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1

We propose a semi-discrete finite difference multiscale scheme for a concrete corrosion model consisting of a system of two-scale reaction-diffusion equations coupled with an ode. We prove energy and regularity estimates and use them to get the necessary compactness of the approximation estimates. Finally, we illustrate numerically the behavior of the two-scale finite difference approximation of the weak solution.

Chalupecký, Vladimír

2011-01-01

2

On second-order mimetic and conservative finite-difference discretization schemes

Directory of Open Access Journals (Sweden)

Full Text Available Although the scheme could be derived on the grounds of a relatively new numerical discretization methodology known as Mimetic Finite-Difference Approach, the derivation of a second-order mimetic finite difference discretization scheme will be presented in a more intuitive way, using Taylor expansions. Since students become familiar with Taylor expansions in earlier calculus and mathematical methods for physicist courses, one finds this approach of presenting this new discretization scheme to be more easily handled in courses on numerical computations of both undergraduate and graduated programs. The robustness of the resulting discretized equations will be illustrated by finding the numerical solution of an essentially hard-to-solve, one-dimensional, boundary-layer-like problem, based on the steady diffusion equation. Moreover, given that the presented mimetic discretization scheme attains second-order accuracy in the entire computational domain (including the boundaries, as a comparative exercise the discretized equations can be readily applied in solving examples commonly found in texbooks on applied numerical methods and solved numerically via other discretization schemes (including some of the standard finite-diffence discretization schemesAunque la derivación del esquema se puede realizar usando la reciente metodología de discretización numérica conocida como Diferencias Finitas Miméticas, estaremos presentando la derivación de un esquema de discretización mimético en diferencias finitas de segundo orden en una forma mas intuitiva, mediante el uso de expansiones de Taylor. Considerando que los estudiantes se familiarizan con expansiones de Taylor en los primeros cursos de cálculo y métodos matemáticos para físicos, pensamos que la presente alternativa de presentar este nuevo esquema de discretización es más favorable de ser asimilada en cursos de computación numérica tanto de pregrado como de postgrado. La robusticidad del esquema será ilustrada encontrando la solución numérica de un problema unidimensional del tipo capa límite difícil de resolver en forma numérica y que se basa en la ecuación de difusión estacionaria. Más aun, dado que el esquema de discretización alcanza segundo orden de precisión en todo el dominio computacional (incluyendo las fronteras, como ejercicio comparativo el mismo puede ser rápidamente aplicado para resolver ejemplos comúnmente encontrados en textos sobre métodos numéricos aplicados y que se resuelven usando otras metodologías numéricas (incluyendo algunos esquemas de discretización en diferencias finitas

S Rojas

2008-12-01

3

On second-order mimetic and conservative finite-difference discretization schemes

Scientific Electronic Library Online (English)

Full Text Available SciELO Mexico | Language: English Abstract in spanish Aunque la derivación del esquema se puede realizar usando la reciente metodología de discretización numérica conocida como Diferencias Finitas Miméticas, estaremos presentando la derivación de un esquema de discretización mimético en diferencias finitas de segundo orden en una forma mas intuitiva, m [...] ediante el uso de expansiones de Taylor. Considerando que los estudiantes se familiarizan con expansiones de Taylor en los primeros cursos de cálculo y métodos matemáticos para físicos, pensamos que la presente alternativa de presentar este nuevo esquema de discretización es más favorable de ser asimilada en cursos de computación numérica tanto de pregrado como de postgrado. La robusticidad del esquema será ilustrada encontrando la solución numérica de un problema unidimensional del tipo capa límite difícil de resolver en forma numérica y que se basa en la ecuación de difusión estacionaria. Más aun, dado que el esquema de discretización alcanza segundo orden de precisión en todo el dominio computacional (incluyendo las fronteras), como ejercicio comparativo el mismo puede ser rápidamente aplicado para resolver ejemplos comúnmente encontrados en textos sobre métodos numéricos aplicados y que se resuelven usando otras metodologías numéricas (incluyendo algunos esquemas de discretización en diferencias finitas) Abstract in english Although the scheme could be derived on the grounds of a relatively new numerical discretization methodology known as Mimetic Finite-Difference Approach, the derivation of a second-order mimetic finite difference discretization scheme will be presented in a more intuitive way, using Taylor expansion [...] s. Since students become familiar with Taylor expansions in earlier calculus and mathematical methods for physicist courses, one finds this approach of presenting this new discretization scheme to be more easily handled in courses on numerical computations of both undergraduate and graduated programs. The robustness of the resulting discretized equations will be illustrated by finding the numerical solution of an essentially hard-to-solve, one-dimensional, boundary-layer-like problem, based on the steady diffusion equation. Moreover, given that the presented mimetic discretization scheme attains second-order accuracy in the entire computational domain (including the boundaries), as a comparative exercise the discretized equations can be readily applied in solving examples commonly found in texbooks on applied numerical methods and solved numerically via other discretization schemes (including some of the standard finite-diffence discretization schemes)

