; Skrbek, L.; Stalp, S.R.

    2001-01-01

    We present experimental data on decaying turbulence, generated by towing a grid through a stationary sample of He II. We describe in detail the experimental apparatus and physical principles that allow observation of up to six orders of magnitude of decaying vortex line density over three orders of magnitude in time using the second sound attenuation technique. (orig.)

  6. Pseudo-spectral method using rotated staggered grid for elastic wave propagation in 3D arbitrary anisotropic media

    KAUST Repository

    Zou, Peng

    2017-05-10

    Staggering grid is a very effective way to reduce the Nyquist errors and to suppress the non-causal ringing artefacts in the pseudo-spectral solution of first-order elastic wave equations. However, the straightforward use of a staggered-grid pseudo-spectral method is problematic for simulating wave propagation when the anisotropy level is greater than orthorhombic or when the anisotropic symmetries are not aligned with the computational grids. Inspired by the idea of rotated staggered-grid finite-difference method, we propose a modified pseudo-spectral method for wave propagation in arbitrary anisotropic media. Compared with an existing remedy of staggered-grid pseudo-spectral method based on stiffness matrix decomposition and a possible alternative using the Lebedev grids, the rotated staggered-grid-based pseudo-spectral method possesses the best balance between the mitigation of artefacts and efficiency. A 2D example on a transversely isotropic model with tilted symmetry axis verifies its effectiveness to suppress the ringing artefacts. Two 3D examples of increasing anisotropy levels demonstrate that the rotated staggered-grid-based pseudo-spectral method can successfully simulate complex wavefields in such anisotropic formations.

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

    KAUST Repository

    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.

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

    KAUST Repository

    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.

  9. Mimetic finite difference method

    Science.gov (United States)

    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.

  10. Experiences with explicit finite-difference schemes for complex fluid dynamics problems on STAR-100 and CYBER-203 computers

    Science.gov (United States)

    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.

  11. Analysis of the optimized H type grid spring by a characterization test and the finite element method under the in-grid boundary

    International Nuclear Information System (INIS)

    Yoon, Kyung Ho; Lee, Kang Hee; Kang, Heung Seok; Song, Kee Nam

    2006-01-01

    Characterization tests (load vs. displacement curve) are conducted for the springs of Zirconium alloy spacer grids for an advanced LWR fuel assembly. Twofold testing is employed: strap-based and assembly-based tests. The assembly-based test satisfies the in situ boundary conditions of the spring within the grid assembly. The aim of the characterization test via the aforementioned two methods is to establish an appropriate assembly-based test method that fulfills the actual boundary conditions. A characterization test under the spacer grid assembly boundary condition is also conducted to investigate the actual behavior of the spring in the core. The stiffness of the characteristic curve is smaller than that of the strap-wised boundary condition. This phenomenon may cause the strap slit condition. A spacer grid consists of horizontal and vertical straps. The strap slit positions are differentiated from each other. They affords examination of the variation of the external load distribution in the grid spring. Localized regions of high stress and their values are analyzed, as they may be affected by the spring shape. Through a comparison of the results of the test and FE analysis, it is concluded that the present assembly-based analysis model and procedure are reasonably well conducted and can be used for spring characterization in the core. Guidelines for improving the mechanical integrity of the spring are also discussed

  12. Importance of Grid Center Arrangement

    Science.gov (United States)

    Pasaogullari, O.; Usul, N.

    2012-12-01

    In Digital Elevation Modeling, grid size is accepted to be the most important parameter. Despite the point density and/or scale of the source data, it is freely decided by the user. Most of the time, arrangement of the grid centers are ignored, even most GIS packages omit the choice of grid center coordinate selection. In our study; importance of the arrangement of grid centers is investigated. Using the analogy between "Raster Grid DEM" and "Bitmap Image", importance of placement of grid centers in DEMs are measured. The study has been conducted on four different grid DEMs obtained from a half ellipsoid. These grid DEMs are obtained in such a way that they are half grid size apart from each other. Resulting grid DEMs are investigated through similarity measures. Image processing scientists use different measures to investigate the dis/similarity between the images and the amount of different information they carry. Grid DEMs are projected to a finer grid in order to co-center. Similarity measures are then applied to each grid DEM pairs. These similarity measures are adapted to DEM with band reduction and real number operation. One of the measures gives function graph and the others give measure matrices. Application of similarity measures to six grid DEM pairs shows interesting results. These four different grid DEMs are created with the same method for the same area, surprisingly; thirteen out of 14 measures state that, the half grid size apart grid DEMs are different from each other. The results indicated that although grid DEMs carry mutual information, they have also additional individual information. In other words, half grid size apart constructed grid DEMs have non-redundant information.; Joint Probability Distributions Function Graphs

  13. 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)

  14. 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

  15. Electromagnetic and mechanical design of gridded radio-frequency cavity windows

    Energy Technology Data Exchange (ETDEWEB)

    Alsharo' a, Mohammad M. [Illinois Inst. of Technology, Chicago, IL (United States)

    2004-12-01

    Electromagnetic, thermal and structural analyses of radio-frequency (RF) cavities were performed as part of a developmental RF cavity program for muon cooling. RF cavities are necessary to provide longitudinal focusing of the muons and to compensate for their energy loss. Closing the cavity ends by electrically conducting windows reduces the power requirement and increases the on-axis electric field for a given maximum surface electric field. Many factors must be considered in the design of RF cavity windows. RF heating can cause the windows to deform in the axial direction of the cavity. The resulting thermal stresses in the window must be maintained below the yield stress of the window material. The out-of-plane deflection must be small enough so that the consequent frequency shift is tolerable. For example, for an 805 MHz cavity, the out-of-plane deflection must be kept below 25 microns to prevent the frequency of the cavity from shifting more than 10 kHz. In addition, the window design should yield smooth electric and magnetic fields, terminate field leakage beyond the window, and minimize beam scattering. In the present thesis, gridded-tube window designs were considered because of their high structural integrity. As a starting point in the analysis, a cylindrical pillbox cavity was considered as a benchmark problem. Analytical and finite element solutions were obtained for the electric and magnetic fields, power loss density, and temperature profile. Excellent agreement was obtained between the analytical and finite element results. The finite element method was then used to study a variety of gridded-tube windows. It was found that cooling of the gridded-tube windows by passing helium gas inside the tubes significantly reduces the out-of-plane deflection and the thermal stresses. Certain tube geometries and grid patterns were found to satisfy all of the design requirements.

  16. 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)

  17. 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 ...

  18. A study of the effects of grid non-orthogonality on the solution of shallow water equations in boundary-fitted coordinate systems

    CERN Document Server

    Sankaranarayanan, S

    2003-01-01

    In the present study, an existing two-dimensional boundary-fitted model [J. Hydraul. Eng.-ASCE 122 (9) (1996) 512] is used to study the effect of grid non-orthogonality on the solution of shallow water equations using boundary-fitted grids. The linearized two-dimensional shallow water equations are expressed in terms of the grid angle and aspect ratio. The truncation errors of the finite difference approximations used in the solution of the governing equations are shown to be dependent on the grid angle and the aspect ratio. The coefficient of the truncation error was shown to increase, with the decrease in the grid angle. The RMS errors in model predicted surface elevations and velocities for the case of seiching in a rectangular basin are found to increase gradually, as the grid resolution decreases from 174 to 80 gridpoints per wavelength or as the grid angle decreases from 90 deg. to 50 deg. and increases rather sharply for a grid angle of 30 deg. at grid resolutions less than 80 gridpoints per wavelength...

  19. 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.

  20. [Analysis on difference of richness of traditional Chinese medicine resources in Chongqing based on grid technology].

    Science.gov (United States)

    Zhang, Xiao-Bo; Qu, Xian-You; Li, Meng; Wang, Hui; Jing, Zhi-Xian; Liu, Xiang; Zhang, Zhi-Wei; Guo, Lan-Ping; Huang, Lu-Qi

    2017-11-01

    After the end of the national and local medicine resources census work, a large number of Chinese medicine resources and distribution of data will be summarized. The species richness between the regions is a valid indicator for objective reflection of inter-regional resources of Chinese medicine. Due to the large difference in the size of the county area, the assessment of the intercropping of the resources of the traditional Chinese medicine by the county as a statistical unit will lead to the deviation of the regional abundance statistics. Based on the rule grid or grid statistical methods, the size of the statistical unit due to different can be reduced, the differences in the richness of traditional Chinese medicine resources are caused. Taking Chongqing as an example, based on the existing survey data, the difference of richness of traditional Chinese medicine resources under different grid scale were compared and analyzed. The results showed that the 30 km grid could be selected and the richness of Chinese medicine resources in Chongqing could reflect the objective situation of intercropping resources richness in traditional Chinese medicine better. Copyright© by the Chinese Pharmaceutical Association.

  1. Perfectly Matched Layer for the Wave Equation Finite Difference Time Domain Method

    Science.gov (United States)

    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.

  2. 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)

  3. Projection of the rotation form Navier-Stokes equation onto the half-staggered grid

    Energy Technology Data Exchange (ETDEWEB)

    Cho, Ji Ryong [Inje University, Kimhae (Korea, Republic of)

    2016-07-15

    A projection method for computing incompressible fluid flow is proposed. For the method, the rotation form Navier-Stokes equation (NSE), for which the velocity and the total pressure are employed, is discretized on the half-staggered, finite difference spatial grid. The total pressure couples the static pressure gradient and the convection of momentum in the continuous NSE while the half-staggered grid provides weak pressure-velocity coupling in discrete space. These two features interact synergistically for the discretized NSE to produce smooth pressure fields without additional numerical artifacts such as the momentum interpolation. The method preserves the kinetic energy at the inviscid limit condition. Numerical solutions of the decaying Taylor vortex, the inviscid Taylor vortex, the sudden expansion channel and the square-prism wake are presented.

  4. 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

  5. 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.

  6. Buckling behavior analysis of spacer grid by lateral impact load

    International Nuclear Information System (INIS)

    Yoon, Kyung Ho; Kang, Heung Seok; Kim, Hyung Kyu; Song, Kee Nam

    2000-05-01

    The spacer grid is one of the main structural components in the fuel assembly, Which supports the fuel rods, guides cooling water, and protects the system from an external impact load, such as earthquakes. Therefore, the mechanical and structural properties of the spacer grids must be extensively examined while designing it. In this report, free fall type shock tests on the several kinds of the specimens of the spacer grids were also carried out in order to compare the results among the candidate grids. A free fall carriage on the specimen accomplishes the test. In addition to this, a finite element method for predicting the critical impact strength of the spacer grids is described. FE method on the buckling behavior of the spacer grids are performed for a various array of sizes of the grids considering that the spacer grid is an assembled structure with thin-walled plates and imposing proper boundary conditions by nonlinear dynamic impact analysis using ABAQUS/explicit code. The simulated results results also similarly predicted the local buckling phenomena and were found to give good correspondence with the shock test results

  7. Integral and finite difference inequalities and applications

    CERN Document Server

    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

  8. 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.)

  9. Differences in body image between anorexics and in-vitro-fertilization patients - a study with Body Grid

    Science.gov (United States)

    Borkenhagen, Ada; Klapp, Burghard F.; Schoeneich, Frank; Brähler, Elmar

    2005-01-01

    Objectives: The purpose of the investigation was to explore the body image disturbance of anorexics and in-vitro-fertilization patients (IvF-patients) with Body Grid and Body Identity Plot. Methods: The paper reports on an empirical study conducted with 32 anorexic patients and 30 IvF-patients. The structure of the body image was derived from the Body Grid, an idiographic approach following the Role Repertory Grid developed by George A. Kelly [17]. The representation of the body image and the degree of body-acceptance is represented graphically. Results: By the Body Grid and Body Identity Plot measures we were able to identify important differences in body image between anorexics and IvF-patients. Conclusion: The tendencies of dissociation in the body image of anorexics which we found must be seen in the sense of a specific body image disturbance which differs significantly from the body-experience profile of IvF-patients. With the grid approach it was possible to elicit the inner structure of body image and determine the acceptance of the body and integration of single body parts. PMID:19742059

  10. Time-domain finite-difference/finite-element hybrid simulations of radio frequency coils in magnetic resonance imaging

    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

  11. A fast finite-difference algorithm for topology optimization of permanent magnets

    Science.gov (United States)

    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.

  12. Non-Galerkin Coarse Grids for Algebraic Multigrid

    Energy Technology Data Exchange (ETDEWEB)

    Falgout, Robert D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Schroder, Jacob B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2014-06-26

    Algebraic multigrid (AMG) is a popular and effective solver for systems of linear equations that arise from discretized partial differential equations. And while AMG has been effectively implemented on large scale parallel machines, challenges remain, especially when moving to exascale. Particularly, stencil sizes (the number of nonzeros in a row) tend to increase further down in the coarse grid hierarchy, and this growth leads to more communication. Therefore, as problem size increases and the number of levels in the hierarchy grows, the overall efficiency of the parallel AMG method decreases, sometimes dramatically. This growth in stencil size is due to the standard Galerkin coarse grid operator, $P^T A P$, where $P$ is the prolongation (i.e., interpolation) operator. For example, the coarse grid stencil size for a simple three-dimensional (3D) seven-point finite differencing approximation to diffusion can increase into the thousands on present day machines, causing an associated increase in communication costs. We therefore consider algebraically truncating coarse grid stencils to obtain a non-Galerkin coarse grid. First, the sparsity pattern of the non-Galerkin coarse grid is determined by employing a heuristic minimal “safe” pattern together with strength-of-connection ideas. Second, the nonzero entries are determined by collapsing the stencils in the Galerkin operator using traditional AMG techniques. The result is a reduction in coarse grid stencil size, overall operator complexity, and parallel AMG solve phase times.

  13. Mapping of grid faults and grid codes[Wind turbines

    Energy Technology Data Exchange (ETDEWEB)

    Iov, F. [Aalborg Univ., Inst. of Energy Technology (Denmark); Hansen, Anca D.; Soerensen, Poul; Cutululis, N.A. [Risoe National Lab. - DTU, Wind Enegy Dept., Roskilde (Denmark)

    2007-06-15

    The objective of this project is to investigate into the consequences of the new grid connection requirements for the fatigue and extreme loads of wind turbines. The goal is also to clarify and define possible new directions in the certification process of power plant wind turbines, namely wind turbines, which participate actively in the stabilisation of power systems. Practical experience shows that there is a need for such investigations. The grid connection requirements for wind turbines have increased significantly during the last 5-10 years. Especially the requirements for wind turbines to stay connected to the grid during and after voltage sags, imply potential challenges in the design of wind turbines. These requirements pose challenges for the design of both the electrical system and the mechanical structure of wind turbines. An overview over the frequency of grid faults and the grid connection requirements in different relevant countries is done in this report. The most relevant study cases for the quantification of the loads' impact on the wind turbines' lifetime are defined. The goal of this report is to present a mapping of different grid fault types and their frequency in different countries. The report provides also a detailed overview of the Low Voltage Ride-Through Capabilities for wind turbines in different relevant countries. The most relevant study cases for the quantification of the loads' impact on the wind turbines' lifetime are defined. (au)

  14. Finite difference discretization of semiconductor drift-diffusion equations for nanowire solar cells

    Science.gov (United States)

    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.

  15. Grid interoperability: the interoperations cookbook

    Energy Technology Data Exchange (ETDEWEB)

    Field, L; Schulz, M [CERN (Switzerland)], E-mail: Laurence.Field@cern.ch, E-mail: Markus.Schulz@cern.ch

    2008-07-01

    Over recent years a number of grid projects have emerged which have built grid infrastructures that are now the computing backbones for various user communities. A significant number of these communities are limited to one grid infrastructure due to the different middleware and procedures used in each grid. Grid interoperation is trying to bridge these differences and enable virtual organizations to access resources independent of the grid project affiliation. This paper gives an overview of grid interoperation and describes the current methods used to bridge the differences between grids. Actual use cases encountered during the last three years are discussed and the most important interfaces required for interoperability are highlighted. A summary of the standardisation efforts in these areas is given and we argue for moving more aggressively towards standards.

  16. Grid interoperability: the interoperations cookbook

    International Nuclear Information System (INIS)

    Field, L; Schulz, M

    2008-01-01

    Over recent years a number of grid projects have emerged which have built grid infrastructures that are now the computing backbones for various user communities. A significant number of these communities are limited to one grid infrastructure due to the different middleware and procedures used in each grid. Grid interoperation is trying to bridge these differences and enable virtual organizations to access resources independent of the grid project affiliation. This paper gives an overview of grid interoperation and describes the current methods used to bridge the differences between grids. Actual use cases encountered during the last three years are discussed and the most important interfaces required for interoperability are highlighted. A summary of the standardisation efforts in these areas is given and we argue for moving more aggressively towards standards

  17. 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.

  18. 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)

  19. High-resolution two-dimensional and three-dimensional modeling of wire grid polarizers and micropolarizer arrays

    Science.gov (United States)

    Vorobiev, Dmitry; Ninkov, Zoran

    2017-11-01

    Recent advances in photolithography allowed the fabrication of high-quality wire grid polarizers for the visible and near-infrared regimes. In turn, micropolarizer arrays (MPAs) based on wire grid polarizers have been developed and used to construct compact, versatile imaging polarimeters. However, the contrast and throughput of these polarimeters are significantly worse than one might expect based on the performance of large area wire grid polarizers or MPAs, alone. We investigate the parameters that affect the performance of wire grid polarizers and MPAs, using high-resolution two-dimensional and three-dimensional (3-D) finite-difference time-domain simulations. We pay special attention to numerical errors and other challenges that arise in models of these and other subwavelength optical devices. Our tests show that simulations of these structures in the visible and near-IR begin to converge numerically when the mesh size is smaller than ˜4 nm. The performance of wire grid polarizers is very sensitive to the shape, spacing, and conductivity of the metal wires. Using 3-D simulations of micropolarizer "superpixels," we directly study the cross talk due to diffraction at the edges of each micropolarizer, which decreases the contrast of MPAs to ˜200∶1.

  20. A Parallel Multiblock Structured Grid Method with Automated Interblocked Unstructured Grids for Chemically Reacting Flows

    Science.gov (United States)

    Spiegel, Seth Christian

    An automated method for using unstructured grids to patch non- C0 interfaces between structured blocks has been developed in conjunction with a finite-volume method for solving chemically reacting flows on unstructured grids. Although the standalone unstructured solver, FVFLO-NCSU, is capable of resolving flows for high-speed aeropropulsion devices with complex geometries, unstructured-mesh algorithms are inherently inefficient when compared to their structured counterparts. However, the advantages of structured algorithms in developing a flow solution in a timely manner can be negated by the amount of time required to develop a mesh for complex geometries. The global domain can be split up into numerous smaller blocks during the grid-generation process to alleviate some of the difficulties in creating these complex meshes. An even greater abatement can be found by allowing the nodes on abutting block interfaces to be nonmatching or non-C 0 continuous. One code capable of solving chemically reacting flows on these multiblock grids is VULCAN, which uses a nonconservative approach for patching non-C0 block interfaces. The developed automated unstructured-grid patching algorithm has been installed within VULCAN to provide it the capability of a fully conservative approach for patching non-C0 block interfaces. Additionally, the FVFLO-NCSU solver algorithms have been deeply intertwined with the VULCAN source code to solve chemically reacting flows on these unstructured patches. Finally, the CGNS software library was added to the VULCAN postprocessor so structured and unstructured data can be stored in a single compact file. This final upgrade to VULCAN has been successfully installed and verified using test cases with particular interest towards those involving grids with non- C0 block interfaces.

  1. Peculiarities of cyclotron magnetic system calculation with the finite difference method using two-dimensional approximation

    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

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

    KAUST Repository

    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.

  3. Computable error estimates of a finite difference scheme for option pricing in exponential Lévy models

    KAUST Repository

    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.

  4. Final Report for DOE grant DE-FG02-07ER64432 "New Grid and Discretization Technologies for Ocean and Ice Simulations"

    Energy Technology Data Exchange (ETDEWEB)

    Gunzburger, Max

    2013-03-12

    The work reported is in pursuit of these goals: high-quality unstructured, non-uniform Voronoi and Delaunay grids; improved finite element and finite volume discretization schemes; and improved finite element and finite volume discretization schemes. These are sought for application to spherical and three-dimensional applications suitable for ocean, atmosphere, ice-sheet, and other climate modeling applications.

  5. Domain decomposition multigrid for unstructured grids

    Energy Technology Data Exchange (ETDEWEB)

    Shapira, Yair

    1997-01-01

    A two-level preconditioning method for the solution of elliptic boundary value problems using finite element schemes on possibly unstructured meshes is introduced. It is based on a domain decomposition and a Galerkin scheme for the coarse level vertex unknowns. For both the implementation and the analysis, it is not required that the curves of discontinuity in the coefficients of the PDE match the interfaces between subdomains. Generalizations to nonmatching or overlapping grids are made.

  6. The LHCb Grid Simulation

    CERN Multimedia

    Baranov, Alexander

    2016-01-01

    The LHCb Grid access if based on the LHCbDirac system. It provides access to data and computational resources to researchers with different geographical locations. The Grid has a hierarchical topology with multiple sites distributed over the world. The sites differ from each other by their number of CPUs, amount of disk storage and connection bandwidth. These parameters are essential for the Grid work. Moreover, job scheduling and data distribution strategy have a great impact on the grid performance. However, it is hard to choose an appropriate algorithm and strategies as they need a lot of time to be tested on the real grid. In this study, we describe the LHCb Grid simulator. The simulator reproduces the LHCb Grid structure with its sites and their number of CPUs, amount of disk storage and bandwidth connection. We demonstrate how well the simulator reproduces the grid work, show its advantages and limitations. We show how well the simulator reproduces job scheduling and network anomalies, consider methods ...

  7. Cosmos++: relativistic magnetohydrodynamics on unstructured grids with local adaptive refinement

    International Nuclear Information System (INIS)

    Salmonson, Jay D; Anninos, Peter; Fragile, P Chris; Camarda, Karen

    2007-01-01

    A code and methodology are introduced for solving the fully general relativistic magnetohydrodynamic (GRMHD) equations using time-explicit, finite-volume discretization. The code has options for solving the GRMHD equations using traditional artificial-viscosity (AV) or non-oscillatory central difference (NOCD) methods, or a new extended AV (eAV) scheme using artificial-viscosity together with a dual energy-flux-conserving formulation. The dual energy approach allows for accurate modeling of highly relativistic flows at boost factors well beyond what has been achieved to date by standard artificial viscosity methods. It provides the benefit of Godunov methods in capturing high Lorentz boosted flows but without complicated Riemann solvers, and the advantages of traditional artificial viscosity methods in their speed and flexibility. Additionally, the GRMHD equations are solved on an unstructured grid that supports local adaptive mesh refinement using a fully threaded oct-tree (in three dimensions) network to traverse the grid hierarchy across levels and immediate neighbors. Some recent studies will be summarized

  8. Differences between downscaling with spectral and grid nudging using WRF

    Directory of Open Access Journals (Sweden)

    P. Liu

    2012-04-01

    Full Text Available Dynamical downscaling has been extensively used to study regional climate forced by large-scale global climate models. During the downscaling process, however, the simulation of regional climate models (RCMs tends to drift away from the driving fields. Developing a solution that addresses this issue, by retaining the large scale features (from the large-scale fields and the small-scale features (from the RCMs has led to the development of "nudging" techniques. Here, we examine the performance of two nudging techniques, grid and spectral nudging, in the downscaling of NCEP/NCAR data with the Weather Research and Forecasting (WRF Model. The simulations are compared against the results with North America Regional Reanalysis (NARR data set at different scales of interest using the concept of similarity. We show that with the appropriate choice of wave numbers, spectral nudging outperforms grid nudging in the capacity of balancing the performance of simulation at the large and small scales.