S, Rojas; J.M, Guevara-Jordan.

2008-12-01

4

Total variation diminishing nonstandard finite difference schemes for conservation laws

Nonstandard finite difference schemes for conservation laws preserving the property of diminishing total variation of the solution are proposed. Computationally simple implicit schemes are derived by using nonlocal approximation of nonlinear terms. Renormalization of the denominator of the discrete derivative is used for deriving explicit schemes of first or higher order. Unlike the standard explicit methods, the solutions of these schemes have diminishing total variation for any time step...

Anguelov, Roumen; Lubuma, Jean M. -s; Minani, Froduald

2009-01-01

5

Applications of nonstandard finite difference schemes

The main purpose of this book is to provide a concise introduction to the methods and philosophy of constructing nonstandard finite difference schemes and illustrate how such techniques can be applied to several important problems. Chapter 1 gives an overview of the subject and summarizes previous work. Chapters 2 and 3 consider in detail the construction and numerical implementation of schemes for physical problems involving convection-diffusion-reaction equations that arise in groundwater pollution and scattering of electromagnetic waves using Maxwell's equations. Chapter 4 examines certain

Mickens, Ronald E

2000-01-01

6

The maximum principle, closely related to the non-negativity property, is a basic characteristic of second order PDEs of parabolic type. Its preservation for solutions to corresponding discretized problems is a natural requirement in reliable and meaningful numerical modeling of various real-life phenomena. Finite difference or finite volume methods on staggered Cartesian grids have the advantage of being easily parallelizable, for example in CUDA GPUs, with several processes performing at th...

Dani, Roberta; Simeoni, Chiara

2014-01-01

7

Finite-difference schemes for anisotropic diffusion

Energy Technology Data Exchange (ETDEWEB)

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.

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

8

Finite-difference schemes for anisotropic diffusion

International Nuclear Information System (INIS)

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 1012 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

9

International Nuclear Information System (INIS)

A new finite difference scheme on a non-uniform staggered grid in cylindrical coordinates is proposed for incompressible flow. The scheme conserves both momentum and kinetic energy for inviscid flow with the exception of the time marching error, provided that the discrete continuity equation is satisfied. A novel pole treatment is also introduced, where a discrete radial momentum equation with the fully conservative convection scheme is introduced at the pole. The pole singularity is removed properly using analytical and numerical techniques. The kinetic energy conservation property is tested for the inviscid concentric annular flow for the proposed and existing staggered finite difference schemes in cylindrical coordinates. The pole treatment is verified for inviscid pipe flow. Mixed second and high order finite difference scheme is also proposed and the effect of the order of accuracy is demonstrated for the large eddy simulation of turbulent pipe flow

10

Explicit and implicit finite difference schemes for fractional Cattaneo equation

In this paper, the numerical solution of fractional (non-integer)-order Cattaneo equation for describing anomalous diffusion has been investigated. Two finite difference schemes namely an explicit predictor-corrector and totally implicit schemes have been developed. In developing each scheme, a separate formulation approach for the governing equations has been considered. The explicit predictor-corrector scheme is the fractional generalization of well-known MacCormack scheme and has been called Generalized MacCormack scheme. This scheme solves two coupled low-order equations and simultaneously computes the flux term with the main variable. Fully implicit scheme however solves a single high-order undecomposed equation. For Generalized MacCormack scheme, stability analysis has been studied through Fourier method. Through a numerical test, the experimental order of convergency of both schemes has been found. Then, the domain of applicability and some numerical properties of each scheme have been discussed.

Ghazizadeh, H. R.; Maerefat, M.; Azimi, A.

2010-09-01

11

Finite difference discretizations of 1D poroelasticity equations with discontinuous coefficients are analyzed. A recently suggested FD discretization of poroelasticity equations with constant coefficients on staggered grid, [5], is used as a basis. A careful treatment of the interfaces leads to harmonic averaging of the discontinuous coefficients. Here, convergence for the pressure and for the displacement is proven in certain norms for the scheme with harmonic averaging (HA). Order of conv...

Ewing, R.; Iliev, O.; Lazarov, R.; Naumovich, A.

2004-01-01

12

Optimised boundary compact finite difference schemes for computational aeroacoustics

A set of optimised boundary closure schemes is presented for use with compact central finite difference schemes in computational aeroacoustics (CAA) involving non-trivial boundaries. The boundary schemes are given in a form of non-central compact finite differences. They maintain fourth-order accuracy, a pentadiagonal matrix system and seven-point stencil which the main interior scheme employs. This paper introduces a new strategy to optimise the boundary schemes in the spectral domain and achieve the best resolution characteristics given a strict tolerance for the dispersion and dissipation errors. The boundary schemes are derived from sophisticated extrapolation of solutions outside the domain. The extrapolation functions are devised by combining polynomials and trigonometric series which contain extra control variables used to optimise the resolution characteristics. The differencing coefficients of the boundary schemes are determined in association with the existing coefficients of the interior scheme which is also optimised through an improved procedure in this paper. The accuracy of the proposed schemes is demonstrated by their application to CAA benchmark problems.

Kim, Jae Wook

2007-07-01

13

An upwind finite difference scheme for meshless solvers

International Nuclear Information System (INIS)

In this paper, we present a new upwind finite difference scheme for meshless solvers. This new scheme, capable of working on any type of grid (structure, unstructured or even a random distribution of points) produces superior results. A means to construct schemes of specified order of accuracy is discussed. Numerical computations for different types of flow over a wide range of Mach numbers are presented. Also, these results were compared with those obtained using a cell vertex finite volume code on the same grids and with theoretical values wherever possible. The present framework has the flexibility to choose between various upwind flux formulas

14

To the convergence ov finite difference schemes on the generalized solutions of the Poisson equation

International Nuclear Information System (INIS)

The rate of convergence of the finite difference schemes on the generalized solutions of Poisson equation is studied by the energy inequality method. The truncation error is analyzed using Bramle-Hilbert lemma. It is proved that commonly used life-point difference scheme for the Direchlet boundary value problem converges with the rate of O(hsup(1+s)) in a discrete Ws21 norm, and with the rate of O(hsup(1+s)|lnh|sup(1/2)) in discrete C-norm, if the solution is from Wsub(2)sup(2+s), s=0.1

15

Variable-step finite difference schemes for the solution of Sturm-Liouville problems

We discuss the solution of regular and singular Sturm-Liouville problems by means of High Order Finite Difference Schemes. We describe a method to define a discrete problem and its numerical solution by means of linear algebra techniques. Different test problems are considered to emphasize the behavior of a code based on the proposed algorithm. The methods solve any regular or singular Sturm-Liouville problem, providing high accuracy and computational efficiency thanks to the powerful strategy of stepsize variation.