  9. Determining Maximum Photovoltaic Penetration in a Distribution Grid considering Grid Operation Limits

    DEFF Research Database (Denmark)

    Kordheili, Reza Ahmadi; Bak-Jensen, Birgitte; Pillai, Jayakrishnan Radhakrishna

    2014-01-01

    High penetration of photovoltaic panels in distribution grid can bring the grid to its operation limits. The main focus of the paper is to determine maximum photovoltaic penetration level in the grid. Three main criteria were investigated for determining maximum penetration level of PV panels...... for this grid: even distribution of PV panels, aggregation of panels at the beginning of each feeder, and aggregation of panels at the end of each feeder. Load modeling is done using Velander formula. Since PV generation is highest in the summer due to irradiation, a summer day was chosen to determine maximum......; maximum voltage deviation of customers, cables current limits, and transformer nominal value. Voltage deviation of different buses was investigated for different penetration levels. The proposed model was simulated on a Danish distribution grid. Three different PV location scenarios were investigated...

  10. Analysis of a grid window structure for RF cavities in a Muon cooling channel

    International Nuclear Information System (INIS)

    Ladran, A.; Li, D.; Moretti, A.; Rimmer, R.; Staples, J.; Virostek, S.; Zisman, M.

    2003-01-01

    We report on the electromagnetic and thermal analysis of a grid window structure for high gradient, low frequency RF cavities. Windows may be utilized to close the beam iris and increase shunt impedance of closed-cell RF cavities. This work complements previous work presented for windows made of solid beryllium foil. An electromagnetic and thermal analysis of the thin wall tubes in a grid pattern was conducted using both MAFIA4 and ANSYS finite element analyses. The results from both codes agreed well for a variety of grid configurations and spacing. The grid configuration where the crossing tubes touched was found to have acceptable E-Fields and H-Fields performance. The thermal profiles for the grid will also be shown to determine a viable cooling profile

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

    KAUST Repository

    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.

  12. Development and application of a parallel finite volume method for flow simulation on unstructured grids with local refinement; Entwicklung und Anwendung eines parallelen Finite-Volumen-Verfahrens zur Stroemungssimulation auf unstrukturierten Gittern mit lokaler Verfeinerung

    Energy Technology Data Exchange (ETDEWEB)

    Seidl, V.

    1997-11-01

    A finite vomume method for calculation of steady and unsteady flow on unstructured grids is parallelized by local spatial and time decomposition. In the first case, a parallel variant of the conjugated gradient method with multiple local preconditioning is formulated and analyzed. The method is tested for simple applications (e.g. flow around a cylinder). The second part of the publication describes a direct numerical simulation of turbulent flow around a sphere at a Reynolds number of 5000 (based on flow velocity and sphere diameter). Current and Reynolds-averaged flow fields are discussed. Particular emphasis is placed on coordinate-independent representation of the anisotropy ratios of the Reynolds tensor and dissipation tensor. (orig.) [Deutsch] Ein Finite-Volumen-Verfahren fuer die Berechnung stationaerer und instationaerer Stroemungen auf unstrukturierten Netzen wird durch Gebietszerlegung im Raum und Zeit parallelisiert. Fuer die raeumliche Zerlegung wird eine parallele Variante der konjugierten Gradienten Methode mit mehrfacher, lokaler Vorkonditionierung formuliert und analysiert. Anhand einfacher Anwendungsbeispiele (Zylinderumstroemung, deckelgetriebene Nischenstroemung) wird das entwickelte Gesamtverfahren getestet und seine Effizienz bestimmt. Der zweite Teil der Arbeit beschreibt eine direkte numerische Simulation der turbulenten Kugelumstroemung bei einer Reynolds-Zahl von 5 000 (basierend auf Anstroemgeschwindigkeit und Kugeldurchmesser). In der Ergebnisauswertung werden augenblickliche und Reynolds-gemittelte Stroemungsfelder diskutiert und besonderer Wert auf eine koordinatenunabhaengige Darstellung der Anisotropieverhaeltnisse des Reynolds-Tensors und des Dissipationstensors gelegt. (orig.)

  13. Sparse Jacobian construction for mapped grid visco-resistive magnetohydrodynamics

    KAUST Repository

    Reynolds, Daniel R.

    2012-01-01

    We apply the automatic differentiation tool OpenAD toward constructing a preconditioner for fully implicit simulations of mapped grid visco-resistive magnetohydrodynamics (MHD), used in modeling tokamak fusion devices. Our simulation framework employs a fully implicit formulation in time, and a mapped finite volume spatial discretization. We solve this model using inexact Newton-Krylov methods. Of critical importance in these iterative solvers is the development of an effective preconditioner, which typically requires knowledge of the Jacobian of the nonlinear residual function. However, due to significant nonlinearity within our PDE system, our mapped spatial discretization, and stencil adaptivity at physical boundaries, analytical derivation of these Jacobian entries is highly nontrivial. This paper therefore focuses on Jacobian construction using automatic differentiation. In particular, we discuss applying OpenAD to the case of a spatially-adaptive stencil patch that automatically handles differences between the domain interior and boundary, and configuring AD for reduced stencil approximations to the Jacobian. We investigate both scalar and vector tangent mode differentiation, along with simple finite difference approaches, to compare the resulting accuracy and efficiency of Jacobian construction in this application. © 2012 Springer-Verlag.

  14. Global 3-D FDTD Maxwell's-Equations Modeling of Ionospheric Disturbances Associated with Earthquakes Using an Optimized Geodesic Grid

    Science.gov (United States)

    Simpson, J. J.; Taflove, A.

    2005-12-01

    We report a finite-difference time-domain (FDTD) computational solution of Maxwell's equations [1] that models the possibility of detecting and characterizing ionospheric disturbances above seismic regions. Specifically, we study anomalies in Schumann resonance spectra in the extremely low frequency (ELF) range below 30 Hz as observed in Japan caused by a hypothetical cylindrical ionospheric disturbance above Taiwan. We consider excitation of the global Earth-ionosphere waveguide by lightning in three major thunderstorm regions of the world: Southeast Asia, South America (Amazon region), and Africa. Furthermore, we investigate varying geometries and characteristics of the ionospheric disturbance above Taiwan. The FDTD technique used in this study enables a direct, full-vector, three-dimensional (3-D) time-domain Maxwell's equations calculation of round-the-world ELF propagation accounting for arbitrary horizontal as well as vertical geometrical and electrical inhomogeneities and anisotropies of the excitation, ionosphere, lithosphere, and oceans. Our entire-Earth model grids the annular lithosphere-atmosphere volume within 100 km of sea level, and contains over 6,500,000 grid-points (63 km laterally between adjacent grid points, 5 km radial resolution). We use our recently developed spherical geodesic gridding technique having a spatial discretization best described as resembling the surface of a soccer ball [2]. The grid is comprised entirely of hexagonal cells except for a small fixed number of pentagonal cells needed for completion. Grid-cell areas and locations are optimized to yield a smoothly varying area difference between adjacent cells, thereby maximizing numerical convergence. We compare our calculated results with measured data prior to the Chi-Chi earthquake in Taiwan as reported by Hayakawa et. al. [3]. Acknowledgement This work was suggested by Dr. Masashi Hayakawa, University of Electro-Communications, Chofugaoka, Chofu Tokyo. References [1] A

  15. Review of the modified finite particle method and application to incompressible solids

    Directory of Open Access Journals (Sweden)

    D Asprone

    2016-10-01

    Full Text Available This paper focuses on the application of the Modified Finite Particle Method (MFPM on incompressibile elasticity problems. MFPM belongs to the class of meshless methods, nowadays widely investigated due to their characteristics of being totally free of any kind of grid or mesh. This characteristic makes meshless methods potentially useful for the study of large deformations problems and fluid dynamics. In particular, the aim of the work is to compare the results obtained with a simple displacement-based formulation, in the limit of incompressibility, and some formulations proposed in the literature for full incompressibility, where the typical divergence-free constraint is replaced by a different equation, the so-called Pressure Poisson Equation. The obtained results show that the MFPM achieves the expected second-order accuracy on formulation where the equations imposed as constraint satisfies also the original incompressibility equation. Other formulations, differently, do not satisfy the incompressibility constraint, and thus, they are not successfully applicable with the Modified Finite Particle Method.

  16. Finite Element Study of Three Different Treatment Designs of a Mandibular Three Implant-Retained Overdenture

    Directory of Open Access Journals (Sweden)

    M. Shishesaz

    Full Text Available Abstract This study compares ball, bar-clip and bar-ball attachment systems for implant-retained mandibular overdentures with three implants. The first implant is placed in the middle of the mandible and the other two are imbedded in the first premolar regions. Linear elastic finite element analysis is used for design analysis. Three dimensional geometry of the mandible is generated from computed tomography. Other parts are modeled using SolidWorks software. The foodstuff is positioned at the right first molar, representing the most frequent masticating situation. To obtain accurate mesh-independent results, finite element models are solved using several mesh grids. They are then validated by means of a detailed convergence analysis. The results demonstrate that the highest von-Mises stress in the bone is always located around the neck of the implant, at its upper threads. Ball and bar-ball attachments transfer the highest and lowest stresses to the bone surrounding the implants, respectively. The lowest stresses in the cortical and cancellous bones are due to bar-ball attachment. Yet, the overdenture gets its maximum movement for this arrangement. Consequently, the use of bar-ball attachment is only recommended for the cases in which stress transferred to peri-implant bone is more important than overdenture stability. Among the three treatment designs, ball attachment seems to exhibit the lowest lateral and overall displacements and hence, better overdenture stability.

  17. Modeling 3D Dynamic Rupture on Arbitrarily-Shaped faults by Boundary-Conforming Finite Difference Method

    Science.gov (United States)

    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.

  18. A new variational formulation of kinetic plasma theory and the application of moving finite elements

    International Nuclear Information System (INIS)

    Glasser, A.H.

    1991-01-01

    A new variational formulation has been developed for the system of equations governing kinetic plasmas and electromagnetic fields. It is used to apply the method of Moving Finite Elements to the electromagnetic fields. The fields are expanded in a basis of linear finite elements on a movable, unstructured grid of triangles in 2D or tetrahedra in 3D, while the plasma distribution function is expanded in a basis of super particles. Minimization of the variational with respect to the time derivatives of the field quantities yields a coupled system of equations for simultaneously advancing the amplitudes and node positions, resulting in adaptive grid motion. The adaptivity of the grid may save a large factor in the size of the grid and the number of particles required in many problems. Minimization of the variational with respect to the time derivatives of the particle positions and velocities gives the equations of motion, providing consistent prescriptions for assigning particles to the grid and fields to the particles. Orthogonality conditions on the particles are derived as conditions for keeping their equations of motion independent. Collisions can be included in a natural way. The relationship between PIC methods and alternative methods of discretizing phase space is clarified

  19. Harmonics Suppression for Single-Phase Grid-Connected Photovoltaic Systems in Different Operation Modes

    DEFF Research Database (Denmark)

    Yang, Yongheng; Zhou, Keliang; Blaabjerg, Frede

    2013-01-01

    -connected PV inverters may be severely affected in different operation modes. In this paper, a detailed analysis is conducted to reveal the relationship between the harmonics level with the power factor and the current level in the PV systems. A current control solution which employs an Internal Model...... Principle (IMP) is proposed to suppress the harmonic currents injected into the grid. Experiments are carried out to verify the analysis and the performance of the proposed control method. It is demonstrated that the proposed method presents an effective solution to harmonics suppression for single......-phase grid-connected PV systems in different operation modes. Especially, it can remove higher order harmonics effectively leading to a better power quality compared to the Proportional plus Multi-Resonant Controller, and it has less computational burden....

  20. An h-adaptive finite element method for turbulent heat transfer

    Energy Technology Data Exchange (ETDEWEB)

    Carriington, David B [Los Alamos National Laboratory

    2009-01-01

    A two-equation turbulence closure model (k-{omega}) using an h-adaptive grid technique and finite element method (FEM) has been developed to simulate low Mach flow and heat transfer. These flows are applicable to many flows in engineering and environmental sciences. Of particular interest in the engineering modeling areas are: combustion, solidification, and heat exchanger design. Flows for indoor air quality modeling and atmospheric pollution transport are typical types of environmental flows modeled with this method. The numerical method is based on a hybrid finite element model using an equal-order projection process. The model includes thermal and species transport, localized mesh refinement (h-adaptive) and Petrov-Galerkin weighting for the stabilizing the advection. This work develops the continuum model of a two-equation turbulence closure method. The fractional step solution method is stated along with the h-adaptive grid method (Carrington and Pepper, 2002). Solutions are presented for 2d flow over a backward-facing step.

  1. Coupling multipoint flux mixed finite element methodswith continuous Galerkin methods for poroelasticity

    KAUST Repository

    Wheeler, Mary; Xue, Guangri; Yotov, Ivan

    2013-01-01

    We study the numerical approximation on irregular domains with general grids of the system of poroelasticity, which describes fluid flow in deformable porous media. The flow equation is discretized by a multipoint flux mixed finite element method

  2. Stress Analysis of Single Spacer Grid Support considering Fuel Rod

    Energy Technology Data Exchange (ETDEWEB)

    Yoo, Y. G.; Jung, D. H.; Kim, J. H. [Chungnam National University, Daejeon (Korea, Republic of); Park, J. K.; Jeon, K. L. [Korea Nuclear Fuel, Daejeon (Korea, Republic of)

    2010-10-15

    Pressurized water reactor (PWR) nuclear fuel assembly is mainly composed of a top-end piece, a bottom-end piece, lots of fuel rods, and several spacer grids. Among them, the main function of spacer grid is protecting fuel rods from Fluid Induced Vibration (FIV). The cross section of spacer grid assembled by laser welding in upper and lower point. When the fuel rod inserted in spacer gird, spring and dimple and around of welded area got a stresses. The main hypothesis of this analysis is the boundary area of HAZ and base metal can get a lot of damage than other area by FIV. So, design factors of spacer grid mainly considered to preventing the fatigue failure in HAZ and spring and dimple of spacer grid. From previous researching, the environment in reactor verified. Pressure and temperature of light water observed 15MPa and 320 .deg. C, and vibration of the fuel rod observed within 0 {approx} 50Hz. In this study, mechanical properties of zirconium alloy that extracted from the test and the spacer grid model which used in the PWR were applied in stress analyzing. General-purpose finite element analysis program was used ANSYS Workbench 12.0.1 version. 3-D CAD program CATIA was used to create spacer grid model

  3. Mapping of grid faults and grid codes

    DEFF Research Database (Denmark)

    Iov, F.; Hansen, Anca Daniela; Sørensen, Poul Ejnar

    loads of wind turbines. The goal is also to clarify and define possible new directions in the certification process of power plant wind turbines, namely wind turbines, which participate actively in the stabilisation of power systems. Practical experience shows that there is a need...... challenges for the design of both the electrical system and the mechanical structure of wind turbines. An overview over the frequency of grid faults and the grid connection requirements in different relevant countries is done in this report. The most relevant study cases for the quantification of the loads......The present report is a part of the research project ''Grid fault and designbasis for wind turbine'' supported by Energinet.dk through the grant PSO F&U 6319. The objective of this project is to investigate into the consequences of the new grid connection requirements for the fatigue and extreme...

  4. A parallel finite-volume finite-element method for transient compressible turbulent flows with heat transfer

    International Nuclear Information System (INIS)

    Masoud Ziaei-Rad

    2010-01-01

    In this paper, a two-dimensional numerical scheme is presented for the simulation of turbulent, viscous, transient compressible flows in the simultaneously developing hydraulic and thermal boundary layer region. The numerical procedure is a finite-volume-based finite-element method applied to unstructured grids. This combination together with a new method applied for the boundary conditions allows for accurate computation of the variables in the entrance region and for a wide range of flow fields from subsonic to transonic. The Roe-Riemann solver is used for the convective terms, whereas the standard Galerkin technique is applied for the viscous terms. A modified κ-ε model with a two-layer equation for the near-wall region combined with a compressibility correction is used to predict the turbulent viscosity. Parallel processing is also employed to divide the computational domain among the different processors to reduce the computational time. The method is applied to some test cases in order to verify the numerical accuracy. The results show significant differences between incompressible and compressible flows in the friction coefficient, Nusselt number, shear stress and the ratio of the compressible turbulent viscosity to the molecular viscosity along the developing region. A transient flow generated after an accidental rupture in a pipeline was also studied as a test case. The results show that the present numerical scheme is stable, accurate and efficient enough to solve the problem of transient wall-bounded flow.

  5. 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...

  6. Generating Free-Form Grid Truss Structures from 3D Scanned Point Clouds

    Directory of Open Access Journals (Sweden)

    Hui Ding

    2017-01-01

    Full Text Available Reconstruction, according to physical shape, is a novel way to generate free-form grid truss structures. 3D scanning is an effective means of acquiring physical form information and it generates dense point clouds on surfaces of objects. However, generating grid truss structures from point clouds is still a challenge. Based on the advancing front technique (AFT which is widely used in Finite Element Method (FEM, a scheme for generating grid truss structures from 3D scanned point clouds is proposed in this paper. Based on the characteristics of point cloud data, the search box is adopted to reduce the search space in grid generating. A front advancing procedure suit for point clouds is established. Delaunay method and Laplacian method are used to improve the quality of the generated grids, and an adjustment strategy that locates grid nodes at appointed places is proposed. Several examples of generating grid truss structures from 3D scanned point clouds of seashells are carried out to verify the proposed scheme. Physical models of the grid truss structures generated in the examples are manufactured by 3D print, which solidifies the feasibility of the scheme.

  7. An unstaggered central scheme on nonuniform grids for the simulation of a compressible two-phase flow model

    Energy Technology Data Exchange (ETDEWEB)

    Touma, Rony [Department of Computer Science & Mathematics, Lebanese American University, Beirut (Lebanon); Zeidan, Dia [School of Basic Sciences and Humanities, German Jordanian University, Amman (Jordan)

    2016-06-08

    In this paper we extend a central finite volume method on nonuniform grids to the case of drift-flux two-phase flow problems. The numerical base scheme is an unstaggered, non oscillatory, second-order accurate finite volume scheme that evolves a piecewise linear numerical solution on a single grid and uses dual cells intermediately while updating the numerical solution to avoid the resolution of the Riemann problems arising at the cell interfaces. We then apply the numerical scheme and solve a classical drift-flux problem. The obtained results are in good agreement with corresponding ones appearing in the recent literature, thus confirming the potential of the proposed scheme.

  8. Finite difference time domain modeling of spiral antennas

    Science.gov (United States)

    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.

  9. 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.

  10. A Posteriori Error Estimation for Finite Element Methods and Iterative Linear Solvers

    Energy Technology Data Exchange (ETDEWEB)

    Melboe, Hallgeir

    2001-10-01

    This thesis addresses a posteriori error estimation for finite element methods and iterative linear solvers. Adaptive finite element methods have gained a lot of popularity over the last decades due to their ability to produce accurate results with limited computer power. In these methods a posteriori error estimates play an essential role. Not only do they give information about how large the total error is, they also indicate which parts of the computational domain should be given a more sophisticated treatment in order to reduce the error. A posteriori error estimates are traditionally aimed at estimating the global error, but more recently so called goal oriented error estimators have been shown a lot of interest. The name reflects the fact that they estimate the error in user-defined local quantities. In this thesis the main focus is on global error estimators for highly stretched grids and goal oriented error estimators for flow problems on regular grids. Numerical methods for partial differential equations, such as finite element methods and other similar techniques, typically result in a linear system of equations that needs to be solved. Usually such systems are solved using some iterative procedure which due to a finite number of iterations introduces an additional error. Most such algorithms apply the residual in the stopping criterion, whereas the control of the actual error may be rather poor. A secondary focus in this thesis is on estimating the errors that are introduced during this last part of the solution procedure. The thesis contains new theoretical results regarding the behaviour of some well known, and a few new, a posteriori error estimators for finite element methods on anisotropic grids. Further, a goal oriented strategy for the computation of forces in flow problems is devised and investigated. Finally, an approach for estimating the actual errors associated with the iterative solution of linear systems of equations is suggested. (author)

  11. 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

  12. Preliminary research on finite difference method to solve radon field distribution over sandstone-type uranium ore body

    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)

  13. A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation

    KAUST Repository

    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.

  14. The Grid2003 Production Grid Principles and Practice

    CERN Document Server

    Foster, I; Gose, S; Maltsev, N; May, E; Rodríguez, A; Sulakhe, D; Vaniachine, A; Shank, J; Youssef, S; Adams, D; Baker, R; Deng, W; Smith, J; Yu, D; Legrand, I; Singh, S; Steenberg, C; Xia, Y; Afaq, A; Berman, E; Annis, J; Bauerdick, L A T; Ernst, M; Fisk, I; Giacchetti, L; Graham, G; Heavey, A; Kaiser, J; Kuropatkin, N; Pordes, R; Sekhri, V; Weigand, J; Wu, Y; Baker, K; Sorrillo, L; Huth, J; Allen, M; Grundhoefer, L; Hicks, J; Luehring, F C; Peck, S; Quick, R; Simms, S; Fekete, G; Van den Berg, J; Cho, K; Kwon, K; Son, D; Park, H; Canon, S; Jackson, K; Konerding, D E; Lee, J; Olson, D; Sakrejda, I; Tierney, B; Green, M; Miller, R; Letts, J; Martin, T; Bury, D; Dumitrescu, C; Engh, D; Gardner, R; Mambelli, M; Smirnov, Y; Voeckler, J; Wilde, M; Zhao, Y; Zhao, X; Avery, P; Cavanaugh, R J; Kim, B; Prescott, C; Rodríguez, J; Zahn, A; McKee, S; Jordan, C; Prewett, J; Thomas, T; Severini, H; Clifford, B; Deelman, E; Flon, L; Kesselman, C; Mehta, G; Olomu, N; Vahi, K; De, K; McGuigan, P; Sosebee, M; Bradley, D; Couvares, P; De Smet, A; Kireyev, C; Paulson, E; Roy, A; Koranda, S; Moe, B; Brown, B; Sheldon, P

    2004-01-01

    The Grid2003 Project has deployed a multi-virtual organization, application-driven grid laboratory ("GridS") that has sustained for several months the production-level services required by physics experiments of the Large Hadron Collider at CERN (ATLAS and CMS), the Sloan Digital Sky Survey project, the gravitational wave search experiment LIGO, the BTeV experiment at Fermilab, as well as applications in molecular structure analysis and genome analysis, and computer science research projects in such areas as job and data scheduling. The deployed infrastructure has been operating since November 2003 with 27 sites, a peak of 2800 processors, work loads from 10 different applications exceeding 1300 simultaneous jobs, and data transfers among sites of greater than 2 TB/day. We describe the principles that have guided the development of this unique infrastructure and the practical experiences that have resulted from its creation and use. We discuss application requirements for grid services deployment and configur...