Amodio, Pierluigi; Settanni, Giuseppina

2015-03-01

16

Approximation of systems of partial differential equations by finite difference schemes

International Nuclear Information System (INIS)

The approximation of Friedrichs' symmetric systems by a finite difference scheme with second order accuracy with respect to the step of discretization is studied. Unconditional stability of such a scheme is proved by the method of energy increase. This implicit scheme is then solved by three iterative methods: the first one, of the gradient type, converges slowly, the second one, of the Gauss-Seidel type, converges only if the system has been regularized to the first order with respect to the step of discretization by an elliptic operator, the last one, of the under-relaxation type, converges rapidly to a second order accurate solution. Explicit schemes for the integration of linear hyperbolic systems of evolution are considered. Conditional stability is proved for different schemes: Crank Nicolson, Leap-frog, Explicit, Predictor-corrector. Results relative to the explicit scheme are generalized to a quasi-linear, monotone system. Finally, stability and convergence in the solution of a finite difference scheme approximating an elliptic-parabolic equation, and an iterative method of relaxation for solving this scheme are studied. (author)

17

A Nonstandard Finite-Difference Scheme for a Dual-Sorption Model of Percutaneous Drug Absorption

A nonstandard discrete model is constructed for the partial differential equation modeling pharmacokinetic profiles in percutaneous drug absorption.^1 This work generalizes the previous study by Gumel, et al^2 and extends to all PDE's taking the form u_t=Q(u)u_xx,<=no(*) where Q(u) is a given function of u. The major constraint used to obtain the finite difference scheme is the imposition of a positivity condition, i.e., if the numerical solution is non-negative at discrete time t_k=(? t)k, then the solution computed at t_k+1 must also be non-negative. The proposed scheme is both explicit, allowing for ease of implementation, and provides a direct connection between the space and time step-sizes. ^1S. K. Chandarasekaran et al., J. Pharm. Sci. 67, 1370 (1978). ^2A. B. Gumel et al., Math. Biosciences 152, 87 (1998).

Oyedeji, Kale; Mickens, Ronald E.

2001-11-01

18

We consider the basic SIR epidemiological model with the Michaelis-Menten formulation of the contact rate. From the study of the Michaelis-Menten basic enzymatic reaction, we design two types of Nonstandard Finite Difference (NSFD) schemes for the SIR model: Exact-related schemes based on the Lambert W function and schemes obtained by using Mickens’s rules of more complex denominator functions for discrete derivatives and nonlocal approximations of nonlinear terms. We compare and investigat...

Chapwanya, Michael; Lubuma, Jean M. -s; Mickens, Ronald E.

2012-01-01

19

Finite-Difference Lattice Boltzmann Scheme for High-Speed Compressible Flow: Two-Dimensional Case

International Nuclear Information System (INIS)

Lattice Boltzmann (LB) modeling of high-speed compressible flows has long been attempted by various authors. One common weakness of most of previous models is the instability problem when the Mach number of the flow is large. In this paper we present a finite-difference LB model, which works for flows with flexible ratios of specific heats and a wide range of Mach number, from 0 to 30 or higher. Besides the discrete-velocity-model by Watari [Physica A 382 (2007) 502], a modified Lax-Wendroff finite difference scheme and an artificial viscosity are introduced. The combination of the finite-difference scheme and the adding of artificial viscosity must find a balance of numerical stability versus accuracy. The proposed model is validated by recovering results of some well-known benchmark tests: shock tubes and shock reflections. The new model may be used to track shock waves and/or to study the non-equilibrium procedure in the transition between the regular and Mach reflections of shock waves, etc

20

Finite-Difference Lattice Boltzmann Scheme for High-Speed Compressible Flow: Two-Dimensional Case

Lattice Boltzmann (LB) modeling of high-speed compressible flows has long been attempted by various authors. One common weakness of most of previous models is the instability problem when the Mach number of the flow is large. In this paper we present a finite-difference LB model, which works for flows with flexible ratios of specific heats and a wide range of Mach number, from 0 to 30 or higher. Besides the discrete-velocity-model by Watari [Physica A 382 (2007) 502], a modified Lax Wendroff finite difference scheme and an artificial viscosity are introduced. The combination of the finite-difference scheme and the adding of artificial viscosity must find a balance of numerical stability versus accuracy. The proposed model is validated by recovering results of some well-known benchmark tests: shock tubes and shock reflections. The new model may be used to track shock waves and/or to study the non-equilibrium procedure in the transition between the regular and Mach reflections of shock waves, etc.

Gan, Yan-Biao; Xu, Ai-Guo; Zhang, Guang-Cai; Zhang, Ping; Zhang, Lei; Li, Ying-Jun

2008-07-01

21

An energy-stable finite-difference scheme for the binary fluid-surfactant system

We present an unconditionally energy stable finite-difference scheme for the binary fluid-surfactant system. The proposed method is based on the convex splitting of the energy functional with two variables. Here are two distinct features: (i) the convex splitting energy method is applied to energy functional with two variables, and (ii) the stability issue is related to the decay of the corresponding energy. The full discrete scheme leads to a decoupled system including a linear sub-system and a nonlinear sub-system. Algebraic multigrid and Newton-multigrid methods are adopted to solve the linear and nonlinear systems, respectively. Numerical experiments are shown to verify the stability of such a scheme.

Gu, Shuting; Zhang, Hui; Zhang, Zhengru

2014-08-01

22

On standard finite difference discretizations of the elliptic Monge-Ampere equation

Given an orthogonal lattice with mesh length h on a bounded convex domain, we show that the Aleksandrov solution of the Monge-Ampere equation is the uniform limit on compact subsets of mesh functions which solve discrete Monge-Ampere equations with the Hessian discretized using the standard finite difference method. The result explains the behavior of methods based on the standard finite difference method and designed to numerically converge to non-smooth solutions. We propo...

Awanou, Gerard

2013-01-01

23

Construction of discrete shell models by geometric finite differences

In the presented work, we make use of the strong reciprocity between kinematics and geometry to build a geometrically nonlinear, shearable low order discrete shell model of Cosserat type defined on triangular meshes, from which we deduce a rotation–free Kirchhoff type model with the triangle vertex positions as degrees of freedom. Both models behave physically plausible already on very coarse meshes, and show good convergence properties on regular meshes. Moreover, from the theoretical s...

Weischedel, C.; Tuganov, A.; Hermansson, T.; Linn, J.; Wardetzky, M.

2012-01-01

24

Converged accelerated finite difference scheme for the multigroup neutron diffusion equation

International Nuclear Information System (INIS)

Computer codes involving neutron transport theory for nuclear engineering applications always require verification to assess improvement. Generally, analytical and semi-analytical benchmarks are desirable, since they are capable of high precision solutions to provide accurate standards of comparison. However, these benchmarks often involve relatively simple problems, usually assuming a certain degree of abstract modeling. In the present work, we show how semi-analytical equivalent benchmarks can be numerically generated using convergence acceleration. Specifically, we investigate the error behavior of a 1D spatial finite difference scheme for the multigroup (MG) steady-state neutron diffusion equation in plane geometry. Since solutions depending on subsequent discretization can be envisioned as terms of an infinite sequence converging to the true solution, extrapolation methods can accelerate an iterative process to obtain the limit before numerical instability sets in. The obtained results have been compared to the analytical solution to the 1D multigroup diffusion equation when available, using FORTRAN as the computational language. Finally, a slowing down problem has been solved using a cascading source update, showing how a finite difference scheme performs for ultra-fine groups (104 groups) in a reasonable computational time using convergence acceleration. (authors)

25

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

Abramopoulos, Frank

1988-01-01

26

a Novel Less Dissipation Finite-Difference Lattice Boltzmann Scheme for Compressible Flows