  15. Current Grid operation and future role of the Grid

    Science.gov (United States)

    Smirnova, O.

    2012-12-01

    Grid-like technologies and approaches became an integral part of HEP experiments. Some other scientific communities also use similar technologies for data-intensive computations. The distinct feature of Grid computing is the ability to federate heterogeneous resources of different ownership into a seamless infrastructure, accessible via a single log-on. Like other infrastructures of similar nature, Grid functioning requires not only technologically sound basis, but also reliable operation procedures, monitoring and accounting. The two aspects, technological and operational, are closely related: weaker is the technology, more burden is on operations, and other way around. As of today, Grid technologies are still evolving: at CERN alone, every LHC experiment uses an own Grid-like system. This inevitably creates a heavy load on operations. Infrastructure maintenance, monitoring and incident response are done on several levels, from local system administrators to large international organisations, involving massive human effort worldwide. The necessity to commit substantial resources is one of the obstacles faced by smaller research communities when moving computing to the Grid. Moreover, most current Grid solutions were developed under significant influence of HEP use cases, and thus need additional effort to adapt them to other applications. Reluctance of many non-HEP researchers to use Grid negatively affects the outlook for national Grid organisations, which strive to provide multi-science services. We started from the situation where Grid organisations were fused with HEP laboratories and national HEP research programmes; we hope to move towards the world where Grid will ultimately reach the status of generic public computing and storage service provider and permanent national and international Grid infrastructures will be established. How far will we be able to advance along this path, depends on us. If no standardisation and convergence efforts will take place

  16. Current Grid operation and future role of the Grid

    International Nuclear Information System (INIS)

    Smirnova, O

    2012-01-01

    Grid-like technologies and approaches became an integral part of HEP experiments. Some other scientific communities also use similar technologies for data-intensive computations. The distinct feature of Grid computing is the ability to federate heterogeneous resources of different ownership into a seamless infrastructure, accessible via a single log-on. Like other infrastructures of similar nature, Grid functioning requires not only technologically sound basis, but also reliable operation procedures, monitoring and accounting. The two aspects, technological and operational, are closely related: weaker is the technology, more burden is on operations, and other way around. As of today, Grid technologies are still evolving: at CERN alone, every LHC experiment uses an own Grid-like system. This inevitably creates a heavy load on operations. Infrastructure maintenance, monitoring and incident response are done on several levels, from local system administrators to large international organisations, involving massive human effort worldwide. The necessity to commit substantial resources is one of the obstacles faced by smaller research communities when moving computing to the Grid. Moreover, most current Grid solutions were developed under significant influence of HEP use cases, and thus need additional effort to adapt them to other applications. Reluctance of many non-HEP researchers to use Grid negatively affects the outlook for national Grid organisations, which strive to provide multi-science services. We started from the situation where Grid organisations were fused with HEP laboratories and national HEP research programmes; we hope to move towards the world where Grid will ultimately reach the status of generic public computing and storage service provider and permanent national and international Grid infrastructures will be established. How far will we be able to advance along this path, depends on us. If no standardisation and convergence efforts will take place

  17. Study of the integration of distributed generation systems in the grid: application in micro-grids

    International Nuclear Information System (INIS)

    Gaztanaga Arantzamendi, H.

    2006-12-01

    The present PhD deals with an original micro-grid concept and its application as a Renewable Energy Source's (RES) grid integration scheme. This micro-grid is composed of RES generators as well as support systems that incorporate additional functionalities in order to improve RES integration into the grid. According to this concept, two practical micro-grid applications have been studied in detail: a residential micro-grid and a wind farm supported by DFACTS systems (STATCOM and DVR). In both applications, the control structures which are implemented at different levels and applied to the different micro-grid elements have been developed, analyzed by means of off-line simulations and finally validated in real-time conditions with physical reduced-scale prototypes. (author)

  18. Dual-mixed finite elements for the three-field Stokes model as a finite volume method on staggered grids

    KAUST Repository

    Kou, Jisheng; Sun, Shuyu

    2017-01-01

    In this paper, a new three-field weak formulation for Stokes problems is developed, and from this, a dual-mixed finite element method is proposed on a rectangular mesh. In the proposed mixed methods, the components of stress tensor are approximated

  19. Energy Stability Analysis of Some Fully Discrete Numerical Schemes for Incompressible Navier–Stokes Equations on Staggered Grids

    KAUST Repository

    Chen, Huangxin

    2017-09-01

    In this paper we consider the energy stability estimates for some fully discrete schemes which both consider time and spatial discretizations for the incompressible Navier–Stokes equations. We focus on three kinds of fully discrete schemes, i.e., the linear implicit scheme for time discretization with the finite difference method (FDM) on staggered grids for spatial discretization, pressure-correction schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations, and pressure-stabilization schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations. The energy stability estimates are obtained for the above each fully discrete scheme. The upwind scheme is used in the discretization of the convection term which plays an important role in the design of unconditionally stable discrete schemes. Numerical results are given to verify the theoretical analysis.

  20. Impact analysis of the spacer grid assembly and shape optimization of the attached spring

    Energy Technology Data Exchange (ETDEWEB)

    Park, K. J.; Lee, Z. N. [Hanyang University, Seoul (Korea)

    2002-04-01

    Spacer grids support fuel rods and maintain geometry from external impact loads. A simulation is performed for the strength of a spacer grid under the impact load. The critical impact load that leads to plastic deformation is identified by a free-fall test. A finite element model is established for the nonlinear simulation of the impact process. The simulation model is tuned based on the free-fall test. The model considers the aspects of welding and the contacts between components. Nonlinear finite element analysis is carried out using a software system called ABAQUS/EXPLICIT. The results are discussed from a design viewpoint. Design requirements are defined and a design process is established. The design process includes mathematical optimization as well as practical design method. The shape of the grid spring is designed to maintain its function during the lifetime of the fuel assembly. A structural optimization method is employed for the shape design. A good design is found. Commercial codes are utilized for structural analysis and optimization. 18 refs., 61 figs., 3 tabs. (Author)

  1. Porting of Scientific Applications to Grid Computing on GridWay

    Directory of Open Access Journals (Sweden)

    J. Herrera

    2005-01-01

    Full Text Available The expansion and adoption of Grid technologies is prevented by the lack of a standard programming paradigm to port existing applications among different environments. The Distributed Resource Management Application API has been proposed to aid the rapid development and distribution of these applications across different Distributed Resource Management Systems. In this paper we describe an implementation of the DRMAA standard on a Globus-based testbed, and show its suitability to express typical scientific applications, like High-Throughput and Master-Worker applications. The DRMAA routines are supported by the functionality offered by the GridWay2 framework, which provides the runtime mechanisms needed for transparently executing jobs on a dynamic Grid environment based on Globus. As cases of study, we consider the implementation with DRMAA of a bioinformatics application, a genetic algorithm and the NAS Grid Benchmarks.

  2. Mapping of grid faults and grid codes

    DEFF Research Database (Denmark)

    Iov, Florin; Hansen, A.D.; Sørensen, P.

    loads of wind turbines. The goal is also to clarify and define possible new directions in the certification process of power plant wind turbines, namely wind turbines, which participate actively in the stabilisation of power systems. Practical experience shows that there is a need...... challenges for the design of both the electrical system and the mechanical structure of wind turbines. An overview over the frequency of grid faults and the grid connection requirements in different relevant countries is done in this report. The most relevant study cases for the quantification of the loads......The present report is a part of the research project "Grid fault and design basis for wind turbine" supported by Energinet.dk through the grant PSO F&U 6319. The objective of this project is to investigate into the consequences of the new grid connection requirements for the fatigue and extreme...

  3. 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.

  4. A Fourier analysis on the maximum acceptable grid size for discrete proton beam dose calculation

    International Nuclear Information System (INIS)

    Li, Haisen S.; Romeijn, H. Edwin; Dempsey, James F.

    2006-01-01

    We developed an analytical method for determining the maximum acceptable grid size for discrete dose calculation in proton therapy treatment plan optimization, so that the accuracy of the optimized dose distribution is guaranteed in the phase of dose sampling and the superfluous computational work is avoided. The accuracy of dose sampling was judged by the criterion that the continuous dose distribution could be reconstructed from the discrete dose within a 2% error limit. To keep the error caused by the discrete dose sampling under a 2% limit, the dose grid size cannot exceed a maximum acceptable value. The method was based on Fourier analysis and the Shannon-Nyquist sampling theorem as an extension of our previous analysis for photon beam intensity modulated radiation therapy [J. F. Dempsey, H. E. Romeijn, J. G. Li, D. A. Low, and J. R. Palta, Med. Phys. 32, 380-388 (2005)]. The proton beam model used for the analysis was a near mono-energetic (of width about 1% the incident energy) and monodirectional infinitesimal (nonintegrated) pencil beam in water medium. By monodirection, we mean that the proton particles are in the same direction before entering the water medium and the various scattering prior to entrance to water is not taken into account. In intensity modulated proton therapy, the elementary intensity modulation entity for proton therapy is either an infinitesimal or finite sized beamlet. Since a finite sized beamlet is the superposition of infinitesimal pencil beams, the result of the maximum acceptable grid size obtained with infinitesimal pencil beam also applies to finite sized beamlet. The analytic Bragg curve function proposed by Bortfeld [T. Bortfeld, Med. Phys. 24, 2024-2033 (1997)] was employed. The lateral profile was approximated by a depth dependent Gaussian distribution. The model included the spreads of the Bragg peak and the lateral profiles due to multiple Coulomb scattering. The dependence of the maximum acceptable dose grid size on the

  5. Hybrid finite difference/finite element solution method development for non-linear superconducting magnet and electrical circuit breakdown transient analysis

    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)

  6. Grid Transmission Expansion Planning Model Based on Grid Vulnerability

    Science.gov (United States)

    Tang, Quan; Wang, Xi; Li, Ting; Zhang, Quanming; Zhang, Hongli; Li, Huaqiang

    2018-03-01

    Based on grid vulnerability and uniformity theory, proposed global network structure and state vulnerability factor model used to measure different grid models. established a multi-objective power grid planning model which considering the global power network vulnerability, economy and grid security constraint. Using improved chaos crossover and mutation genetic algorithm to optimize the optimal plan. For the problem of multi-objective optimization, dimension is not uniform, the weight is not easy given. Using principal component analysis (PCA) method to comprehensive assessment of the population every generation, make the results more objective and credible assessment. the feasibility and effectiveness of the proposed model are validated by simulation results of Garver-6 bus system and Garver-18 bus.

  7. Finite-Element 2D and 3D PIC Modeling of RF Devices with Applications to Multipacting

    CERN Document Server

    De Ford, John F; Petillo, John

    2005-01-01

    Multipacting currently limits the performance of many high power radio-frequency (RF) devices, particularly couplers and windows. Models have helped researchers understand and mitigate this problem in 2D structures, but useful multipacting models for complicated 3D structures are still a challenge. A combination of three recent technologies that have been developed in the Analyst and MICHELLE codes begin to address this challenge: high-order adaptive finite-element RF field calculations, advanced particle tracking on unstructured grids, and comprehensive secondary emission models. Analyst employs high-order adaptive finite-element methods to accurately compute driven RF fields and eigenmodes in complex geometries, particularly near edges, corners, and curved surfaces. To perform a multipacting analysis, we use the mesh and fields from Analyst in a modified version of the self-consistent, finite-element gun code MICHELLE. MICHELLE has both a fast, accurate, and reliable particle tracker for unstructured grids ...

  8. Moving finite elements: A continuously adaptive method for computational fluid dynamics

    International Nuclear Information System (INIS)

    Glasser, A.H.; Miller, K.; Carlson, N.

    1991-01-01

    Moving Finite Elements (MFE), a recently developed method for computational fluid dynamics, promises major advances in the ability of computers to model the complex behavior of liquids, gases, and plasmas. Applications of computational fluid dynamics occur in a wide range of scientifically and technologically important fields. Examples include meteorology, oceanography, global climate modeling, magnetic and inertial fusion energy research, semiconductor fabrication, biophysics, automobile and aircraft design, industrial fluid processing, chemical engineering, and combustion research. The improvements made possible by the new method could thus have substantial economic impact. Moving Finite Elements is a moving node adaptive grid method which has a tendency to pack the grid finely in regions where it is most needed at each time and to leave it coarse elsewhere. It does so in a manner which is simple and automatic, and does not require a large amount of human ingenuity to apply it to each particular problem. At the same time, it often allows the time step to be large enough to advance a moving shock by many shock thicknesses in a single time step, moving the grid smoothly with the solution and minimizing the number of time steps required for the whole problem. For 2D problems (two spatial variables) the grid is composed of irregularly shaped and irregularly connected triangles which are very flexible in their ability to adapt to the evolving solution. While other adaptive grid methods have been developed which share some of these desirable properties, this is the only method which combines them all. In many cases, the method can save orders of magnitude of computing time, equivalent to several generations of advancing computer hardware

  9. High-order asynchrony-tolerant finite difference schemes for partial differential equations

    Science.gov (United States)

    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.

  10. Domain-adaptive finite difference methods for collapsing annular liquid jets

    Science.gov (United States)

    Ramos, J. I.

    1993-01-01

    A domain-adaptive technique which maps a time-dependent, curvilinear geometry into a unit square is used to determine the steady state mass absorption rate and the collapse of annular liquid jets. A method of lines is used to solve the one-dimensional fluid dynamics equations written in weak conservation-law form, and upwind differences are employed to evaluate the axial convective fluxes. The unknown, time-dependent, axial location of the downstream boundary is determined from the solution of an ordinary differential equation which is nonlinearly coupled to the fluid dynamics and gas concentration equations. The equation for the gas concentration in the annular liquid jet is written in strong conservation-law form and solved by means of a method of lines at high Peclet numbers and a line Gauss-Seidel method at low Peclet numbers. The effects of the number of grid points along and across the annular jet, time step, and discretization of the radial convective fluxes on both the steady state mass absorption rate and the jet's collapse rate have been analyzed on staggered and non-staggered grids. The steady state mass absorption rate and the collapse of annular liquid jets are determined as a function of the Froude, Peclet and Weber numbers, annular jet's thickness-to-radius ratio at the nozzle exit, initial pressure difference across the annular jet, nozzle exit angle, temperature of the gas enclosed by the annular jet, pressure of the gas surrounding the jet, solubilities at the inner and outer interfaces of the annular jet, and gas concentration at the nozzle exit. It is shown that the steady state mass absorption rate is proportional to the inverse square root of the Peclet number except for low values of this parameter, and that the possible mathematical incompatibilities in the concentration field at the nozzle exit exert a great influence on the steady state mass absorption rate and on the jet collapse. It is also shown that the steady state mass absorption

  11. 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

  12. 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.

  13. 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

  14. Examining inter-family differences in intra-family (parent-adolescent) dynamics using grid-sequence analysis.

    Science.gov (United States)

    Brinberg, Miriam; Fosco, Gregory M; Ram, Nilam

    2017-12-01

    Family systems theorists have forwarded a set of theoretical principles meant to guide family scientists and practitioners in their conceptualization of patterns of family interaction-intra-family dynamics-that, over time, give rise to family and individual dysfunction and/or adaptation. In this article, we present an analytic approach that merges state space grid methods adapted from the dynamic systems literature with sequence analysis methods adapted from molecular biology into a "grid-sequence" method for studying inter-family differences in intra-family dynamics. Using dyadic data from 86 parent-adolescent dyads who provided up to 21 daily reports about connectedness, we illustrate how grid-sequence analysis can be used to identify a typology of intrafamily dynamics and to inform theory about how specific types of intrafamily dynamics contribute to adolescent behavior problems and family members' mental health. Methodologically, grid-sequence analysis extends the toolbox of techniques for analysis of family experience sampling and daily diary data. Substantively, we identify patterns of family level microdynamics that may serve as new markers of risk/protective factors and potential points for intervention in families. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

  15. Comparative analysis of the application of different Low Power Wide Area Network technologies in power grid

    Science.gov (United States)

    Wang, Hao; Sui, Hong; Liao, Xing; Li, Junhao

    2018-03-01

    Low Power Wide Area Network (LPWAN) technologies developed rapidly in recent years, but the application principle of different LPWAN technologies in power grid is still not clear. This paper gives a comparative analysis of two mainstream LPWAN technologies including NB-IoT and LoRa, and gives an application suggestion of these two LPWAN technologies, which can guide the planning and construction of LPWAN in power grid.

  16. Trends in life science grid: from computing grid to knowledge grid

    Directory of Open Access Journals (Sweden)

    Konagaya Akihiko

    2006-12-01

    Full Text Available Abstract Background Grid computing has great potential to become a standard cyberinfrastructure for life sciences which often require high-performance computing and large data handling which exceeds the computing capacity of a single institution. Results This survey reviews the latest grid technologies from the viewpoints of computing grid, data grid and knowledge grid. Computing grid technologies have been matured enough to solve high-throughput real-world life scientific problems. Data grid technologies are strong candidates for realizing "resourceome" for bioinformatics. Knowledge grids should be designed not only from sharing explicit knowledge on computers but also from community formulation for sharing tacit knowledge among a community. Conclusion Extending the concept of grid from computing grid to knowledge grid, it is possible to make use of a grid as not only sharable computing resources, but also as time and place in which people work together, create knowledge, and share knowledge and experiences in a community.

  17. Lagrangian displacement tracking using a polar grid between endocardial and epicardial contours for cardiac strain imaging.

    Science.gov (United States)

    Ma, Chi; Varghese, Tomy

    2012-04-01

    Accurate cardiac deformation analysis for cardiac displacement and strain imaging over time requires Lagrangian description of deformation of myocardial tissue structures. Failure to couple the estimated displacement and strain information with the correct myocardial tissue structures will lead to erroneous result in the displacement and strain distribution over time. Lagrangian based tracking in this paper divides the tissue structure into a fixed number of pixels whose deformation is tracked over the cardiac cycle. An algorithm that utilizes a polar-grid generated between the estimated endocardial and epicardial contours for cardiac short axis images is proposed to ensure Lagrangian description of the pixels. Displacement estimates from consecutive radiofrequency frames were then mapped onto the polar grid to obtain a distribution of the actual displacement that is mapped to the polar grid over time. A finite element based canine heart model coupled with an ultrasound simulation program was used to verify this approach. Segmental analysis of the accumulated displacement and strain over a cardiac cycle demonstrate excellent agreement between the ideal result obtained directly from the finite element model and our Lagrangian approach to strain estimation. Traditional Eulerian based estimation results, on the other hand, show significant deviation from the ideal result. An in vivo comparison of the displacement and strain estimated using parasternal short axis views is also presented. Lagrangian displacement tracking using a polar grid provides accurate tracking of myocardial deformation demonstrated using both finite element and in vivo radiofrequency data acquired on a volunteer. In addition to the cardiac application, this approach can also be utilized for transverse scans of arteries, where a polar grid can be generated between the contours delineating the outer and inner wall of the vessels from the blood flowing though the vessel.

  18. Non Standard Finite Difference Scheme for Mutualistic Interaction Description

    OpenAIRE

    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...

  19. 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.

  20. 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.

  1. A finite element propagation model for extracting normal incidence impedance in nonprogressive acoustic wave fields

    Science.gov (United States)

    Watson, Willie R.; Jones, Michael G.; Tanner, Sharon E.; Parrott, Tony L.

    1995-01-01

    A propagation model method for extracting the normal incidence impedance of an acoustic material installed as a finite length segment in a wall of a duct carrying a nonprogressive wave field is presented. The method recasts the determination of the unknown impedance as the minimization of the normalized wall pressure error function. A finite element propagation model is combined with a coarse/fine grid impedance plane search technique to extract the impedance of the material. Results are presented for three different materials for which the impedance is known. For each material, the input data required for the prediction scheme was computed from modal theory and then contaminated by random error. The finite element method reproduces the known impedance of each material almost exactly for random errors typical of those found in many measurement environments. Thus, the method developed here provides a means for determining the impedance of materials in a nonprogressirve wave environment such as that usually encountered in a commercial aircraft engine and most laboratory settings.

  2. Development of a multi-grid FDTD code for three-dimensional simulation of large microwave sintering experiments

    Energy Technology Data Exchange (ETDEWEB)

    White, M.J.; Iskander, M.F. [Univ. of Utah, Salt Lake City, UT (United States). Electrical Engineering Dept.; Kimrey, H.D. [Oak Ridge National Lab., TN (United States)

    1996-12-31

    The Finite-Difference Time-Domain (FDTD) code available at the University of Utah has been used to simulate sintering of ceramics in single and multimode cavities, and many useful results have been reported in literature. More detailed and accurate results, specifically around and including the ceramic sample, are often desired to help evaluate the adequacy of the heating procedure. In electrically large multimode cavities, however, computer memory requirements limit the number of the mathematical cells, and the desired resolution is impractical to achieve due to limited computer resources. Therefore, an FDTD algorithm which incorporates multiple-grid regions with variable-grid sizes is required to adequately perform the desired simulations. In this paper the authors describe the development of a three-dimensional multi-grid FDTD code to help focus a large number of cells around the desired region. Test geometries were solved using a uniform-grid and the developed multi-grid code to help validate the results from the developed code. Results from these comparisons, as well as the results of comparisons between the developed FDTD code and other available variable-grid codes are presented. In addition, results from the simulation of realistic microwave sintering experiments showed improved resolution in critical sites inside the three-dimensional sintering cavity. With the validation of the FDTD code, simulations were performed for electrically large, multimode, microwave sintering cavities to fully demonstrate the advantages of the developed multi-grid FDTD code.

  3. 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...

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

    CERN Document Server

    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.

  5. Micro grids toward the smart grid

    International Nuclear Information System (INIS)

    Guerrero, J.

    2011-01-01

    Worldwide electrical grids are expecting to become smarter in the near future, with interest in Microgrids likely to grow. A microgrid can be defined as a part of the grid with elements of prime energy movers, power electronics converters, distributed energy storage systems and local loads, that can operate autonomously but also interacting with main grid. Thus, the ability of intelligent Microgrids to operate in island mode or connected to the grid will be a keypoint to cope with new functionalities and the integration of renewable energy resources. The functionalities expected for these small grids are: black start operation, frequency and voltage stability, active and reactive power flow control, active power filter capabilities, and storage energy management. In this presentation, a review of the main concepts related to flexible Microgrids will be introduced, with examples of real Microgrids. AC and DC Microgrids to integrate renewable and distributed energy resources will also be presented, as well as distributed energy storage systems, and standardization issues of these Microgrids. Finally, Microgrid hierarchical control will be analyzed looking at three different levels: i) a primary control based on the droop method, including an output impedance virtual loop; ii) a secondary control, which enables restoring any deviations produced by the primary control; and iii) a tertiary control to manage the power flow between the microgrid and the external electrical distribution system.