In this paper, a new smoothness indicator is proposed to improve the finite-difference lattice Boltzmann method (FDLBM). The necessary and sufficient conditions for convergence are derived. A detailed analysis reveals that the convergence order is higher than that of the previous finite-difference scheme. The coupled double distribution function (DDF) model is used to describe discontinuity flows and verify the improvement. Numerical simulations of compressible flows with shock wave show that the improved finite-difference lattice Boltzmann scheme is accurate and has less dissipation. The numerical results are found to be in good agreement with the analytical results and better than those of the previous scheme.

Chen, Q.; Zhang, X. B.

2012-11-01

27

A High Order Finite Difference Scheme with Sharp Shock Resolution for the Euler Equations

We derive a high-order finite difference scheme for the Euler equations that satisfies a semi-discrete energy estimate, and present an efficient strategy for the treatment of discontinuities that leads to sharp shock resolution. The formulation of the semi-discrete energy estimate is based on a symmetrization of the Euler equations that preserves the homogeneity of the flux vector, a canonical splitting of the flux derivative vector, and the use of difference operators that satisfy a discrete analogue to the integration by parts procedure used in the continuous energy estimate. Around discontinuities or sharp gradients, refined grids are created on which the discrete equations are solved after adding a newly constructed artificial viscosity. The positioning of the sub-grids and computation of the viscosity are aided by a detection algorithm which is based on a multi-scale wavelet analysis of the pressure grid function. The wavelet theory provides easy to implement mathematical criteria to detect discontinuities, sharp gradients and spurious oscillations quickly and efficiently.

Gerritsen, Margot; Olsson, Pelle

1996-01-01

28

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

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.

Fisher, Travis C.; Carpenter, Mark H.

2013-01-01

29

Dynamically consistent nonstandard finite difference schemes for epidemiological models

This work is the numerical analysis and computational companion of the paper by Kamgang and Sallet [J.C. Kamgang, G. Sallet, Computation of threshold conditions for epidemiological models and global stability of the disease free equilibrium (DFE), Mathematical Biosciences 213 (2008) 1–12] where threshold conditions for epidemiological models and the global stability of the disease-free equilibrium (DFE) are studied. We establish a discrete counterpart of the main continuous result that guar...

Anguelov, Roumen; Dumont, Yves; Lubuma, Jean M. -s; Shillor, M.

2013-01-01

30

A FINITE-DIFFERENCE, DISCRETE-WAVENUMBER METHOD FOR CALCULATING RADAR TRACES

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

31

A finite difference scheme for a degenerated diffusion equation arising in microbial ecology

Directory of Open Access Journals (Sweden)

Full Text Available A finite difference scheme is presented for a density-dependent diffusion equation that arises in the mathematical modelling of bacterial biofilms. The peculiarity of the underlying model is that it shows degeneracy as the dependent variable vanishes, as well as a singularity as the dependent variable approaches its a priori known upper bound. The first property leads to a finite speed of interface propagation if the initial data have compact support, while the second one introduces counter-acting super diffusion. This squeezing property of this model leads to steep gradients at the interface. Moving interface problems of this kind are known to be problematic for classical numerical methods and introduce non-physical and non-mathematical solutions. The proposed method is developed to address this observation. The central idea is a non-local (in time representation of the diffusion operator. It can be shown that the proposed method is free of oscillations at the interface, that the discrete interface satisfies a discrete version of the continuous interface condition and that the effect of interface smearing is quantitatively small.