  6. 3D CSEM inversion based on goal-oriented adaptive finite element method

    Science.gov (United States)

    Zhang, Y.; Key, K.

    2016-12-01

    We present a parallel 3D frequency domain controlled-source electromagnetic inversion code name MARE3DEM. Non-linear inversion of observed data is performed with the Occam variant of regularized Gauss-Newton optimization. The forward operator is based on the goal-oriented finite element method that efficiently calculates the responses and sensitivity kernels in parallel using a data decomposition scheme where independent modeling tasks contain different frequencies and subsets of the transmitters and receivers. To accommodate complex 3D conductivity variation with high flexibility and precision, we adopt the dual-grid approach where the forward mesh conforms to the inversion parameter grid and is adaptively refined until the forward solution converges to the desired accuracy. This dual-grid approach is memory efficient, since the inverse parameter grid remains independent from fine meshing generated around the transmitter and receivers by the adaptive finite element method. Besides, the unstructured inverse mesh efficiently handles multiple scale structures and allows for fine-scale model parameters within the region of interest. Our mesh generation engine keeps track of the refinement hierarchy so that the map of conductivity and sensitivity kernel between the forward and inverse mesh is retained. We employ the adjoint-reciprocity method to calculate the sensitivity kernels which establish a linear relationship between changes in the conductivity model and changes in the modeled responses. Our code uses a direcy solver for the linear systems, so the adjoint problem is efficiently computed by re-using the factorization from the primary problem. Further computational efficiency and scalability is obtained in the regularized Gauss-Newton portion of the inversion using parallel dense matrix-matrix multiplication and matrix factorization routines implemented with the ScaLAPACK library. We show the scalability, reliability and the potential of the algorithm to deal with

  7. 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

  8. 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

  9. SuperGrid or SmartGrid: Competing strategies for large-scale integration of intermittent renewables?

    International Nuclear Information System (INIS)

    Blarke, Morten B.; Jenkins, Bryan M.

    2013-01-01

    This paper defines and compares two strategies for integrating intermittent renewables: SuperGrid and SmartGrid. While conventional energy policy suggests that these strategies may be implemented alongside each other, the paper identifies significant technological and socio-economic conflicts of interest between the two. The article identifies differences between a domestic strategy for the integration of intermittent renewables, vis-à-vis the SmartGrid, and a cross-system strategy, vis-à-vis the SuperGrid. Policy makers and transmission system operators must understand the need for both strategies to evolve in parallel, but in different territories, or with strategic integration, avoiding for one strategy to undermine the feasibility of the other. A strategic zoning strategy is introduced from which attentive societies as well as the global community stand to benefit. The analysis includes a paradigmatic case study from West Denmark which supports the hypothesis that these strategies are mutually exclusive. The case study shows that increasing cross-system transmission capacity jeopardizes the feasibility of SmartGrid technology investments. A political effort is required for establishing dedicated SmartGrid innovation zones, while also redefining infrastructure to avoid the narrow focus on grids and cables. SmartGrid Investment Trusts could be supported from reallocation of planned transmission grid investments to provide for the equitable development of SmartGrid strategies. - Highlights: • Compares SuperGrid and SmartGrid strategies for integrating intermittent renewables. • Identifies technological and socio-economic conflicts of interest between the two. • Proposes a strategic zoning strategy allowing for both strategies to evolve. • Presents a paradigmatic case study showing that strategies are mutually exclusive. • Proposes dedicated SmartGrid innovation zones and SmartGrid investment trusts

  10. Application of the finite-difference approximation to electrostatic problems in gaseous proportional counters

    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)

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

    KAUST Repository

    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

  12. Vibration analysis of a dummy fuel rod continuously supported by spacer grids

    International Nuclear Information System (INIS)

    Choi, Myoung-Hwan; Kang, Heung-Seok; Yoon, Kyung-Ho; Song, Kee-Nam; Jung, Youn-Ho

    2003-01-01

    A modal testing and a finite element (FE) analysis using ABAQUS on a dummy fuel rod continuously supported by Optimized H type (OHT) and New Doublet (ND) spacer grids are performed to obtain the vibration characteristics such as natural frequencies and mode shapes and to verify the FE model used. The results from the test and the FE analysis are compared according to modal assurance criteria values. The natural frequency differences between the two methods as well as the mode comparison results for the rod with OHT SG are better than those with ND SG. That is, in the case of the ND grid model using beam-spring elements, there was a large discrepancy between the two methods. Thus, we tried to modify the FE model for ND SG considering the contact phenomena between the fuel rod and the SG. The results of the new model showed good agreement with the experiment compared with those of a beam-spring model

  13. LHC computing grid

    International Nuclear Information System (INIS)

    Novaes, Sergio

    2011-01-01

    Full text: We give an overview of the grid computing initiatives in the Americas. High-Energy Physics has played a very important role in the development of grid computing in the world and in Latin America it has not been different. Lately, the grid concept has expanded its reach across all branches of e-Science, and we have witnessed the birth of the first nationwide infrastructures and its use in the private sector. (author)

  14. Hybrid mesh finite volume CFD code for studying heat transfer in a forward-facing step

    Energy Technology Data Exchange (ETDEWEB)

    Jayakumar, J S; Kumar, Inder [Bhabha Atomic Research Center, Mumbai (India); Eswaran, V, E-mail: jsjayan@gmail.com, E-mail: inderk@barc.gov.in, E-mail: eswar@iitk.ac.in [Indian Institute of Technology, Kanpur (India)

    2010-12-15

    Computational fluid dynamics (CFD) methods employ two types of grid: structured and unstructured. Developing the solver and data structures for a finite-volume solver is easier than for unstructured grids. But real-life problems are too complicated to be fitted flexibly by structured grids. Therefore, unstructured grids are widely used for solving real-life problems. However, using only one type of unstructured element consumes a lot of computational time because the number of elements cannot be controlled. Hence, a hybrid grid that contains mixed elements, such as the use of hexahedral elements along with tetrahedral and pyramidal elements, gives the user control over the number of elements in the domain, and thus only the domain that requires a finer grid is meshed finer and not the entire domain. This work aims to develop such a finite-volume hybrid grid solver capable of handling turbulence flows and conjugate heat transfer. It has been extended to solving flow involving separation and subsequent reattachment occurring due to sudden expansion or contraction. A significant effect of mixing high- and low-enthalpy fluid occurs in the reattached regions of these devices. This makes the study of the backward-facing and forward-facing step with heat transfer an important field of research. The problem of the forward-facing step with conjugate heat transfer was taken up and solved for turbulence flow using a two-equation model of k-{omega}. The variation in the flow profile and heat transfer behavior has been studied with the variation in Re and solid to fluid thermal conductivity ratios. The results for the variation in local Nusselt number, interface temperature and skin friction factor are presented.

  15. Hybrid mesh finite volume CFD code for studying heat transfer in a forward-facing step

    Science.gov (United States)

    Jayakumar, J. S.; Kumar, Inder; Eswaran, V.

    2010-12-01

    Computational fluid dynamics (CFD) methods employ two types of grid: structured and unstructured. Developing the solver and data structures for a finite-volume solver is easier than for unstructured grids. But real-life problems are too complicated to be fitted flexibly by structured grids. Therefore, unstructured grids are widely used for solving real-life problems. However, using only one type of unstructured element consumes a lot of computational time because the number of elements cannot be controlled. Hence, a hybrid grid that contains mixed elements, such as the use of hexahedral elements along with tetrahedral and pyramidal elements, gives the user control over the number of elements in the domain, and thus only the domain that requires a finer grid is meshed finer and not the entire domain. This work aims to develop such a finite-volume hybrid grid solver capable of handling turbulence flows and conjugate heat transfer. It has been extended to solving flow involving separation and subsequent reattachment occurring due to sudden expansion or contraction. A significant effect of mixing high- and low-enthalpy fluid occurs in the reattached regions of these devices. This makes the study of the backward-facing and forward-facing step with heat transfer an important field of research. The problem of the forward-facing step with conjugate heat transfer was taken up and solved for turbulence flow using a two-equation model of k-ω. The variation in the flow profile and heat transfer behavior has been studied with the variation in Re and solid to fluid thermal conductivity ratios. The results for the variation in local Nusselt number, interface temperature and skin friction factor are presented.

  16. Hybrid mesh finite volume CFD code for studying heat transfer in a forward-facing step

    International Nuclear Information System (INIS)

    Jayakumar, J S; Kumar, Inder; Eswaran, V

    2010-01-01

    Computational fluid dynamics (CFD) methods employ two types of grid: structured and unstructured. Developing the solver and data structures for a finite-volume solver is easier than for unstructured grids. But real-life problems are too complicated to be fitted flexibly by structured grids. Therefore, unstructured grids are widely used for solving real-life problems. However, using only one type of unstructured element consumes a lot of computational time because the number of elements cannot be controlled. Hence, a hybrid grid that contains mixed elements, such as the use of hexahedral elements along with tetrahedral and pyramidal elements, gives the user control over the number of elements in the domain, and thus only the domain that requires a finer grid is meshed finer and not the entire domain. This work aims to develop such a finite-volume hybrid grid solver capable of handling turbulence flows and conjugate heat transfer. It has been extended to solving flow involving separation and subsequent reattachment occurring due to sudden expansion or contraction. A significant effect of mixing high- and low-enthalpy fluid occurs in the reattached regions of these devices. This makes the study of the backward-facing and forward-facing step with heat transfer an important field of research. The problem of the forward-facing step with conjugate heat transfer was taken up and solved for turbulence flow using a two-equation model of k-ω. The variation in the flow profile and heat transfer behavior has been studied with the variation in Re and solid to fluid thermal conductivity ratios. The results for the variation in local Nusselt number, interface temperature and skin friction factor are presented.

  17. 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)

  18. Construction of stable explicit finite-difference schemes for Schroedinger type differential equations

    Science.gov (United States)

    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.

  19. Numerical study on flow fields and aerodynamics of tilt rotor aircraft in conversion mode based on embedded grid and actuator model

    Directory of Open Access Journals (Sweden)

    Ying Zhang

    2015-02-01

    Full Text Available A method combining rotor actuator disk model and embedded grid technique is presented in this paper, aimed at predicting the flow fields and aerodynamic characteristics of tilt rotor aircraft in conversion mode more efficiently and effectively. In this method, rotor’s influence is considered in terms of the momentum it impacts to the fluid around it; transformation matrixes among different coordinate systems are deduced to extend actuator method’s utility to conversion mode flow fields’ calculation. Meanwhile, an embedded grid system is designed, in which grids generated around fuselage and actuator disk are regarded as background grid and minor grid respectively, and a new method is presented for ‘donor searching’ and ‘hole cutting’ during grid assembling. Based on the above methods, flow fields of tilt rotor aircraft in conversion mode are simulated, with three-dimensional Navier–Stokes equations discretized by a second-order upwind finite-volume scheme and an implicit lower–upper symmetric Gauss–Seidel (LU-SGS time-stepping scheme. Numerical results demonstrate that the proposed CFD method is very effective in simulating the conversion mode flow fields of tilt rotor aircraft.

  20. 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...

  1. Coupling multipoint flux mixed finite element methodswith continuous Galerkin methods for poroelasticity

    KAUST Repository

    Wheeler, Mary

    2013-11-16

    We study the numerical approximation on irregular domains with general grids of the system of poroelasticity, which describes fluid flow in deformable porous media. The flow equation is discretized by a multipoint flux mixed finite element method and the displacements are approximated by a continuous Galerkin finite element method. First-order convergence in space and time is established in appropriate norms for the pressure, velocity, and displacement. Numerical results are presented that illustrate the behavior of the method. © Springer Science+Business Media Dordrecht 2013.

  2. Exploring virtualisation tools with a new virtualisation provisioning method to test dynamic grid environments for ALICE grid jobs over ARC grid middleware

    International Nuclear Information System (INIS)

    Wagner, B; Kileng, B

    2014-01-01

    The Nordic Tier-1 centre for LHC is distributed over several computing centres. It uses ARC as the internal computing grid middleware. ALICE uses its own grid middleware AliEn to distribute jobs and the necessary software application stack. To make use of most of the AliEn infrastructure and software deployment methods for running ALICE grid jobs on ARC, we are investigating different possible virtualisation technologies. For this a testbed and possible framework for bridging different middleware systems is under development. It allows us to test a variety of virtualisation methods and software deployment technologies in the form of different virtual machines.

  3. Effects of grid potentials and geometric dimensions on the multi-electrode probe measurements

    International Nuclear Information System (INIS)

    Elakshar, F.F.; Abdul El-Raoof, W.S.

    1986-01-01

    A hollow anode plasma source is used to produce low temperature plasma which is injected into a magnetic field. The effects of the grid potentials, collector potential and geometric dimensions on multi-electrode probe measurements, in the presence of a magnetic field, are investigated. It is found that the collector potential plays a substantial role in the measurement of temperatures and densities. The finite-size of the geometric dimensions of the probe influences the data and high values of temperature are obtained when a small ratio of the discriminator grid radius to the separation distance is used, providing that the repeller grid potentials is low. Reliable measurements can only be obtained if the multi-electrode probe is used in the presence of a magnetic field strong enough to reduce electron Larmor radii to less than the grid mesh radius. (author)

  4. 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

  5. Calculation approaches for grid usage fees to influence the load curve in the distribution grid level

    International Nuclear Information System (INIS)

    Illing, Bjoern

    2014-01-01

    Dominated by the energy policy the decentralized German energy market is changing. One mature target of the government is to increase the contribution of renewable generation to the gross electricity consumption. In order to achieve this target disadvantages like an increased need for capacity management occurs. Load reduction and variable grid fees offer the grid operator solutions to realize capacity management by influencing the load profile. The evolution of the current grid fees towards more causality is required to adapt these approaches. Two calculation approaches are developed in this assignment. On the one hand multivariable grid fees keeping the current components demand and energy charge. Additional to the grid costs grid load dependent parameters like the amount of decentralized feed-ins, time and local circumstances as well as grid capacities are considered. On the other hand the grid fee flat-rate which represents a demand based model on a monthly level. Both approaches are designed to meet the criteria for future grid fees. By means of a case study the effects of the grid fees on the load profile at the low voltage grid is simulated. Thereby the consumption is represented by different behaviour models and the results are scaled at the benchmark grid area. The resulting load curve is analyzed concerning the effects of peak load reduction as well as the integration of renewable energy sources. Additionally the combined effect of grid fees and electricity tariffs is evaluated. Finally the work discusses the launching of grid fees in the tense atmosphere of politics, legislation and grid operation. Results of this work are two calculation approaches designed for grid operators to define the grid fees. Multivariable grid fees are based on the current calculation scheme. Hereby demand and energy charges are weighted by time, locational and load related dependencies. The grid fee flat-rate defines a limitation in demand extraction. Different demand levels

  6. 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)

  7. 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.

  8. Tests of a 3D Self Magnetic Field Solver in the Finite Element Gun Code MICHELLE

    CERN Document Server

    Nelson, Eric M

    2005-01-01

    We have recently implemented a prototype 3d self magnetic field solver in the finite-element gun code MICHELLE. The new solver computes the magnetic vector potential on unstructured grids. The solver employs edge basis functions in the curl-curl formulation of the finite-element method. A novel current accumulation algorithm takes advantage of the unstructured grid particle tracker to produce a compatible source vector, for which the singular matrix equation is easily solved by the conjugate gradient method. We will present some test cases demonstrating the capabilities of the prototype 3d self magnetic field solver. One test case is self magnetic field in a square drift tube. Another is a relativistic axisymmetric beam freely expanding in a round pipe.

  9. 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

  10. The play grid

    DEFF Research Database (Denmark)

    Fogh, Rune; Johansen, Asger

    2013-01-01

    In this paper we propose The Play Grid, a model for systemizing different play types. The approach is psychological by nature and the actual Play Grid is based, therefore, on two pairs of fundamental and widely acknowledged distinguishing characteristics of the ego, namely: extraversion vs. intro...

  11. Robust mixed finite element methods to deal with incompressibility in finite strain in an industrial framework

    International Nuclear Information System (INIS)

    Al-Akhrass, Dina

    2014-01-01

    Simulations in solid mechanics exhibit several difficulties, as dealing with incompressibility, with nonlinearities due to finite strains, contact laws, or constitutive laws. The basic motivation of our work is to propose efficient finite element methods capable of dealing with incompressibility in finite strain context, and using elements of low order. During the three last decades, many approaches have been proposed in the literature to overcome the incompressibility problem. Among them, mixed formulations offer an interesting theoretical framework. In this work, a three-field mixed formulation (displacement, pressure, volumetric strain) is investigated. In some cases, this formulation can be condensed in a two-field (displacement - pressure) mixed formulation. However, it is well-known that the discrete problem given by the Galerkin finite element technique, does not inherit the 'inf-sup' stability condition from the continuous problem. Hence, the interpolation orders in displacement and pressure have to be chosen in a way to satisfy the Brezzi-Babuska stability conditions when using Galerkin approaches. Interpolation orders must be chosen so as to satisfy this condition. Two possibilities are considered: to use stable finite element satisfying this requirement, or to use finite element that does not satisfy this condition, and to add terms stabilizing the FE Galerkin formulation. The latter approach allows the use of equal order interpolation. In this work, stable finite element P2/P1 and P2/P1/P1 are used as reference, and compared to P1/P1 and P1/P1/P1 formulations stabilized with a bubble function or with a VMS method (Variational Multi-Scale) based on a sub-grid-space orthogonal to the FE space. A finite strain model based on logarithmic strain is selected. This approach is extended to three and two field mixed formulations with stable or stabilized elements. These approaches are validated on academic cases and used on industrial cases. (author)

  12. 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.

  13. 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

  14. Rotational degree-of-freedom synthesis: An optimised finite difference method for non-exact data

    Science.gov (United States)

    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.

  15. A Parallel, Finite-Volume Algorithm for Large-Eddy Simulation of Turbulent Flows

    Science.gov (United States)

    Bui, Trong T.

    1999-01-01

    A parallel, finite-volume algorithm has been developed for large-eddy simulation (LES) of compressible turbulent flows. This algorithm includes piecewise linear least-square reconstruction, trilinear finite-element interpolation, Roe flux-difference splitting, and second-order MacCormack time marching. Parallel implementation is done using the message-passing programming model. In this paper, the numerical algorithm is described. To validate the numerical method for turbulence simulation, LES of fully developed turbulent flow in a square duct is performed for a Reynolds number of 320 based on the average friction velocity and the hydraulic diameter of the duct. Direct numerical simulation (DNS) results are available for this test case, and the accuracy of this algorithm for turbulence simulations can be ascertained by comparing the LES solutions with the DNS results. The effects of grid resolution, upwind numerical dissipation, and subgrid-scale dissipation on the accuracy of the LES are examined. Comparison with DNS results shows that the standard Roe flux-difference splitting dissipation adversely affects the accuracy of the turbulence simulation. For accurate turbulence simulations, only 3-5 percent of the standard Roe flux-difference splitting dissipation is needed.

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

    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)

  17. Profitability of smart grid solutions applied in power grid

    Directory of Open Access Journals (Sweden)

    Katić Nenad A.

    2016-01-01

    Full Text Available The idea of a Smart Grid solution has been developing for years, as complete solution for a power utility, consisting of different advanced technologies aimed at improving of the efficiency of operation. The trend of implementing various smart systems continues, e.g. Energy Management Systems, Grid Automation Systems, Advanced Metering Infrastructure, Smart power equipment, Distributed Energy Resources, Demand Response systems, etc. Futhermore, emerging technologies, such as energy storages, electrical vehicles or distributed generators, become integrated in distribution networks and systems. Nowadays, the idea of a Smart Grid solution becomes more realistic by full integration of all advanced operation technologies (OT within IT environment, providing the complete digitalization of an Utility (IT/OT integration. The overview of smart grid solutions, estimation of investments, operation costs and possible benefits are presented in this article, with discusison about profitability of such systems.

  18. Analysis of turbine-grid interaction of grid-connected wind turbine using HHT

    Science.gov (United States)

    Chen, A.; Wu, W.; Miao, J.; Xie, D.

    2018-05-01

    This paper processes the output power of the grid-connected wind turbine with the denoising and extracting method based on Hilbert Huang transform (HHT) to discuss the turbine-grid interaction. At first, the detailed Empirical Mode Decomposition (EMD) and the Hilbert Transform (HT) are introduced. Then, on the premise of decomposing the output power of the grid-connected wind turbine into a series of Intrinsic Mode Functions (IMFs), energy ratio and power volatility are calculated to detect the unessential components. Meanwhile, combined with vibration function of turbine-grid interaction, data fitting of instantaneous amplitude and phase of each IMF is implemented to extract characteristic parameters of different interactions. Finally, utilizing measured data of actual parallel-operated wind turbines in China, this work accurately obtains the characteristic parameters of turbine-grid interaction of grid-connected wind turbine.

  19. Wing-Body Aeroelasticity Using Finite-Difference Fluid/Finite-Element Structural Equations on Parallel Computers

    Science.gov (United States)

    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.

  20. Differences in Visual-Spatial Input May Underlie Different Compression Properties of Firing Fields for Grid Cell Modules in Medial Entorhinal Cortex

    Science.gov (United States)

    2015-11-19

    funders had no role in study design, data collection and analysis , decision to publish, or preparation of the manuscript. a box. In contrast, grid cells...of grid cells. This visualization and analysis of compression effects does not depend on the type of grid cell model used. The results are the same...that of a grid cell. The grid pattern for the static feature system remains intact (Fig 4P ). Thus, the grid cells driven by the static feature system

  1. Influence of Different Coupling Modes on the Robustness of Smart Grid under Targeted Attack

    Directory of Open Access Journals (Sweden)

    WenJie Kang

    2018-05-01

    Full Text Available Many previous works only focused on the cascading failure of global coupling of one-to-one structures in interdependent networks, but the local coupling of dual coupling structures has rarely been studied due to its complex structure. This will result in a serious consequence that many conclusions of the one-to-one structure may be incorrect in the dual coupling network and do not apply to the smart grid. Therefore, it is very necessary to subdivide the dual coupling link into a top-down coupling link and a bottom-up coupling link in order to study their influence on network robustness by combining with different coupling modes. Additionally, the power flow of the power grid can cause the load of a failed node to be allocated to its neighboring nodes and trigger a new round of load distribution when the load of these nodes exceeds their capacity. This means that the robustness of smart grids may be affected by four factors, i.e., load redistribution, local coupling, dual coupling link and coupling mode; however, the research on the influence of those factors on the network robustness is missing. In this paper, firstly, we construct the smart grid as a two-layer network with a dual coupling link and divide the power grid and communication network into many subnets based on the geographical location of their nodes. Secondly, we define node importance ( N I as an evaluation index to access the impact of nodes on the cyber or physical network and propose three types of coupling modes based on N I of nodes in the cyber and physical subnets, i.e., Assortative Coupling in Subnets (ACIS, Disassortative Coupling in Subnets (DCIS, and Random Coupling in Subnets (RCIS. Thirdly, a cascading failure model is proposed for studying the effect of local coupling of dual coupling link in combination with ACIS, DCIS, and RCIS on the robustness of the smart grid against a targeted attack, and the survival rate of functional nodes is used to assess the robustness of

  2. Influence of Different Coupling Modes on the Robustness of Smart Grid under Targeted Attack.

    Science.gov (United States)

    Kang, WenJie; Hu, Gang; Zhu, PeiDong; Liu, Qiang; Hang, Zhi; Liu, Xin

    2018-05-24

    Many previous works only focused on the cascading failure of global coupling of one-to-one structures in interdependent networks, but the local coupling of dual coupling structures has rarely been studied due to its complex structure. This will result in a serious consequence that many conclusions of the one-to-one structure may be incorrect in the dual coupling network and do not apply to the smart grid. Therefore, it is very necessary to subdivide the dual coupling link into a top-down coupling link and a bottom-up coupling link in order to study their influence on network robustness by combining with different coupling modes. Additionally, the power flow of the power grid can cause the load of a failed node to be allocated to its neighboring nodes and trigger a new round of load distribution when the load of these nodes exceeds their capacity. This means that the robustness of smart grids may be affected by four factors, i.e., load redistribution, local coupling, dual coupling link and coupling mode; however, the research on the influence of those factors on the network robustness is missing. In this paper, firstly, we construct the smart grid as a two-layer network with a dual coupling link and divide the power grid and communication network into many subnets based on the geographical location of their nodes. Secondly, we define node importance ( N I ) as an evaluation index to access the impact of nodes on the cyber or physical network and propose three types of coupling modes based on N I of nodes in the cyber and physical subnets, i.e., Assortative Coupling in Subnets (ACIS), Disassortative Coupling in Subnets (DCIS), and Random Coupling in Subnets (RCIS). Thirdly, a cascading failure model is proposed for studying the effect of local coupling of dual coupling link in combination with ACIS, DCIS, and RCIS on the robustness of the smart grid against a targeted attack, and the survival rate of functional nodes is used to assess the robustness of the smart grid

  3. Multitasking for flows about multiple body configurations using the chimera grid scheme

    Science.gov (United States)

    Dougherty, F. C.; Morgan, R. L.

    1987-01-01

    The multitasking of a finite-difference scheme using multiple overset meshes is described. In this chimera, or multiple overset mesh approach, a multiple body configuration is mapped using a major grid about the main component of the configuration, with minor overset meshes used to map each additional component. This type of code is well suited to multitasking. Both steady and unsteady two dimensional computations are run on parallel processors on a CRAY-X/MP 48, usually with one mesh per processor. Flow field results are compared with single processor results to demonstrate the feasibility of running multiple mesh codes on parallel processors and to show the increase in efficiency.

  4. Wind energy in offshore grids

    DEFF Research Database (Denmark)

    Schröder, Sascha Thorsten

    special characteristics of offshore grids. With an operational real options approach, it is furthermore illustrated how different support schemes and connections to additional countries affect the investment case of an offshore wind farm and the income of the transmission system operator. The investment...... and investment implications under different regulatory frameworks are a hitherto underrepresented research field. They are addressed by this thesis. Offshore grids between several countries combine the absorption of wind energy with international power trading. However, the inclusion into an offshore grid......This cumulative PhD thesis deals with wind integration in offshore grids from an economic point of view. It is composed of a generic part and eight papers. As the topic has mostly been analysed with a focus on topology and technical issues until now, market-operational questions in offshore grids...

  5. 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.

  6. Controlling the numerical Cerenkov instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction

    International Nuclear Information System (INIS)

    Li, Fei; Yu, Peicheng; Xu, Xinlu; Fiuza, Frederico; Decyk, Viktor K.

    2017-01-01

    In this study we present a customized finite-difference-time-domain (FDTD) Maxwell solver for the particle-in-cell (PIC) algorithm. The solver is customized to effectively eliminate the numerical Cerenkov instability (NCI) which arises when a plasma (neutral or non-neutral) relativistically drifts on a grid when using the PIC algorithm. We control the EM dispersion curve in the direction of the plasma drift of a FDTD Maxwell solver by using a customized higher order finite difference operator for the spatial derivative along the direction of the drift (1^ direction). We show that this eliminates the main NCI modes with moderate |k_1|, while keeps additional main NCI modes well outside the range of physical interest with higher |k_1|. These main NCI modes can be easily filtered out along with first spatial aliasing NCI modes which are also at the edge of the fundamental Brillouin zone. The customized solver has the possible advantage of improved parallel scalability because it can be easily partitioned along 1^ which typically has many more cells than other directions for the problems of interest. We show that FFTs can be performed locally to current on each partition to filter out the main and first spatial aliasing NCI modes, and to correct the current so that it satisfies the continuity equation for the customized spatial derivative. This ensures that Gauss’ Law is satisfied. Lastly, we present simulation examples of one relativistically drifting plasma, of two colliding relativistically drifting plasmas, and of nonlinear laser wakefield acceleration (LWFA) in a Lorentz boosted frame that show no evidence of the NCI can be observed when using this customized Maxwell solver together with its NCI elimination scheme.

  7. 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...

  8. Grid simulator for power quality assessment of micro-grids

    DEFF Research Database (Denmark)

    Carrasco, Joaquin Eloy Garcia; Vasquez, Juan Carlos; Guerrero, Josep M.

    2013-01-01

    voltages, low-order harmonics and flicker. The aim of this equipment is to test the performance of a given system under such distorted voltages. A prototype of the simulator, consisting of two inverters connected back-to-back to a 380 V three-phase grid and feeding a micro-grid composed of two......-inverter interfaced distributed generators and a critical load was built and tested. A set of experimental results for linear purely resistive loads, non-linear loads and current-controlled inverters is presented to prove the capabilities of the simulator. Finally, a case study is presented by testing a micro-grid.......In this study, a grid simulator based on a back-to-back inverter topology with resonant controllers is presented. The simulator is able to generate three-phase voltages for a range of amplitudes and frequencies with different types of perturbations, such as voltage sags, steady-state unbalanced...

  9. Mapping PetaSHA Applications to TeraGrid Architectures

    Science.gov (United States)

    Cui, Y.; Moore, R.; Olsen, K.; Zhu, J.; Dalguer, L. A.; Day, S.; Cruz-Atienza, V.; Maechling, P.; Jordan, T.

    2007-12-01

    The Southern California Earthquake Center (SCEC) has a science program in developing an integrated cyberfacility - PetaSHA - for executing physics-based seismic hazard analysis (SHA) computations. The NSF has awarded PetaSHA 15 million allocation service units this year on the fastest supercomputers available within the NSF TeraGrid. However, one size does not fit all, a range of systems are needed to support this effort at different stages of the simulations. Enabling PetaSHA simulations on those TeraGrid architectures to solve both dynamic rupture and seismic wave propagation have been a challenge from both hardware and software levels. This is an adaptation procedure to meet specific requirements of each architecture. It is important to determine how fundamental system attributes affect application performance. We present an adaptive approach in our PetaSHA application that enables the simultaneous optimization of both computation and communication at run-time using flexible settings. These techniques optimize initialization, source/media partition and MPI-IO output in different ways to achieve optimal performance on the target machines. The resulting code is a factor of four faster than the orignial version. New MPI-I/O capabilities have been added for the accurate Staggered-Grid Split-Node (SGSN) method for dynamic rupture propagation in the velocity-stress staggered-grid finite difference scheme (Dalguer and Day, JGR, 2007), We use execution workflow across TeraGrid sites for managing the resulting data volumes. Our lessons learned indicate that minimizing time to solution is most critical, in particular when scheduling large scale simulations across supercomputer sites. The TeraShake platform has been ported to multiple architectures including TACC Dell lonestar and Abe, Cray XT3 Bigben and Blue Gene/L. Parallel efficiency of 96% with the PetaSHA application Olsen-AWM has been demonstrated on 40,960 Blue Gene/L processors at IBM TJ Watson Center. Notable

  10. Near-Body Grid Adaption for Overset Grids

    Science.gov (United States)

    Buning, Pieter G.; Pulliam, Thomas H.

    2016-01-01

    A solution adaption capability for curvilinear near-body grids has been implemented in the OVERFLOW overset grid computational fluid dynamics code. The approach follows closely that used for the Cartesian off-body grids, but inserts refined grids in the computational space of original near-body grids. Refined curvilinear grids are generated using parametric cubic interpolation, with one-sided biasing based on curvature and stretching ratio of the original grid. Sensor functions, grid marking, and solution interpolation tasks are implemented in the same fashion as for off-body grids. A goal-oriented procedure, based on largest error first, is included for controlling growth rate and maximum size of the adapted grid system. The adaption process is almost entirely parallelized using MPI, resulting in a capability suitable for viscous, moving body simulations. Two- and three-dimensional examples are presented.

  11. A simple finite-difference scheme for handling topography with the first-order wave equation

    Science.gov (United States)

    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.

  12. Optimization of the cooling circuit and thermo-mechanical analysis for the extraction grid of ELISE

    International Nuclear Information System (INIS)

    Nocentini, R.; Gutser, R.; Heinemann, B.; Froeschle, M.; Riedl, R.

    2011-01-01

    The NNBI test facility ELISE ('Extraction from a Large Ion Source Experiment'), presently under construction at IPP, will have an extraction area with the same width and half the height of the ITER source, acceleration up to 60 kV, for 10 s, every 180 s, and plasma generation up to 1 h. Electrons are co-extracted from the ion source. Suppression magnets in the extraction grid deflect the electrons onto the extraction grid surface. For 30 mA/cm 2 extracted electron current density and 10 kV extraction voltage, localized power density is in the order of 39 MW/m 2 near the grid apertures and a total heat load of 150 kW is deposited onto each extraction grid segment. Heat removal is provided by a water circuit inside the grid. For ELISE, a new cooling circuit has been developed to provide a more reliable operation. The optimization of the cooling circuit and the thermo-mechanical analysis of the extraction grid of ELISE, considering maximum grid temperature, mechanical stresses and grid deformation, has been performed using the codes KOBRA3, TrajAn, the ANSYS finite element package and the fluid dynamics code CFX.

  13. Gridded Data in the Arctic; Benefits and Perils of Publicly Available Grids

    Science.gov (United States)

    Coakley, B.; Forsberg, R.; Gabbert, R.; Beale, J.; Kenyon, S. C.

    2015-12-01

    Our understanding of the Arctic Ocean has been hugely advanced by release of gridded bathymetry and potential field anomaly grids. The Arctic Gravity Project grid achieves excellent, near-isotropic coverage of the earth north of 64˚N by combining land, satellite, airborne, submarine, surface ship and ice set-out measurements of gravity anomalies. Since the release of the V 2.0 grid in 2008, there has been extensive icebreaker activity across the Amerasia Basin due to mapping of the Arctic coastal nation's Extended Continental Shelves (ECS). While grid resolution has been steadily improving over time, addition of higher resolution and better navigated data highlights some distortions in the grid that may influence interpretation. In addition to the new ECS data sets, gravity anomaly data has been collected from other vessels; notably the Korean Icebreaker Araon, the Japanese icebreaker Mirai and the German icebreaker Polarstern. Also the GRAV-D project of the US National Geodetic Survey has flown airborne surveys over much of Alaska. These data will be Included in the new AGP grid, which will result in a much improved product when version 3.0 is released in 2015. To make use of these measurements, it is necessary to compile them into a continuous spatial representation. Compilation is complicated by differences in survey parameters, gravimeter sensitivity and reduction methods. Cross-over errors are the classic means to assess repeatability of track measurements. Prior to the introduction of near-universal GPS positioning, positional uncertainty was evaluated by cross-over analysis. GPS positions can be treated as more or less true, enabling evaluation of differences due to contrasting sensitivity, reference and reduction techniques. For the most part, cross-over errors for racks of gravity anomaly data collected since 2008 are less than 0.5 mGals, supporting the compilation of these data with only slight adjustments. Given the different platforms used for various

  14. Design of a Carbon Fiber Composite Grid Structure for the GLAST Spacecraft Using a Novel Manufacturing Technique

    Energy Technology Data Exchange (ETDEWEB)

    Hicks, M

    2004-04-12

    The Gamma-Ray Large Area Space Telescope is an orbital observatory being planned as a joint DOE/NASA mission. The primary support of the instrument requires a grid structure which is very stiff, strong, light-weight, and thermally conductive. A carbon fiber composite grid design using a novel manufacture technique is proposed which meets or exceeds an aluminum design in all performance criteria and is economically competitive as well. Finite element analysis, confirmed by testing of a sample grid, is used to examine trade-offs for the materials and layups. Based on these analyses, recommendations are given for a viable design.

  15. Mass, momentum and energy conserving (MaMEC) discretizations on general grids for the compressible Euler and shallow water equations

    International Nuclear Information System (INIS)

    Hof, Bas van’t; Veldman, Arthur E.P.

    2012-01-01

    The paper explains a method by which discretizations of the continuity and momentum equations can be designed, such that they can be combined with an equation of state into a discrete energy equation. The resulting ‘MaMEC’ discretizations conserve mass, momentum as well as energy, although no explicit conservation law for the total energy is present. Essential ingredients are (i) discrete convection that leaves the discrete energy invariant, and (ii) discrete consistency between the thermodynamic terms. Of particular relevance is the way in which finite volume fluxes are related to nodal values. The method is an extension of existing methods based on skew-symmetry of discrete operators, because it allows arbitrary equations of state and a larger class of grids than earlier methods. The method is first illustrated with a one-dimensional example on a highly stretched staggered grid, in which the MaMEC method calculates qualitatively correct results and a non-skew-symmetric finite volume method becomes unstable. A further example is a two-dimensional shallow water calculation on a rectilinear grid as well as on an unstructured grid. The conservation of mass, momentum and energy is checked, and losses are found negligible up to machine accuracy.

  16. The MammoGrid Project Grids Architecture

    CERN Document Server

    McClatchey, Richard; Hauer, Tamas; Estrella, Florida; Saiz, Pablo; Rogulin, Dmitri; Buncic, Predrag; Clatchey, Richard Mc; Buncic, Predrag; Manset, David; Hauer, Tamas; Estrella, Florida; Saiz, Pablo; Rogulin, Dmitri

    2003-01-01

    The aim of the recently EU-funded MammoGrid project is, in the light of emerging Grid technology, to develop a European-wide database of mammograms that will be used to develop a set of important healthcare applications and investigate the potential of this Grid to support effective co-working between healthcare professionals throughout the EU. The MammoGrid consortium intends to use a Grid model to enable distributed computing that spans national borders. This Grid infrastructure will be used for deploying novel algorithms as software directly developed or enhanced within the project. Using the MammoGrid clinicians will be able to harness the use of massive amounts of medical image data to perform epidemiological studies, advanced image processing, radiographic education and ultimately, tele-diagnosis over communities of medical "virtual organisations". This is achieved through the use of Grid-compliant services [1] for managing (versions of) massively distributed files of mammograms, for handling the distri...

  17. Distribution Grid Integration of Photovoltaic Systems in Germany – Implications on Grid Planning and Grid Operation

    International Nuclear Information System (INIS)

    Stetz, Thomas

    2017-01-01

    Photovoltaic is the most dispersed renewable energy source in Germany, typically interconnected to low and medium voltage systems. In recent years, cost-intensive grid reinforcements had to be undertaken all across Germany’s distribution grids in order to increase their hosting capacity for these photovoltaic installations. This paper presents an overview on research results which show that photovoltaic itself can provide ancillary services to reduce its cost of interconnection. Especially the provision of reactive power turned out to be a technically effective and economically efficient method to increase a grid’s hosting capacity for photovoltaic capacity. Different reactive power control methods were investigated, revealing significant differences with regards to their grid operation implications. Business cases for residential-scale photovoltaic applications have shifted from feed-in-tariff based active power feed-in to self-consumption. However, increasing the photovoltaic self-consumption by additional battery-storage systems is still not economically reliable in Germany. (author)

  18. Switching overvoltages in offshore wind power grids

    DEFF Research Database (Denmark)

    Arana Aristi, Ivan

    and cables are presented. In Chapter 4 results from time domain measurements and simulations of switching operations in offshore wind power grids are described. Specifically, switching operations on a single wind turbine, the collection grid, the export system and the external grid measured in several real...... offshore wind farms are shown together with simulation results. Switching operations in offshore wind power grids can be simulated with different electromagnetic transient programs. Different programs were used in the project and compared results are included in Chapter 4. Also in Chapter 4 different......Switching transients in wind turbines, the collection grid, the export system and the external grid in offshore wind farms, during normal or abnormal operation, are the most important phenomena when conducting insulation coordination studies. However, the recommended models and methods from...

  19. 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.

  20. Optimizing Grid Patterns on Photovoltaic Cells

    Science.gov (United States)

    Burger, D. R.

    1984-01-01

    CELCAL computer program helps in optimizing grid patterns for different photovoltaic cell geometries and metalization processes. Five different powerloss phenomena associated with front-surface metal grid pattern on photovoltaic cells.

  1. Hosting Capacity of Solar Photovoltaics in Distribution Grids under Different Pricing Schemes

    DEFF Research Database (Denmark)

    Carollo, Riccardo; Chaudhary, Sanjay Kumar; Pillai, Jayakrishnan Radhakrishna

    2015-01-01

    Most of the solar photovoltaic (SPV) installations are connected to distribution networks. The majority of these systems are represented by single-phase rooftop SPVs connected to residential low voltage (LV) grids. The large SPV shares lead to grid integration issues such as voltage rise....... The results show that with the present TOU tariffs the EV integration in LV networks does not ease the grid bottlenecks for large PV penetration. Under the Net metering and DLMP the EV integration in LV grids tend to increase the PV hosting capacity......., overloading of the network components, voltage phase unbalance etc. A rapid expansion of Electric Vehicles (EVs) technology is estimated, whose connection is also expected to take place in the LV networks. EVs might represent a possible solution to the SPV integration issues as they can be used as fast...

  2. Ambiguities in the grid-inefficiency correction for Frisch-Grid Ionization Chambers

    International Nuclear Information System (INIS)

    Al-Adili, A.; Hambsch, F.-J.; Bencardino, R.; Oberstedt, S.; Pomp, S.

    2012-01-01

    Ionization chambers with Frisch grids have been very successfully applied to neutron-induced fission-fragment studies during the past 20 years. They are radiation resistant and can be easily adapted to the experimental conditions. The use of Frisch grids has the advantage to remove the angular dependency from the charge induced on the anode plate. However, due to the Grid Inefficiency (GI) in shielding the charges, the anode signal remains slightly angular dependent. The correction for the GI is, however, essential to determine the correct energy of the ionizing particles. GI corrections can amount to a few percent of the anode signal. Presently, two contradicting correction methods are considered in literature. The first method adding the angular-dependent part of the signal to the signal pulse height; the second method subtracting the former from the latter. Both additive and subtractive approaches were investigated in an experiment where a Twin Frisch-Grid Ionization Chamber (TFGIC) was employed to detect the spontaneous fission fragments (FF) emitted by a 252 Cf source. Two parallel-wire grids with different wire spacing (1 and 2 mm, respectively), were used individually, in the same chamber side. All the other experimental conditions were unchanged. The 2 mm grid featured more than double the GI of the 1 mm grid. The induced charge on the anode in both measurements was compared, before and after GI correction. Before GI correction, the 2 mm grid resulted in a lower pulse-height distribution than the 1 mm grid. After applying both GI corrections to both measurements only the additive approach led to consistent grid independent pulse-height distributions. The application of the subtractive correction on the contrary led to inconsistent, grid-dependent results. It is also shown that the impact of either of the correction methods is small on the FF mass distributions of 235 U(n th , f).

  3. Grid connectivity issues and the importance of GCC. [GCC - Grid Code Compliance

    Energy Technology Data Exchange (ETDEWEB)

    Das, A.; Schwartz, M.-K. [GL Renewable Certification, Malleswaram, Bangalore (India)

    2012-07-01

    In India, the wind energy is concentrated in rural areas with a very high penetration. In these cases, the wind power has an increasing influence on the power quality on the grids. Another aspect is the influence of weak grids on the operation of wind turbines. Hence it becomes very much essential to introduce such a strong grid code which is particularly applicable to wind sector and suitable for Indian environmental grid conditions. This paper focuses on different international grid codes and their requirement with regard to the connection of wind farms to the electric power systems to mitigate the grid connectivity issues. The requirements include the ways to achieve voltage and frequency stability in the grid-tied wind power system. In this paper, comparative overview and analysis of the main grid connecting requirements will be conducted, comprising several national and regional codes from many countries where high wind penetration levels have been achieved or are expected in the future. The objective of these requirements is to provide wind farms with the control and regulation capabilities encountered in conventional power plants and are necessary for the safe, reliable and economic operation of the power system. This paper also provides a brief idea on the Grid Code Compliance (GCC) certification procedure implemented by the leading accredited certifying body like Germanischer Lloyd Renewables Certification (GL RC), who checks the conformity of the wind turbines as per region specific grid codes. (Author)

  4. 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.

  5. Different Optimal Control Strategies for Exploitation of Demand Response in the Smart Grid

    DEFF Research Database (Denmark)

    Zong, Yi; Bindner, Henrik W.; Gehrke, Oliver

    2012-01-01

    To achieve a Danish energy supply based on 100% renewable energy from combinations of wind, biomass, wave and solar power in 2050 and to cover 50% of the Danish electricity consumption by wind power in 2025, it requires coordinated management of large numbers of distributed and demand response...... resources, intermittent renewable energy resources in the Smart Grid. This paper presents different optimal control (Genetic Algorithm-based and Model Predictive Control-based) algorithms that schedule controlled loads in the industrial and residential sectors, based on dynamic price and weather forecast......, considering users’ comfort settings to meet an optimization objective, such as maximum profit or minimum energy consumption. It is demonstrated in this work that the GA-based and MPC-based optimal control strategies are able to achieve load shifting for grid reliability and energy savings, including demand...

  6. Integration of Heat Pumps in Distribution Grids: Economic Motivation for Grid Control

    NARCIS (Netherlands)

    Nykamp, Stefan; Molderink, Albert; Bakker, Vincent; Toersche, Hermen; Hurink, Johann L.; Smit, Gerardus Johannes Maria

    2012-01-01

    Electric heat pumps combined with heat buffers are important elements in smart grids since they together allow to shift the consumption of electricity in time. In this paper the effects of different control algorithms for heat pumps on the investment costs for distribution grids are investigated.

  7. Integration of heat pumps in distribution grids: economic motivation for grid control

    NARCIS (Netherlands)

    Nykamp, Stefan; Molderink, Albert; Bakker, Vincent; Toersche, Hermen; Hurink, Johann L.; Smit, Gerardus Johannes Maria

    2012-01-01

    Electric heat pumps combined with heat buffers are important elements in smart grids since they together allow to shift the consumption of electricity in time. In this paper the effects of different control algorithms for heat pumps on the investment costs for distribution grids are investigated.

  8. Urban micro-grids

    International Nuclear Information System (INIS)

    Faure, Maeva; Salmon, Martin; El Fadili, Safae; Payen, Luc; Kerlero, Guillaume; Banner, Arnaud; Ehinger, Andreas; Illouz, Sebastien; Picot, Roland; Jolivet, Veronique; Michon Savarit, Jeanne; Strang, Karl Axel

    2017-02-01

    ENEA Consulting published the results of a study on urban micro-grids conducted in partnership with the Group ADP, the Group Caisse des Depots, ENEDIS, Omexom, Total and the Tuck Foundation. This study offers a vision of the definition of an urban micro-grid, the value brought by a micro-grid in different contexts based on real case studies, and the upcoming challenges that micro-grid stakeholders will face (regulation, business models, technology). The electric production and distribution system, as the backbone of an increasingly urbanized and energy dependent society, is urged to shift towards a more resilient, efficient and environment-friendly infrastructure. Decentralisation of electricity production into densely populated areas is a promising opportunity to achieve this transition. A micro-grid enhances local production through clustering electricity producers and consumers within a delimited electricity network; it has the ability to disconnect from the main grid for a limited period of time, offering an energy security service to its customers during grid outages for example. However: The islanding capability is an inherent feature of the micro-grid concept that leads to a significant premium on electricity cost, especially in a system highly reliant on intermittent electricity production. In this case, a smart grid, with local energy production and no islanding capability, can be customized to meet relevant sustainability and cost savings goals at lower costs For industrials, urban micro-grids can be economically profitable in presence of high share of reliable energy production and thermal energy demand micro-grids face strong regulatory challenges that should be overcome for further development Whether islanding is or is not implemented into the system, end-user demand for a greener, more local, cheaper and more reliable energy, as well as additional services to the grid, are strong drivers for local production and consumption. In some specific cases

  9. Moving magnets in a micromagnetic finite-difference framework

    Science.gov (United States)

    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.

  10. Biomechanical Evaluations of Hip Fracture Using Finite Element Model that Models Individual Differences of Femur

    OpenAIRE

    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...

  11. Non linear fe analysis on the static buckling behavior of the spacer grid structures

    International Nuclear Information System (INIS)

    Song, K.N.; Yoon, K.H.

    2001-01-01

    In this study considered is the static buckling behavior of spacer grids in the fuel assembly, which are required to have a sufficient strength against an accident like earthquake. Special attention is given to the finite element modeling of the spot-welding and the constraints between the spacer strips assembled together: it is found that a proper treatment of the constraints is critical for accurate assessment of the buckling behavior including strain localization at the point of spot welding. The buckling strength of the 17 x 17 spacer grid, which is difficult to analyze due to a large number of degrees of freedom, is estimated from analysis for the smaller models 3 x 3, 5 x 5, 7 x 7, and 9 x 9 spacer grids. (authors)

  12. Investigation of nonlinear 2D bottom transportation dynamics in coastal zone on optimal curvilinear boundary adaptive grids

    Directory of Open Access Journals (Sweden)

    Sukhinov Alexander

    2017-01-01

    Full Text Available One of the practically important tasks of hydrophysics for sea coastal systems is the problem of modeling and forecasting bottom sediment transportation. A number of problems connected to ship safety traffic, water medium condition near the coastal line etc. depends on forecasting bottom deposit transportation under natural and technogenic influences. Coastal systems are characterized by a complicated form of coastline - the presence of long, narrow and curvilinear peninsulas and bays. Water currents and waves near the beach are strongly depend on complicated coastal line and in turn, exert on the bottom sediment transportation near the shore. The use of rectangular grids in the construction of discrete models leads to significant errors in both the specification of boundary conditions and in the modeling of hydrophysical processes in the coastal zone. In this paper, we consider the construction of a finite-element approximation of the initial-boundary value problem for the spatially two-dimensional linearized equation of sediment transportation using optimal boundary-adaptive grid. First, the linearization of a spatially two-dimensional nonlinear parabolic equation on the time grid is performed-when the coefficients of the equation that are nonlinearly dependent on the bottom relief function are set on the previous time layer, and the corresponding initial conditions are used on the first time layer. The algorithm for constructing the grid is based on the procedure for minimizing the generalized Dirichlet functional. On the constructed grid, finite element approximation using bilinear basis functions is performed, which completes the construction of a discrete model for the given problem. The using of curvilinear boundary adaptive grids leads to decreasing of total grid number in 5-20 times and respectively the total modeling time and/or it allows to improve modeling accuracy.

  13. A finite Hankel algorithm for intense optical beam propagation in saturable medium

    International Nuclear Information System (INIS)

    Bardin, C.; Babuel-Peyrissac, J.P.; Marinier, J.P.; Mattar, F.P.

    1985-01-01

    Many physical problems, especially light-propagation, that involve the Laplacian operator, are naturally connected with Fourier or Hankel transforms (in case of axial symmetry), which both remove the Laplacian term in the transformed space. Sometimes the analytical calculation can be handled at its end, giving a series or an integral representation of the solution. Otherwise, an analytical pre-treatment of the original equation may be done, leading to numerical computation techniques as opposed to self-adaptive stretching and rezoning techniques, which do not use Fourier or Hankel transforms. The authors present here some basic mathematical properties of infinite and finite Hankel transform, their connection with physics and their adaptation to numerical calculation. The finite Hankel transform is well-suited to numerical computation, because it deals with a finite interval, and the precision of the calculation can be easily controlled by the number of zeros of J 0 (x) to be taken. Moreover, they use a special quadrature formula which is well connected to integral conservation laws. The inconvenience of having to sum a series is reduced by the use of vectorized computers, and in the future will be still more reduced with parallel processors. A finite-Hankel code has been performed on CRAY-XMP in order to solve the propagation of a CW optical beam in a saturable absorber. For large diffractions or when a very small radial grid is required for the description of the optical field, this FHT algorithm has been found to perform better than a direct finite-difference code

  14. Study of the key factors affecting the triple grid lifetime of the LIPS-300 ion thruster

    Science.gov (United States)

    Mingming, SUN; Liang, WANG; Juntai, YANG; Xiaodong, WEN; Yongjie, HUANG; Meng, WANG

    2018-04-01

    In order to ascertain the key factors affecting the lifetime of the triple grids in the LIPS-300 ion thruster, the thermal deformation, upstream ion density and component lifetime of the grids are simulated with finite element analysis, fluid simulation and charged-particle tracing simulation methods on the basis of a 1500 h short lifetime test. The key factor affecting the lifetime of the triple grids in the LIPS-300 ion thruster is obtained and analyzed through the test results. The results show that ion sputtering erosion of the grids in 5 kW operation mode is greater than in the case of 3 kW. In 5 kW mode, the decelerator grid shows the most serious corrosion, the accelerator grid shows moderate corrosion, and the screen grid shows the least amount of corrosion. With the serious corrosion of the grids in 5 kW operation mode, the intercept current of the acceleration and deceleration grids increases substantially. Meanwhile, the cold gap between the accelerator grid and the screen grid decreases from 1 mm to 0.7 mm, while the cold gap between the accelerator grid and the decelerator grid increases from 1 mm to 1.25 mm after 1500 h of thruster operation. At equilibrium temperature with 5 kW power, the finite element method (FEM) simulation results show that the hot gap between the screen grid and the accelerator grid reduces to 0.2 mm. Accordingly, the hot gap between the accelerator grid and the decelerator grid increases to 1.5 mm. According to the fluid method, the plasma density simulated in most regions of the discharge chamber is 1 × 1018‑8 × 1018 m‑3. The upstream plasma density of the screen grid is in the range 6 × 1017‑6 × 1018 m‑3 and displays a parabolic characteristic. The charged particle tracing simulation method results show that the ion beam current without the thermal deformation of triple grids has optimal perveance status. The ion sputtering rates of the accelerator grid hole and the decelerator hole are 5.5 × 10‑14 kg s‑1 and

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

    Energy Technology Data Exchange (ETDEWEB)

    Karlsen, Kenneth Hvistendal; Risebro, Nils Henrik

    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)

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2016-10-25

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

  17. Effect of grid resolution on large eddy simulation of wall-bounded turbulence

    Science.gov (United States)

    Rezaeiravesh, S.; Liefvendahl, M.

    2018-05-01

    The effect of grid resolution on a large eddy simulation (LES) of a wall-bounded turbulent flow is investigated. A channel flow simulation campaign involving a systematic variation of the streamwise (Δx) and spanwise (Δz) grid resolution is used for this purpose. The main friction-velocity-based Reynolds number investigated is 300. Near the walls, the grid cell size is determined by the frictional scaling, Δx+ and Δz+, and strongly anisotropic cells, with first Δy+ ˜ 1, thus aiming for the wall-resolving LES. Results are compared to direct numerical simulations, and several quality measures are investigated, including the error in the predicted mean friction velocity and the error in cross-channel profiles of flow statistics. To reduce the total number of channel flow simulations, techniques from the framework of uncertainty quantification are employed. In particular, a generalized polynomial chaos expansion (gPCE) is used to create metamodels for the errors over the allowed parameter ranges. The differing behavior of the different quality measures is demonstrated and analyzed. It is shown that friction velocity and profiles of the velocity and Reynolds stress tensor are most sensitive to Δz+, while the error in the turbulent kinetic energy is mostly influenced by Δx+. Recommendations for grid resolution requirements are given, together with the quantification of the resulting predictive accuracy. The sensitivity of the results to the subgrid-scale (SGS) model and varying Reynolds number is also investigated. All simulations are carried out with second-order accurate finite-volume-based solver OpenFOAM. It is shown that the choice of numerical scheme for the convective term significantly influences the error portraits. It is emphasized that the proposed methodology, involving the gPCE, can be applied to other modeling approaches, i.e., other numerical methods and the choice of SGS model.

  18. 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)

  19. Main formulations of the finite element method for the problems of structural mechanics. Part 2

    Directory of Open Access Journals (Sweden)

    Ignat’ev Aleksandr Vladimirovich

    Full Text Available The author offers a classification of Finite Element formulations, which allows orienting in a great number of the published and continuing to be published works on the problem of raising the efficiency of this widespread numerical method. The second part of the article offers examination of straight formulations of FEM in the form of displacement approach, area method and classical mixed-mode method. The question of solution convergence according to FEM in the form of classical mixed-mode method is considered on the example of single-input single-output system of a beam in case of finite element grid refinement. The author draws a conclusion, that extinction of algebraic equations system of FEM in case of passage to the limit is not a peculiar feature of this method in general, but manifests itself only in some particular cases. At the same time the obtained results prove that FEM in mixed-mode form provides obtaining more stable results in case of finite element grid refinement in comparison with FEM in the form of displacement approach. It is quite obvious that the same qualities will appear also in two-dimensional systems.

  20. SAFE-AXISYM, Stress Analysis of Axisymmetric Composite Structure by Finite Elements Method

    International Nuclear Information System (INIS)

    Cornell, D.C.

    1967-01-01

    1 - Nature of physical problem solved: SAFE-AXISYM is a program for the analysis of multi-material axisymmetric composite structures. It is designed for the analysis of heterogeneous structures such as reinforced and/or prestressed concrete vessels. The structure is assumed to be linearly elastic, and only bodies of revolution subjected to axisymmetric loading can be treated. 2 - Method of solution: SAFE-AXISYM uses a finite element method with a modified Gauss-Seidel iteration scheme. A reference grid subdivides the structure into ring-like small, finite elements, the vertices of which are called nodes. The grid may be generated by hand, by the computer or by a combination of the two methods. Each node has two degrees of freedom, translation in the and in the axial direction. Both zero and non-zero fixed displacement constraints may be assumed, and the loading condition may be mechanical and/or thermal. 3 - Restrictions on the complexity of the problem: Multi-material structures with varying rigidities converge very slowly. Not valid for incompressible materials. Maximum number of nodes = 475. Maximum number of elements = 1100

  1. Grid cut-off-effect

    International Nuclear Information System (INIS)

    Fischer, U.; Vosshenrich, R.; Grabbe, E.

    1992-01-01

    Tilting of a grid during portable radiography leads to uneven exposures, and errors greater than 3 0 can lead to errors in interpretation. Differentiation from abnormal findings can be made by recognising exposure difference of extrathoracic comparable areas. The difficulties caused by tilting of the grid can be reduced by increasing the film focus distance and by using suitable grids. A new cassette holder with an integrated balance makes it possible to correct tilting of the grid rapidly and effectively. This results in improved image quality which can be applied not only to conventional exposure systems but is also of advantage when using digital methods. (orig.) [de

  2. A Finite Element Theory for Predicting the Attenuation of Extended-Reacting Liners

    Science.gov (United States)

    Watson, W. R.; Jones, M. G.

    2009-01-01

    A non-modal finite element theory for predicting the attenuation of an extended-reacting liner containing a porous facesheet and located in a no-flow duct is presented. The mathematical approach is to solve separate wave equations in the liner and duct airway and to couple these two solutions by invoking kinematic constraints at the facesheet that are consistent with a continuum theory of fluid motion. Given the liner intrinsic properties, a weak Galerkin finite element formulation with cubic polynomial basis functions is used as the basis for generating a discrete system of acoustic equations that are solved to obtain the coupled acoustic field. A state-of-the-art, asymmetric, parallel, sparse equation solver is implemented that allows tens of thousands of grid points to be analyzed. A grid refinement study is presented to show that the predicted attenuation converges. Excellent comparison of the numerically predicted attenuation to that of a mode theory (using a Haynes 25 metal foam liner) is used to validate the computational approach. Simulations are also presented for fifteen porous plate, extended-reacting liners. The construction of some of the porous plate liners suggest that they should behave as resonant liners while the construction of others suggest that they should behave as broadband attenuators. In each case the finite element theory is observed to predict the proper attenuation trend.

  3. 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

  4. 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.

  5. Monitoring the EGEE/WLCG grid services

    International Nuclear Information System (INIS)

    Duarte, A; Nyczyk, P; Retico, A; Vicinanza, D

    2008-01-01

    Grids have the potential to revolutionise computing by providing ubiquitous, on demand access to computational services and resources. They promise to allow for on demand access and composition of computational services provided by multiple independent sources. Grids can also provide unprecedented levels of parallelism for high-performance applications. On the other hand, grid characteristics, such as high heterogeneity, complexity and distribution create many new technical challenges. Among these technical challenges, failure management is a key area that demands much progress. A recent survey revealed that fault diagnosis is still a major problem for grid users. When a failure appears at the user screen, it becomes very difficult for the user to identify whether the problem is in the application, somewhere in the grid middleware, or even lower in the fabric that comprises the grid. In this paper we present a tool able to check if a given grid service works as expected for a given set of users (Virtual Organisation) on the different resources available on a grid. Our solution deals with grid services as single components that should produce an expected output to a pre-defined input, what is quite similar to unit testing. The tool, called Service Availability Monitoring or SAM, is being currently used by several different Virtual Organizations to monitor more than 300 grid sites belonging to the largest grids available today. We also discuss how this tool is being used by some of those VOs and how it is helping in the operation of the EGEE/WLCG grid

  6. A finite volume method for cylindrical heat conduction problems based on local analytical solution

    KAUST Repository

    Li, Wang

    2012-10-01

    A new finite volume method for cylindrical heat conduction problems based on local analytical solution is proposed in this paper with detailed derivation. The calculation results of this new method are compared with the traditional second-order finite volume method. The newly proposed method is more accurate than conventional ones, even though the discretized expression of this proposed method is slightly more complex than the second-order central finite volume method, making it cost more calculation time on the same grids. Numerical result shows that the total CPU time of the new method is significantly less than conventional methods for achieving the same level of accuracy. © 2012 Elsevier Ltd. All rights reserved.

  7. A finite volume method for cylindrical heat conduction problems based on local analytical solution

    KAUST Repository

    Li, Wang; Yu, Bo; Wang, Xinran; Wang, Peng; Sun, Shuyu

    2012-01-01

    A new finite volume method for cylindrical heat conduction problems based on local analytical solution is proposed in this paper with detailed derivation. The calculation results of this new method are compared with the traditional second-order finite volume method. The newly proposed method is more accurate than conventional ones, even though the discretized expression of this proposed method is slightly more complex than the second-order central finite volume method, making it cost more calculation time on the same grids. Numerical result shows that the total CPU time of the new method is significantly less than conventional methods for achieving the same level of accuracy. © 2012 Elsevier Ltd. All rights reserved.

  8. A Review on the Modified Finite Point Method

    Directory of Open Access Journals (Sweden)

    Nan-Jing Wu

    2014-01-01

    Full Text Available The objective of this paper is to make a review on recent advancements of the modified finite point method, named MFPM hereafter. This MFPM method is developed for solving general partial differential equations. Benchmark examples of employing this method to solve Laplace, Poisson, convection-diffusion, Helmholtz, mild-slope, and extended mild-slope equations are verified and then illustrated in fluid flow problems. Application of MFPM to numerical generation of orthogonal grids, which is governed by Laplace equation, is also demonstrated.

  9. Failure probability analysis of optical grid

    Science.gov (United States)

    Zhong, Yaoquan; Guo, Wei; Sun, Weiqiang; Jin, Yaohui; Hu, Weisheng

    2008-11-01

    Optical grid, the integrated computing environment based on optical network, is expected to be an efficient infrastructure to support advanced data-intensive grid applications. In optical grid, the faults of both computational and network resources are inevitable due to the large scale and high complexity of the system. With the optical network based distributed computing systems extensive applied in the processing of data, the requirement of the application failure probability have been an important indicator of the quality of application and an important aspect the operators consider. This paper will present a task-based analysis method of the application failure probability in optical grid. Then the failure probability of the entire application can be quantified, and the performance of reducing application failure probability in different backup strategies can be compared, so that the different requirements of different clients can be satisfied according to the application failure probability respectively. In optical grid, when the application based DAG (directed acyclic graph) is executed in different backup strategies, the application failure probability and the application complete time is different. This paper will propose new multi-objective differentiated services algorithm (MDSA). New application scheduling algorithm can guarantee the requirement of the failure probability and improve the network resource utilization, realize a compromise between the network operator and the application submission. Then differentiated services can be achieved in optical grid.

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

    KAUST Repository

    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.

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

    KAUST Repository

    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.

  12. 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.

  13. Modeling of NiTiHf using finite difference method

    Science.gov (United States)

    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.

  14. GENECODIS-Grid: An online grid-based tool to predict functional information in gene lists

    International Nuclear Information System (INIS)

    Nogales, R.; Mejia, E.; Vicente, C.; Montes, E.; Delgado, A.; Perez Griffo, F. J.; Tirado, F.; Pascual-Montano, A.

    2007-01-01

    In this work we introduce GeneCodis-Grid, a grid-based alternative to a bioinformatics tool named Genecodis that integrates different sources of biological information to search for biological features (annotations) that frequently co-occur in a set of genes and rank them by statistical significance. GeneCodis-Grid is a web-based application that takes advantage of two independent grid networks and a computer cluster managed by a meta-scheduler and a web server that host the application. The mining of concurrent biological annotations provides significant information for the functional analysis of gene list obtained by high throughput experiments in biology. Due to the large popularity of this tool, that has registered more than 13000 visits since its publication in January 2007, there is a strong need to facilitate users from different sites to access the system simultaneously. In addition, the complexity of some of the statistical tests used in this approach has made this technique a good candidate for its implementation in a Grid opportunistic environment. (Author)

  15. Smart grid

    International Nuclear Information System (INIS)

    Choi, Dong Bae

    2001-11-01

    This book describes press smart grid from basics to recent trend. It is divided into ten chapters, which deals with smart grid as green revolution in energy with introduction, history, the fields, application and needed technique for smart grid, Trend of smart grid in foreign such as a model business of smart grid in foreign, policy for smart grid in U.S.A, Trend of smart grid in domestic with international standard of smart grid and strategy and rood map, smart power grid as infrastructure of smart business with EMS development, SAS, SCADA, DAS and PQMS, smart grid for smart consumer, smart renewable like Desertec project, convergence IT with network and PLC, application of an electric car, smart electro service for realtime of electrical pricing system, arrangement of smart grid.

  16. Wind Penetration with different wind turbine technologies in a weak grid

    International Nuclear Information System (INIS)

    Santos Fuentefria, Ariel; Castro Fernandez, Miguel A.; Martínez García, Antonio

    2012-01-01

    The insertion of wind energy into electric network may provoke stability problems due to stochastic character of wind. The variation in the wind causes voltage variation in the Point of Common Coupling (PCC). In a weakest system that variation is high. Another important factor is wind turbine technology. The use of grid-connected fixed speed wind generator introduces a great consumption of reactive power that can be compensated using different devices as capacitors bank or static var compensator (SVC or STATCOM). In the other hand the variable speed wind turbine have an electronic converter to control the reactive consumption to maintain the PCC voltage more stable. In this paper a comparison between the different types of wind turbines technology is show. It's analyzing the impact in wind power limit for different wind turbine technologies in a weak system. (author)

  17. Safe Grid

    Science.gov (United States)

    Chow, Edward T.; Stewart, Helen; Korsmeyer, David (Technical Monitor)

    2003-01-01

    The biggest users of GRID technologies came from the science and technology communities. These consist of government, industry and academia (national and international). The NASA GRID is moving into a higher technology readiness level (TRL) today; and as a joint effort among these leaders within government, academia, and industry, the NASA GRID plans to extend availability to enable scientists and engineers across these geographical boundaries collaborate to solve important problems facing the world in the 21 st century. In order to enable NASA programs and missions to use IPG resources for program and mission design, the IPG capabilities needs to be accessible from inside the NASA center networks. However, because different NASA centers maintain different security domains, the GRID penetration across different firewalls is a concern for center security people. This is the reason why some IPG resources are been separated from the NASA center network. Also, because of the center network security and ITAR concerns, the NASA IPG resource owner may not have full control over who can access remotely from outside the NASA center. In order to obtain organizational approval for secured remote access, the IPG infrastructure needs to be adapted to work with the NASA business process. Improvements need to be made before the IPG can be used for NASA program and mission development. The Secured Advanced Federated Environment (SAFE) technology is designed to provide federated security across NASA center and NASA partner's security domains. Instead of one giant center firewall which can be difficult to modify for different GRID applications, the SAFE "micro security domain" provide large number of professionally managed "micro firewalls" that can allow NASA centers to accept remote IPG access without the worry of damaging other center resources. The SAFE policy-driven capability-based federated security mechanism can enable joint organizational and resource owner approved remote

  18. Smart Grid facets in the world; Les visages de Smart Grid dans le monde

    Energy Technology Data Exchange (ETDEWEB)

    Marcoux, Benoit; Bauchot, Frederic

    2010-09-15

    There is a certain consensus on what is the Smart Grid, but priorities vary from one world region to the next. These differences bring business strategies and objectives that vary from one electrical company to the next. However: Smart Grid programs of electrical companies are based on the same elements. -Smart Grid benefits are mainly gained by a greater integration at all levels. -Implementation priorities vary from one region to the next; the regions studied in this paper are the United States, Quebec, France, Denmark and China. [French] Un certain consensus se forme sur ce que constitue le Smart Grid, mais les priorites varient d'une region du monde a l'autre. Ces differences amenent des strategies et des objectifs d'affaires qui varient d'une entreprise d'electricite a l'autre. Cependant : -Les programmes de Smart Grid des entreprises d'electricite se basent sur les memes elements. -Les benefices du Smart Grid passe avant tout par une plus grande integration a tous les niveaux. -Les priorites d'implantation varient d'une region a l'autre; les regions etudiees dans ce papier sont les etats-Unis, le Quebec, la France, le Danemark et la Chine.

  19. Lowrank seismic-wave extrapolation on a staggered grid

    KAUST Repository

    Fang, Gang

    2014-05-01

    © 2014 Society of Exploration Geophysicists. We evaluated a new spectral method and a new finite-difference (FD) method for seismic-wave extrapolation in time. Using staggered temporal and spatial grids, we derived a wave-extrapolation operator using a lowrank decomposition for a first-order system of wave equations and designed the corresponding FD scheme. The proposed methods extend previously proposed lowrank and lowrank FD wave extrapolation methods from the cases of constant density to those of variable density. Dispersion analysis demonstrated that the proposed methods have high accuracy for a wide wavenumber range and significantly reduce the numerical dispersion. The method of manufactured solutions coupled with mesh refinement was used to verify each method and to compare numerical errors. Tests on 2D synthetic examples demonstrated that the proposed method is highly accurate and stable. The proposed methods can be used for seismic modeling or reverse-time migration.

  20. Lowrank seismic-wave extrapolation on a staggered grid

    KAUST Repository

    Fang, Gang; Fomel, Sergey; Du, Qizhen; Hu, Jingwei

    2014-01-01

    © 2014 Society of Exploration Geophysicists. We evaluated a new spectral method and a new finite-difference (FD) method for seismic-wave extrapolation in time. Using staggered temporal and spatial grids, we derived a wave-extrapolation operator using a lowrank decomposition for a first-order system of wave equations and designed the corresponding FD scheme. The proposed methods extend previously proposed lowrank and lowrank FD wave extrapolation methods from the cases of constant density to those of variable density. Dispersion analysis demonstrated that the proposed methods have high accuracy for a wide wavenumber range and significantly reduce the numerical dispersion. The method of manufactured solutions coupled with mesh refinement was used to verify each method and to compare numerical errors. Tests on 2D synthetic examples demonstrated that the proposed method is highly accurate and stable. The proposed methods can be used for seismic modeling or reverse-time migration.

  1. GridCom, Grid Commander: graphical interface for Grid jobs and data management

    International Nuclear Information System (INIS)

    Galaktionov, V.V.

    2011-01-01

    GridCom - the software package for maintenance of automation of access to means of distributed system Grid (jobs and data). The client part, executed in the form of Java-applets, realises the Web-interface access to Grid through standard browsers. The executive part Lexor (LCG Executor) is started by the user in UI (User Interface) machine providing performance of Grid operations

  2. Grid modeling, analysis and simulation of different scenarios for a smart low-voltage distribution grid

    DEFF Research Database (Denmark)

    Mihet-Popa, Lucian; Han, Xue; Bindner, Henrik W.

    2013-01-01

    , the number of cabinets and customers and the load per customer. The aim of the model is to design, implement and test the proposed configuration and to investigate whether the low-voltage distribution grid is prepared for the expected future increase of PV penetration, heat pumps and electric cars. The model...

  3. Four-level conservative finite-difference schemes for Boussinesq paradigm equation

    Science.gov (United States)

    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.

  4. A multigrid algorithm for the cell-centered finite difference scheme

    Science.gov (United States)

    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.

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

    KAUST Repository

    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.

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

    KAUST Repository

    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.

  7. 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

  8. Test Functions for Three-Dimensional Control-Volume Mixed Finite-Element Methods on Irregular Grids

    National Research Council Canada - National Science Library

    Naff, R. L; Russell, T. F; Wilson, J. D

    2000-01-01

    .... For control-volume mixed finite-element methods, vector shape functions are used to approximate the distribution of velocities across cells and vector test functions are used to minimize the error...

  9. 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

  10. Impact of Considering 110 kV Grid Structures on the Congestion Management in the German Transmission Grid

    Science.gov (United States)

    Hoffrichter, André; Barrios, Hans; Massmann, Janek; Venkataramanachar, Bhavasagar; Schnettler, Armin

    2018-02-01

    The structural changes in the European energy system lead to an increase of renewable energy sources that are primarily connected to the distribution grid. Hence the stationary analysis of the transmission grid and the regionalization of generation capacities are strongly influenced by subordinate grid structures. To quantify the impact on the congestion management in the German transmission grid, a 110 kV grid model is derived using publicly available data delivered by Open Street Map and integrated into an existing model of the European transmission grid. Power flow and redispatch simulations are performed for three different regionalization methods and grid configurations. The results show a significant impact of the 110 kV system and prove an overestimation of power flows in the transmission grid when neglecting subordinate grids. Thus, the redispatch volume in Germany to dissolve bottlenecks in case of N-1 contingencies decreases by 38 % when considering the 110 kV grid.

  11. Overview of Grid Codes for Photovoltaic Integration

    DEFF Research Database (Denmark)

    Zheng, Qianwei; Li, Jiaming; Ai, Xiaomeng

    2017-01-01

    The increasing grid-connected photovoltaic (PV) power stations might threaten the safety and stability of power system. Therefore, the grid code is developed for PV power stations to ensure the security of PV integrated power systems. In this paper, requirements for PV power integration in differ...... in different grid codes are first investigated. On this basis, the future advocacy is concluded. Finally, several evaluation indices are proposed to quantify the grid code compliance so that the system operators can validate all these requirements by simulation....

  12. Generalized multiscale finite element methods: Oversampling strategies

    KAUST Repository

    Efendiev, Yalchin R.; Galvis, Juan; Li, Guanglian; Presho, Michael

    2014-01-01

    In this paper, we propose oversampling strategies in the generalized multiscale finite element method (GMsFEM) framework. The GMsFEM, which has been recently introduced in Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], allows solving multiscale parameter-dependent problems at a reduced computational cost by constructing a reduced-order representation of the solution on a coarse grid. The main idea of the method consists of (1) the construction of snapshot space, (2) the construction of the offline space, and (3) construction of the online space (the latter for parameter-dependent problems). In Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], it was shown that the GMsFEM provides a flexible tool to solve multiscale problems with a complex input space by generating appropriate snapshot, offline, and online spaces. In this paper, we develop oversampling techniques to be used in this context (see Hou and Wu (1997) where oversampling is introduced for multiscale finite element methods). It is known (see Hou and Wu (1997)) that the oversampling can improve the accuracy of multiscale methods. In particular, the oversampling technique uses larger regions (larger than the target coarse block) in constructing local basis functions. Our motivation stems from the analysis presented in this paper, which shows that when using oversampling techniques in the construction of the snapshot space and offline space, GMsFEM will converge independent of small scales and high contrast under certain assumptions. We consider the use of a multiple eigenvalue problems to improve the convergence and discuss their relation to single spectral problems that use oversampled regions. The oversampling procedures proposed in this paper differ from those in Hou and Wu (1997). In particular, the oversampling domains are partially used in constructing local

  13. 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

  14. Additional Security Considerations for Grid Management

    Science.gov (United States)

    Eidson, Thomas M.

    2003-01-01

    The use of Grid computing environments is growing in popularity. A Grid computing environment is primarily a wide area network that encompasses multiple local area networks, where some of the local area networks are managed by different organizations. A Grid computing environment also includes common interfaces for distributed computing software so that the heterogeneous set of machines that make up the Grid can be used more easily. The other key feature of a Grid is that the distributed computing software includes appropriate security technology. The focus of most Grid software is on the security involved with application execution, file transfers, and other remote computing procedures. However, there are other important security issues related to the management of a Grid and the users who use that Grid. This note discusses these additional security issues and makes several suggestions as how they can be managed.

  15. Smart grid in Denmark 2.0. Implementing three key recommendations from the Smart Grid Network. [DanGrid]; Smart Grid i Danmark 2.0. Implementering af tre centrale anbefalinger fra Smart Grid netvaerket

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    2012-11-01

    In 2011 the Smart Grid Network, established by the Danish Climate and Energy minister in 2010, published a report which identifies 35 recommendations for implementing smart grid in Denmark. The present report was prepared by the Danish Energy Association and Energinet.dk and elaborates three of these recommendations: Concept for controlling the power system; Information model for the dissemination of data; Roadmap for deployment of smart grid. Concept of Smart Grid: The concept mobilizes and enables electric power demand response and production from smaller customers. This is done by customers or devices connected to the power system modify their behavior to meet the needs of the power system. The concept basically distinguishes between two different mechanisms to enable flexibility. One is the use of price signals (variable network tariffs and electricity prices), which gives customers a financial incentive to move their electricity consumption and production to times when it is of less inconvenience to the power system. The second is flexibility products, where a pre-arranged and well-specified performance - for example, a load reduction in a defined network area - can be activated as required by grid operators and / or Energinet.dk at an agreed price. Information Model for Disseminating Data: The future power system is complex with a large number of physical units, companies and individuals are actively involved in the power system. Similarly, the amount of information needed to be collected, communicated and processed grows explosively, and it is therefore essential to ensure a well-functioning IT infrastructure. A crucial element is a standardized information model in the Danish power system. The concept therefore indicates to use international standards to define an information model. Roadmap Focusing on Grid Companies' Role: There is a need to remove two key barriers. The first barrier is that the existing regulation does not support the grid using

  16. 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.

  17. Fuel Cell Backup Power System for Grid Service and Micro-Grid in Telecommunication Applications: Preprint

    Energy Technology Data Exchange (ETDEWEB)

    Ma, Zhiwen [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Eichman, Joshua D [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Kurtz, Jennifer M [National Renewable Energy Laboratory (NREL), Golden, CO (United States)

    2018-03-22

    This paper presents the feasibility and economics of using fuel cell backup power systems in telecommunication cell towers to provide grid services (e.g., ancillary services, demand response). The fuel cells are able to provide power for the cell tower during emergency conditions. This study evaluates the strategic integration of clean, efficient, and reliable fuel cell systems with the grid for improved economic benefits. The backup systems have potential as enhanced capability through information exchanges with the power grid to add value as grid services that depend on location and time. The economic analysis has been focused on the potential revenue for distributed telecommunications fuel cell backup units to provide value-added power supply. This paper shows case studies on current fuel cell backup power locations and regional grid service programs. The grid service benefits and system configurations for different operation modes provide opportunities for expanding backup fuel cell applications responsive to grid needs.

  18. Temperature field due to time-dependent heat sources in a large rectangular grid - Derivation of analytical solution

    International Nuclear Information System (INIS)

    Claesson, J.; Probert, T.

    1996-01-01

    The temperature field in rock due to a large rectangular grid of heat releasing canisters containing nuclear waste is studied. The solution is by superposition divided into different parts. There is a global temperature field due to the large rectangular canister area, while a local field accounts for the remaining heat source problem. The global field is reduced to a single integral. The local field is also solved analytically using solutions for a finite line heat source and for an infinite grid of point sources. The local solution is reduced to three parts, each of which depends on two spatial coordinates only. The temperatures at the envelope of a canister are given by a single thermal resistance, which is given by an explicit formula. The results are illustrated by a few numerical examples dealing with the KBS-3 concept for storage of nuclear waste. 8 refs

  19. The Incorporation of Truncated Fourier Series into Finite Difference Approximations of Structural Stability Equations

    Science.gov (United States)

    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.

  20. 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)

  1. SuperGrid or SmartGrid: Competing strategies for large-scale integration of intermittent renewables?

    DEFF Research Database (Denmark)

    Blarke, Morten; M. Jenkins, Bryan

    2013-01-01

    This paper defines and compares two strategies for integrating intermittent renewables: SuperGrid and SmartGrid. While conventional energy policy suggests that these strategies may be implemented alongside each other, the paper identifies significant technological and socio-economic conflicts...... of interest between the two. The article identifies differences between a domestic strategy for the integration of intermittent renewables, vis-à-vis the SmartGrid, and a cross-system strategy, vis-à-vis the SuperGrid. Policy makers and transmission system operators must understand the need for both...... a paradigmatic case study from West Denmark which supports the hypothesis that these strategies are mutually exclusive. The case study shows that increasing cross-system transmission capacity jeopardizes the feasibility of SmartGrid technology investments. A political effort is required for establishing...

  2. Power grids

    International Nuclear Information System (INIS)

    Viterbo, J.

    2012-01-01

    The implementation of renewable energies represents new challenges for electrical systems. The objective: making power grids smarter so they can handle intermittent production. The advent of smart grids will allow flexible operations like distributing energy in a multidirectional manner instead of just one way and it will make electrical systems capable of integrating actions by different users, consumers and producers in order to maintain efficient, sustainable, economical and secure power supplies. Practically speaking, they associate sensors, instrumentation and controls with information processing and communication systems in order to create massively automated networks. Smart grids require huge investments: for example more than 7 billion dollars have been invested in China and in the Usa in 2010 and France is ranked 9. worldwide with 265 million dollars invested. It is expected that smart grids will promote the development of new business models and a change in the value chain for energy. Decentralized production combined with the probable introduction of more or less flexible rates for sales or purchases and of new supplier-customer relationships will open the way to the creation of new businesses. (A.C.)

  3. Computational electrodynamics the finite-difference time-domain method

    CERN Document Server

    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.

  4. Vertical grid of retrieved atmospheric profiles

    International Nuclear Information System (INIS)

    Ceccherini, Simone; Carli, Bruno; Raspollini, Piera

    2016-01-01

    The choice of the vertical grid of atmospheric profiles retrieved from remote sensing observations is discussed considering the two cases of profiles used to represent the results of individual measurements and of profiles used for subsequent data fusion applications. An ozone measurement of the MIPAS instrument is used to assess, for different vertical grids, the quality of the retrieved profiles in terms of profile values, retrieval errors, vertical resolutions and number of degrees of freedom. In the case of individual retrievals no evident advantage is obtained with the use of a grid finer than the one with a reduced number of grid points, which are optimized according to the information content of the observations. Nevertheless, this instrument dependent vertical grid, which seems to extract all the available information, provides very poor results when used for data fusion applications. A loss of about a quarter of the degrees of freedom is observed when the data fusion is made using the instrument dependent vertical grid relative to the data fusion made using a vertical grid optimized for the data fusion product. This result is explained by the analysis of the eigenvalues of the Fisher information matrix and leads to the conclusion that different vertical grids must be adopted when data fusion is the expected application. - Highlights: • Data fusion application is taken into account for the choice of the vertical grid. • The study is performed using ozone profiles retrieved from MIPAS measurements. • A very fine vertical grid is not needed for the analysis of a single instrument. • The instrument dependent vertical grid is not the best choice for data fusion. • A data fusion dependent vertical grid must be used for profiles that will be fused.

  5. Grid Integration of PV Power based on PHIL testing using different Interface Algorithms

    DEFF Research Database (Denmark)

    Craciun, Bogdan-Ionut; Kerekes, Tamas; Sera, Dezso

    2013-01-01

    to be more active in grid support. Therefore, a better understanding and detailed analysis of the PV systems interaction with the grid is needed; hence power hardware in the loop (PHIL) testing involving PV power became an interesting subject to look into. To test PV systems for grid code (GC) compliance......Photovoltaic (PV) power among all renewable energies had the most accelerated growth rate in terms of installed capacity in recent years. Transmission System Operators (TSOs) changed their perspective about PV power and started to include it into their planning and operation, imposing PV systems...

  6. A Development of Lightweight Grid Interface

    International Nuclear Information System (INIS)

    Iwai, G; Kawai, Y; Sasaki, T; Watase, Y

    2011-01-01

    In order to help a rapid development of Grid/Cloud aware applications, we have developed API to abstract the distributed computing infrastructures based on SAGA (A Simple API for Grid Applications). SAGA, which is standardized in the OGF (Open Grid Forum), defines API specifications to access distributed computing infrastructures, such as Grid, Cloud and local computing resources. The Universal Grid API (UGAPI), which is a set of command line interfaces (CLI) and APIs, aims to offer simpler API to combine several SAGA interfaces with richer functionalities. These CLIs of the UGAPI offer typical functionalities required by end users for job management and file access to the different distributed computing infrastructures as well as local computing resources. We have also built a web interface for the particle therapy simulation and demonstrated the large scale calculation using the different infrastructures at the same time. In this paper, we would like to present how the web interface based on UGAPI and SAGA achieve more efficient utilization of computing resources over the different infrastructures with technical details and practical experiences.

  7. Assessment of grid optimisation measures for the German transmission grid using open source grid data

    Science.gov (United States)

    Böing, F.; Murmann, A.; Pellinger, C.; Bruckmeier, A.; Kern, T.; Mongin, T.

    2018-02-01

    The expansion of capacities in the German transmission grid is a necessity for further integration of renewable energy sources into the electricity sector. In this paper, the grid optimisation measures ‘Overhead Line Monitoring’, ‘Power-to-Heat’ and ‘Demand Response in the Industry’ are evaluated and compared against conventional grid expansion for the year 2030. Initially, the methodical approach of the simulation model is presented and detailed descriptions of the grid model and the used grid data, which partly originates from open-source platforms, are provided. Further, this paper explains how ‘Curtailment’ and ‘Redispatch’ can be reduced by implementing grid optimisation measures and how the depreciation of economic costs can be determined considering construction costs. The developed simulations show that the conventional grid expansion is more efficient and implies more grid relieving effects than the evaluated grid optimisation measures.

  8. 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

  9. Grid support capabilities of wind turbines

    DEFF Research Database (Denmark)

    Michalke, Gabriele; Hansen, Anca Daniela

    2013-01-01

    Wind power has gained a significant penetration level in several power systems all over the world. Due to this reason modern wind turbines are requested to contribute to power system support. Power system operators have thus introduced grid codes, which specify a set of requirements for wind...... turbines, such as fault ride-through and reactive power supply during voltage sags. To date different wind turbine concepts exist on the market comprising different control features in order to provide ancillary services to the power system. In the first place the present chapter emphasizes the most...... important issues related to wind power grid integration. Then different wind turbine concepts are characterized and their grid support capabilities are analysed and compared. Simulation cases are presented in which the respective wind turbine concepts are subjected to a voltage dip specified in a grid code....

  10. Generalized multiscale finite element methods (GMsFEM)

    KAUST Repository

    Efendiev, Yalchin R.; Galvis, Juan; Hou, Thomasyizhao

    2013-01-01

    In this paper, we propose a general approach called Generalized Multiscale Finite Element Method (GMsFEM) for performing multiscale simulations for problems without scale separation over a complex input space. As in multiscale finite element methods (MsFEMs), the main idea of the proposed approach is to construct a small dimensional local solution space that can be used to generate an efficient and accurate approximation to the multiscale solution with a potentially high dimensional input parameter space. In the proposed approach, we present a general procedure to construct the offline space that is used for a systematic enrichment of the coarse solution space in the online stage. The enrichment in the online stage is performed based on a spectral decomposition of the offline space. In the online stage, for any input parameter, a multiscale space is constructed to solve the global problem on a coarse grid. The online space is constructed via a spectral decomposition of the offline space and by choosing the eigenvectors corresponding to the largest eigenvalues. The computational saving is due to the fact that the construction of the online multiscale space for any input parameter is fast and this space can be re-used for solving the forward problem with any forcing and boundary condition. Compared with the other approaches where global snapshots are used, the local approach that we present in this paper allows us to eliminate unnecessary degrees of freedom on a coarse-grid level. We present various examples in the paper and some numerical results to demonstrate the effectiveness of our method. © 2013 Elsevier Inc.

  11. Generalized multiscale finite element methods (GMsFEM)

    KAUST Repository

    Efendiev, Yalchin R.

    2013-10-01

    In this paper, we propose a general approach called Generalized Multiscale Finite Element Method (GMsFEM) for performing multiscale simulations for problems without scale separation over a complex input space. As in multiscale finite element methods (MsFEMs), the main idea of the proposed approach is to construct a small dimensional local solution space that can be used to generate an efficient and accurate approximation to the multiscale solution with a potentially high dimensional input parameter space. In the proposed approach, we present a general procedure to construct the offline space that is used for a systematic enrichment of the coarse solution space in the online stage. The enrichment in the online stage is performed based on a spectral decomposition of the offline space. In the online stage, for any input parameter, a multiscale space is constructed to solve the global problem on a coarse grid. The online space is constructed via a spectral decomposition of the offline space and by choosing the eigenvectors corresponding to the largest eigenvalues. The computational saving is due to the fact that the construction of the online multiscale space for any input parameter is fast and this space can be re-used for solving the forward problem with any forcing and boundary condition. Compared with the other approaches where global snapshots are used, the local approach that we present in this paper allows us to eliminate unnecessary degrees of freedom on a coarse-grid level. We present various examples in the paper and some numerical results to demonstrate the effectiveness of our method. © 2013 Elsevier Inc.

  12. Multiscale Finite Element Methods for Flows on Rough Surfaces

    KAUST Repository

    Efendiev, Yalchin

    2013-01-01

    In this paper, we present the Multiscale Finite Element Method (MsFEM) for problems on rough heterogeneous surfaces. We consider the diffusion equation on oscillatory surfaces. Our objective is to represent small-scale features of the solution via multiscale basis functions described on a coarse grid. This problem arises in many applications where processes occur on surfaces or thin layers. We present a unified multiscale finite element framework that entails the use of transformations that map the reference surface to the deformed surface. The main ingredients of MsFEM are (1) the construction of multiscale basis functions and (2) a global coupling of these basis functions. For the construction of multiscale basis functions, our approach uses the transformation of the reference surface to a deformed surface. On the deformed surface, multiscale basis functions are defined where reduced (1D) problems are solved along the edges of coarse-grid blocks to calculate nodalmultiscale basis functions. Furthermore, these basis functions are transformed back to the reference configuration. We discuss the use of appropriate transformation operators that improve the accuracy of the method. The method has an optimal convergence if the transformed surface is smooth and the image of the coarse partition in the reference configuration forms a quasiuniform partition. In this paper, we consider such transformations based on harmonic coordinates (following H. Owhadi and L. Zhang [Comm. Pure and Applied Math., LX(2007), pp. 675-723]) and discuss gridding issues in the reference configuration. Numerical results are presented where we compare the MsFEM when two types of deformations are used formultiscale basis construction. The first deformation employs local information and the second deformation employs a global information. Our numerical results showthat one can improve the accuracy of the simulations when a global information is used. © 2013 Global-Science Press.

  13. The Wigner distribution function for the su(2) finite oscillator and Dyck paths

    International Nuclear Information System (INIS)

    Oste, Roy; Jeugt, Joris Van der

    2014-01-01

    Recently, a new definition for a Wigner distribution function for a one-dimensional finite quantum system, in which the position and momentum operators have a finite (multiplicity-free) spectrum, was developed. This distribution function is defined on discrete phase-space (a finite square grid), and can thus be referred to as the Wigner matrix. In the current paper, we compute this Wigner matrix (or rather, the pre-Wigner matrix, which is related to the Wigner matrix by a simple matrix multiplication) for the case of the su(2) finite oscillator. The first expression for the matrix elements involves sums over squares of Krawtchouk polynomials, and follows from standard techniques. We also manage to present a second solution, where the matrix elements are evaluations of Dyck polynomials. These Dyck polynomials are defined in terms of the well-known Dyck paths. This combinatorial expression of the pre-Wigner matrix elements turns out to be particularly simple. (paper)

  14. Finite volume model for two-dimensional shallow environmental flow

    Science.gov (United States)

    Simoes, F.J.M.

    2011-01-01

    This paper presents the development of a two-dimensional, depth integrated, unsteady, free-surface model based on the shallow water equations. The development was motivated by the desire of balancing computational efficiency and accuracy by selective and conjunctive use of different numerical techniques. The base framework of the discrete model uses Godunov methods on unstructured triangular grids, but the solution technique emphasizes the use of a high-resolution Riemann solver where needed, switching to a simpler and computationally more efficient upwind finite volume technique in the smooth regions of the flow. Explicit time marching is accomplished with strong stability preserving Runge-Kutta methods, with additional acceleration techniques for steady-state computations. A simplified mass-preserving algorithm is used to deal with wet/dry fronts. Application of the model is made to several benchmark cases that show the interplay of the diverse solution techniques.

  15. Replica consistency in a Data Grid

    International Nuclear Information System (INIS)

    Domenici, Andrea; Donno, Flavia; Pucciani, Gianni; Stockinger, Heinz; Stockinger, Kurt

    2004-01-01

    A Data Grid is a wide area computing infrastructure that employs Grid technologies to provide storage capacity and processing power to applications that handle very large quantities of data. Data Grids rely on data replication to achieve better performance and reliability by storing copies of data sets on different Grid nodes. When a data set can be modified by applications, the problem of maintaining consistency among existing copies arises. The consistency problem also concerns metadata, i.e., additional information about application data sets such as indices, directories, or catalogues. This kind of metadata is used both by the applications and by the Grid middleware to manage the data. For instance, the Replica Management Service (the Grid middleware component that controls data replication) uses catalogues to find the replicas of each data set. Such catalogues can also be replicated and their consistency is crucial to the correct operation of the Grid. Therefore, metadata consistency generally poses stricter requirements than data consistency. In this paper we report on the development of a Replica Consistency Service based on the middleware mainly developed by the European Data Grid Project. The paper summarises the main issues in the replica consistency problem, and lays out a high-level architectural design for a Replica Consistency Service. Finally, results from simulations of different consistency models are presented

  16. 3D Voronoi grid dedicated software for modeling gas migration in deep layered sedimentary formations with TOUGH2-TMGAS

    Science.gov (United States)

    Bonduà, Stefano; Battistelli, Alfredo; Berry, Paolo; Bortolotti, Villiam; Consonni, Alberto; Cormio, Carlo; Geloni, Claudio; Vasini, Ester Maria

    2017-11-01

    As is known, a full three-dimensional (3D) unstructured grid permits a great degree of flexibility when performing accurate numerical reservoir simulations. However, when the Integral Finite Difference Method (IFDM) is used for spatial discretization, constraints (arising from the required orthogonality between the segment connecting the blocks nodes and the interface area between blocks) pose difficulties in the creation of grids with irregular shaped blocks. The full 3D Voronoi approach guarantees the respect of IFDM constraints and allows generation of grids conforming to geological formations and structural objects and at the same time higher grid resolution in volumes of interest. In this work, we present dedicated pre- and post-processing gridding software tools for the TOUGH family of numerical reservoir simulators, developed by the Geothermal Research Group of the DICAM Department, University of Bologna. VORO2MESH is a new software coded in C++, based on the voro++ library, allowing computation of the 3D Voronoi tessellation for a given domain and the creation of a ready to use TOUGH2 MESH file. If a set of geological surfaces is available, the software can directly generate the set of Voronoi seed points used for tessellation. In order to reduce the number of connections and so to decrease computation time, VORO2MESH can produce a mixed grid with regular blocks (orthogonal prisms) and irregular blocks (polyhedron Voronoi blocks) at the point of contact between different geological formations. In order to visualize 3D Voronoi grids together with the results of numerical simulations, the functionality of the TOUGH2Viewer post-processor has been extended. We describe an application of VORO2MESH and TOUGH2Viewer to validate the two tools. The case study deals with the simulation of the migration of gases in deep layered sedimentary formations at basin scale using TOUGH2-TMGAS. A comparison between the simulation performances of unstructured and structured

  17. A Numerical Analysis on the Local Deformation of a Spacer Grid Structure for Nuclear Fuel Cells

    International Nuclear Information System (INIS)

    Jang, Myung-Geun; Na, Geum Ju; Kim, Jong-Bong; Shin, Hyunho

    2016-01-01

    The result of a preliminary numerical investigation on local deformation characteristics of a multi-layered spacer-grid structure with five guide tubes is reported based on implicit finite element analysis. For the numerical analysis, displacements of top and bottom cross sections of each guide tube in a single-layer model were constrained while a lateral displacement was imposed on the single layer. Unlike the impact hammer test that is generally employed to characterize the deformation characteristics of the space-grid structure, the buckling phenomenon occurs locally in this study; it takes place at the inner grids around each tube and the degree of bucking is more apparent for tubes near the lateral surface where the lateral displacement was imposed. (paper)

  18. Discontinuous Galerkin Subgrid Finite Element Method for Heterogeneous Brinkman’s Equations

    KAUST Repository

    Iliev, Oleg P.

    2010-01-01

    We present a two-scale finite element method for solving Brinkman\\'s equations with piece-wise constant coefficients. This system of equations model fluid flows in highly porous, heterogeneous media with complex topology of the heterogeneities. We make use of the recently proposed discontinuous Galerkin FEM for Stokes equations by Wang and Ye in [12] and the concept of subgrid approximation developed for Darcy\\'s equations by Arbogast in [4]. In order to reduce the error along the coarse-grid interfaces we have added a alternating Schwarz iteration using patches around the coarse-grid boundaries. We have implemented the subgrid method using Deal.II FEM library, [7], and we present the computational results for a number of model problems. © 2010 Springer-Verlag Berlin Heidelberg.

  19. Finite Boltzmann schemes

    NARCIS (Netherlands)

    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

  20. A Three-Dimensional, Immersed Boundary, Finite Volume Method for the Simulation of Incompressible Heat Transfer Flows around Complex Geometries

    Directory of Open Access Journals (Sweden)

    Hassan Badreddine

    2017-01-01

    Full Text Available The current work focuses on the development and application of a new finite volume immersed boundary method (IBM to simulate three-dimensional fluid flows and heat transfer around complex geometries. First, the discretization of the governing equations based on the second-order finite volume method on Cartesian, structured, staggered grid is outlined, followed by the description of modifications which have to be applied to the discretized system once a body is immersed into the grid. To validate the new approach, the heat conduction equation with a source term is solved inside a cavity with an immersed body. The approach is then tested for a natural convection flow in a square cavity with and without circular cylinder for different Rayleigh numbers. The results computed with the present approach compare very well with the benchmark solutions. As a next step in the validation procedure, the method is tested for Direct Numerical Simulation (DNS of a turbulent flow around a surface-mounted matrix of cubes. The results computed with the present method compare very well with Laser Doppler Anemometry (LDA measurements of the same case, showing that the method can be used for scale-resolving simulations of turbulence as well.

  1. Finite Element Methods On Very Large, Dynamic Tubular Grid Encoded Implicit Surfaces

    DEFF Research Database (Denmark)

    Nemitz, Oliver; Nielsen, Michael Bang; Rumpf, Martin

    2009-01-01

    dynamic tubular grid encoding format for a narrow band. A reaction diffusion model on a fixed surface and surface evolution driven by a nonlinear geometric diffusion approach, by isotropic or truly anisotropic curvature motion, are investigated as characteristic model problems. The proposed methods...

  2. Production grid systems and their programming

    CERN Document Server

    Kacsuk, P; Stefan, P

    2004-01-01

    Summary form only given. There are a large variety of grid test-beds that can be used for experimental purposes by a small community. However, the number of production grid systems that can be used as a service for a large community is very limited. The current tutorial provides introduction to three of these very few production grid systems. They represent different models and policies of using grid resources and hence understanding and comparing them is an extremely useful exercise to everyone interested in grid technology. The Hungarian ClusterGrid infrastructure connects clusters during the nights and weekends. These clusters are used during the day for educational purposes at the Hungarian universities and polytechnics. Therefore, a unique feature of this grid is the switching mechanism by which the day time and night time working modes are loaded to the computers. In order to manage the system as a production, one, the system is homogeneous, all the machines should install the same grid software package...

  3. Triple-layer smart grid business model

    DEFF Research Database (Denmark)

    Ma, Zheng; Lundgaard, Morten; Jørgensen, Bo Nørregaard

    2016-01-01

    Viewing the smart grid with the theory of business models may open opportunities in understanding and capturing values in new markets. This study tries to discover and map the smart grid ecosystem-based business model framework with two different environments (sub-Saharan Africa and Denmark......), and identifies the parameters for the smart grid solutions to the emerging markets. This study develops a triple-layer business model including the organizational (Niche), environmental (Intermediate), and global (Dominators) factors. The result uncovers an interface of market factors and stakeholders...... in a generic smart grid constellation. The findings contribute the transferability potential of the smart grid solutions between countries, and indicate the potential to export and import smart grid solutions based on the business modeling....

  4. MrGrid: a portable grid based molecular replacement pipeline.

    Directory of Open Access Journals (Sweden)

    Jason W Schmidberger

    Full Text Available BACKGROUND: The crystallographic determination of protein structures can be computationally demanding and for difficult cases can benefit from user-friendly interfaces to high-performance computing resources. Molecular replacement (MR is a popular protein crystallographic technique that exploits the structural similarity between proteins that share some sequence similarity. But the need to trial permutations of search models, space group symmetries and other parameters makes MR time- and labour-intensive. However, MR calculations are embarrassingly parallel and thus ideally suited to distributed computing. In order to address this problem we have developed MrGrid, web-based software that allows multiple MR calculations to be executed across a grid of networked computers, allowing high-throughput MR. METHODOLOGY/PRINCIPAL FINDINGS: MrGrid is a portable web based application written in Java/JSP and Ruby, and taking advantage of Apple Xgrid technology. Designed to interface with a user defined Xgrid resource the package manages the distribution of multiple MR runs to the available nodes on the Xgrid. We evaluated MrGrid using 10 different protein test cases on a network of 13 computers, and achieved an average speed up factor of 5.69. CONCLUSIONS: MrGrid enables the user to retrieve and manage the results of tens to hundreds of MR calculations quickly and via a single web interface, as well as broadening the range of strategies that can be attempted. This high-throughput approach allows parameter sweeps to be performed in parallel, improving the chances of MR success.

  5. Models for the modern power grid

    Science.gov (United States)

    Nardelli, Pedro H. J.; Rubido, Nicolas; Wang, Chengwei; Baptista, Murilo S.; Pomalaza-Raez, Carlos; Cardieri, Paulo; Latva-aho, Matti

    2014-10-01

    This article reviews different kinds of models for the electric power grid that can be used to understand the modern power system, the smart grid. From the physical network to abstract energy markets, we identify in the literature different aspects that co-determine the spatio-temporal multilayer dynamics of power system. We start our review by showing how the generation, transmission and distribution characteristics of the traditional power grids are already subject to complex behaviour appearing as a result of the the interplay between dynamics of the nodes and topology, namely synchronisation and cascade effects. When dealing with smart grids, the system complexity increases even more: on top of the physical network of power lines and controllable sources of electricity, the modernisation brings information networks, renewable intermittent generation, market liberalisation, prosumers, among other aspects. In this case, we forecast a dynamical co-evolution of the smart grid and other kind of networked systems that cannot be understood isolated. This review compiles recent results that model electric power grids as complex systems, going beyond pure technological aspects. From this perspective, we then indicate possible ways to incorporate the diverse co-evolving systems into the smart grid model using, for example, network theory and multi-agent simulation.

  6. Integrating renewables in distribution grids: Storage, regulation and the interaction of different stakeholders in future grids

    NARCIS (Netherlands)

    Nykamp, Stefan

    2013-01-01

    In recent years, the transition of the power supply chain towards a sustainable system based on “green‿ electricity generation out of renewable energy sources (RES-E) has become a main challenge for grid operators and further stakeholders in the power system. To enable the evaluation of new concepts

  7. Integrating renewables in distribution grids: storage, regulation and the interactions of different stakeholders in future grids

    NARCIS (Netherlands)

    Nykamp, Stefan

    2013-01-01

    In recent years, the transition of the power supply chain towards a sustainable system based on “green” electricity generation out of renewable energy sources (RES-E) has become a main challenge for grid operators and further stakeholders in the power system. To enable the evaluation of new concepts

  8. Arbitrary-Lagrangian-Eulerian Discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes

    Science.gov (United States)

    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

  9. Flow simulation of a Pelton bucket using finite volume particle method

    International Nuclear Information System (INIS)

    Vessaz, C; Jahanbakhsh, E; Avellan, F

    2014-01-01

    The objective of the present paper is to perform an accurate numerical simulation of the high-speed water jet impinging on a Pelton bucket. To reach this goal, the Finite Volume Particle Method (FVPM) is used to discretize the governing equations. FVPM is an arbitrary Lagrangian-Eulerian method, which combines attractive features of Smoothed Particle Hydrodynamics and conventional mesh-based Finite Volume Method. This method is able to satisfy free surface and no-slip wall boundary conditions precisely. The fluid flow is assumed weakly compressible and the wall boundary is represented by one layer of particles located on the bucket surface. In the present study, the simulations of the flow in a stationary bucket are investigated for three different impinging angles: 72°, 90° and 108°. The particles resolution is first validated by a convergence study. Then, the FVPM results are validated with available experimental data and conventional grid-based Volume Of Fluid simulations. It is shown that the wall pressure field is in good agreement with the experimental and numerical data. Finally, the torque evolution and water sheet location are presented for a simulation of five rotating Pelton buckets

  10. 2011 Population Grid for Spain. Methodological assessment of different construction possibilities

    Directory of Open Access Journals (Sweden)

    Francisco J. Goerlich Gisbert

    2017-08-01

    Full Text Available This paper presents an evaluation, from the user point of view, of the regular population grid, with 1 km2 resolution, that the Spanish National Statistical Institute (INE, has released as a product from the last Population and Dwellings Census 2011. This way of disseminating population data is novel, and has a lot of analytical potential uses, since population is no longer linked to administrative divisions. For the first time this information about the population distribution has been generated using a bottom-up approach for the whole of Spain, this is, by georeferencing the population at its place of residence. The availability of another grid at the same spatial resolution, but generated using a top-down approach, this is, by spatial disaggregation methods from administrative population data and other auxiliary land cover information, allow us to explore the benefits associated to georeferencing the population in the context of the methodological changes introduced by the Population and Dwellings Census 2011. At the same time, we are able to evaluate the merits of the census grid .

  11. Effect of Finite Particle Size on Convergence of Point Particle Models in Euler-Lagrange Multiphase Dispersed Flow

    Science.gov (United States)

    Nili, Samaun; Park, Chanyoung; Haftka, Raphael T.; Kim, Nam H.; Balachandar, S.

    2017-11-01

    Point particle methods are extensively used in simulating Euler-Lagrange multiphase dispersed flow. When particles are much smaller than the Eulerian grid the point particle model is on firm theoretical ground. However, this standard approach of evaluating the gas-particle coupling at the particle center fails to converge as the Eulerian grid is reduced below particle size. We present an approach to model the interaction between particles and fluid for finite size particles that permits convergence. We use the generalized Faxen form to compute the force on a particle and compare the results against traditional point particle method. We apportion the different force components on the particle to fluid cells based on the fraction of particle volume or surface in the cell. The application is to a one-dimensional model of shock propagation through a particle-laden field at moderate volume fraction, where the convergence is achieved for a well-formulated force model and back coupling for finite size particles. Comparison with 3D direct fully resolved numerical simulations will be used to check if the approach also improves accuracy compared to the point particle model. Work supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program, under Contract No. DE-NA0002378.

  12. GridCom, Grid Commander: graphical interface for Grid jobs and data management; GridCom, Grid Commander: graficheskij interfejs dlya raboty s zadachami i dannymi v gride

    Energy Technology Data Exchange (ETDEWEB)

    Galaktionov, V V

    2011-07-01

    GridCom - the software package for maintenance of automation of access to means of distributed system Grid (jobs and data). The client part, executed in the form of Java-applets, realises the Web-interface access to Grid through standard browsers. The executive part Lexor (LCG Executor) is started by the user in UI (User Interface) machine providing performance of Grid operations

  13. A numerical formulation using unstructured grids for modeling two-phase flows in porous media considering heterogeneities and capillarity effects

    International Nuclear Information System (INIS)

    Hurtado, F.S.V.; Maliska, C.R.

    2005-01-01

    This paper briefly describes a two-dimensional numerical formulation using unstructured grids, developed for simulating two-phase immiscible displacements in porous media. The Element-based Finite Volume Method (EbFVM) is used for discretizing the model differential equations. (authors)

  14. A numerical formulation using unstructured grids for modeling two-phase flows in porous media considering heterogeneities and capillarity effects

    Energy Technology Data Exchange (ETDEWEB)

    Hurtado, F.S.V.; Maliska, C.R. [Santa Catarina Federal Univ., Computational Fluid Dynamics Lab., Mechanical Engineering Dept., Florianopolis, SC (Brazil)

    2005-07-01

    This paper briefly describes a two-dimensional numerical formulation using unstructured grids, developed for simulating two-phase immiscible displacements in porous media. The Element-based Finite Volume Method (EbFVM) is used for discretizing the model differential equations. (authors)

  15. Development and Operation of the D-Grid Infrastructure

    Science.gov (United States)

    Fieseler, Thomas; Gűrich, Wolfgang

    D-Grid is the German national grid initiative, granted by the German Federal Ministry of Education and Research. In this paper we present the Core D-Grid which acts as a condensation nucleus to build a production grid and the latest developments of the infrastructure. The main difference compared to other international grid initiatives is the support of three middleware systems, namely LCG/gLite, Globus, and UNICORE for compute resources. Storage resources are connected via SRM/dCache and OGSA-DAI. In contrast to homogeneous communities, the partners in Core D-Grid have different missions and backgrounds (computing centres, universities, research centres), providing heterogeneous hardware from single processors to high performance supercomputing systems with different operating systems. We present methods to integrate these resources and services for the DGrid infrastructure like a point of information, centralized user and virtual organization management, resource registration, software provision, and policies for the implementation (firewalls, certificates, user mapping).

  16. Progress in Grid Generation: From Chimera to DRAGON Grids

    Science.gov (United States)

    Liou, Meng-Sing; Kao, Kai-Hsiung

    1994-01-01

    Hybrid grids, composed of structured and unstructured grids, combines the best features of both. The chimera method is a major stepstone toward a hybrid grid from which the present approach is evolved. The chimera grid composes a set of overlapped structured grids which are independently generated and body-fitted, yielding a high quality grid readily accessible for efficient solution schemes. The chimera method has been shown to be efficient to generate a grid about complex geometries and has been demonstrated to deliver accurate aerodynamic prediction of complex flows. While its geometrical flexibility is attractive, interpolation of data in the overlapped regions - which in today's practice in 3D is done in a nonconservative fashion, is not. In the present paper we propose a hybrid grid scheme that maximizes the advantages of the chimera scheme and adapts the strengths of the unstructured grid while at the same time keeps its weaknesses minimal. Like the chimera method, we first divide up the physical domain by a set of structured body-fitted grids which are separately generated and overlaid throughout a complex configuration. To eliminate any pure data manipulation which does not necessarily follow governing equations, we use non-structured grids only to directly replace the region of the arbitrarily overlapped grids. This new adaptation to the chimera thinking is coined the DRAGON grid. The nonstructured grid region sandwiched between the structured grids is limited in size, resulting in only a small increase in memory and computational effort. The DRAGON method has three important advantages: (1) preserving strengths of the chimera grid; (2) eliminating difficulties sometimes encountered in the chimera scheme, such as the orphan points and bad quality of interpolation stencils; and (3) making grid communication in a fully conservative and consistent manner insofar as the governing equations are concerned. To demonstrate its use, the governing equations are

  17. 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

  18. MPFA algorithm for solving stokes-brinkman equations on quadrilateral grids

    KAUST Repository

    Iliev, Oleg

    2014-01-01

    This work is concerned with the development of a robust and accurate numerical method for solving the Stokes-Brinkman system of equations, which describes a free fluid flow coupled with a flow in porous media. Quadrilateral boundary fitted grid with a sophisticated finite volume method, namely MPFA O-method, is used to discretize the system of equations. Numerical results for two examples are presented, namely, channel flow and flow in a ring with a rolled porous medium. © Springer International Publishing Switzerland 2014.

  19. Scalable Open Source Smart Grid Simulator (SGSim)

    DEFF Research Database (Denmark)

    Ebeid, Emad Samuel Malki; Jacobsen, Rune Hylsberg; Stefanni, Francesco

    2017-01-01

    . This paper presents an open source smart grid simulator (SGSim). The simulator is based on open source SystemC Network Simulation Library (SCNSL) and aims to model scalable smart grid applications. SGSim has been tested under different smart grid scenarios that contain hundreds of thousands of households...

  20. Variational Multiscale Finite Element Method for Flows in Highly Porous Media

    KAUST Repository

    Iliev, O.; Lazarov, R.; Willems, J.

    2011-01-01

    We present a two-scale finite element method (FEM) for solving Brinkman's and Darcy's equations. These systems of equations model fluid flows in highly porous and porous media, respectively. The method uses a recently proposed discontinuous Galerkin FEM for Stokes' equations by Wang and Ye and the concept of subgrid approximation developed by Arbogast for Darcy's equations. In order to reduce the "resonance error" and to ensure convergence to the global fine solution, the algorithm is put in the framework of alternating Schwarz iterations using subdomains around the coarse-grid boundaries. The discussed algorithms are implemented using the Deal.II finite element library and are tested on a number of model problems. © 2011 Society for Industrial and Applied Mathematics.