Hermann J. Eberl

2007-02-01

32

The dispersion and dissipation properties of a scheme are of great importance for the simulation of flow fields which involve a broad range of length scales. In order to improve the spectral properties of the finite difference scheme, the authors have previously proposed the idea of optimizing the dispersion and dissipation properties separately and a fourth order scheme based on the minimized dispersion and controllable dissipation (MDCD) technique is thus constructed [29]. In the present paper, we further investigate this technique and extend it to a sixth order finite difference scheme to solve the Euler and Navier-Stokes equations. The dispersion properties of the scheme is firstly optimized by minimizing an elaborately designed integrated error function. Then the dispersion-dissipation condition which is newly derived by Hu and Adams [30] is introduced to supply sufficient dissipation to damp the unresolved wavenumbers. Furthermore, the optimized scheme is blended with an optimized Weighted Essentially Non-Oscillation (WENO) scheme to make it possible for the discontinuity-capturing. In this process, the approximation-dispersion-relation (ADR) approach is employed to optimize the spectral properties of the nonlinear scheme to yield the true wave propagation behavior of the finite difference scheme. Several benchmark test problems, which include broadband fluctuations and strong shock waves, are solved to validate the high-resolution, the good discontinuity-capturing capability and the high-efficiency of the proposed scheme.

Sun, Zhen-sheng; Luo, Lei; Ren, Yu-xin; Zhang, Shi-ying

2014-08-01

33

Error analysis of finite difference schemes applied to hyperbolic initial boundary value problems

Finite difference methods for the numerical solution of mixed initial boundary value problems for hyperbolic equations are studied. The reported investigation has the objective to develop a technique for the total error analysis of a finite difference scheme, taking into account initial approximations, boundary conditions, and interior approximation. Attention is given to the Cauchy problem and the initial approximation, the homogeneous problem in an infinite strip with inhomogeneous boundary data, the reflection of errors in the boundaries, and two different boundary approximations for the leapfrog scheme with a fourth order accurate difference operator in space.

Skollermo, G.

1979-01-01

34

Classical and new numerical schemes are generated using evolutionary computing. Differential Evolution is used to find the coefficients of finite difference approximations of function derivatives, and of single and multi-step integration methods. The coefficients are reverse engineered based on samples from a target function and its derivative used for training. The Runge-Kutta schemes are trained using the order condition equations. An appealing feature of the evolutionary ...

Erdbrink, C. D.; Krzhizhanovskaya, V. V.; Sloot, P. M. A.

2013-01-01

35

Single-cone real-space finite difference schemes for the Dirac von Neumann equation

Two finite difference schemes for the numerical treatment of the von Neumann equation for the (2+1)D Dirac Hamiltonian are presented. Both utilize a single-cone staggered space-time grid which ensures a single-cone energy dispersion to formulate a numerical treatment of the mixed-state dynamics within the von Neumann equation. The first scheme executes the time-derivative according to the product rule for "bra" and "ket" indices of the density operator. It therefore directly inherits all the favorable properties of the difference scheme for the pure-state Dirac equation and conserves positivity. The second scheme proposed here performs the time-derivative in one sweep. This direct scheme is investigated regarding stability and convergence. Both schemes are tested numerically for elementary simulations using parameters which pertain to topological insulator surface states. Application of the schemes to a Dirac Lindblad equation and real-space-time Green's function formulations are discussed.

Schreilechner, Magdalena

2015-01-01

36

Invariant meshless discretization schemes

International Nuclear Information System (INIS)

A method is introduced for the construction of meshless discretization schemes which preserve Lie symmetries of the differential equations that these schemes approximate. The method exploits the fact that equivariant moving frames provide a way of associating invariant functions with non-invariant functions. An invariant meshless approximation of a nonlinear diffusion equation is constructed. Comparative numerical tests with a non-invariant meshless scheme are presented. These tests yield that invariant meshless schemes can lead to substantially improved numerical solutions compared to numerical solutions generated by non-invariant meshless schemes. (fast track communication)

37

Invariant meshless discretization schemes

A method is introduced for the construction of meshless discretization schemes which preserve Lie symmetries of the differential equations that these schemes approximate. The method exploits the fact that equivariant moving frames provide a way of associating invariant functions to non-invariant functions. An invariant meshless approximation of a nonlinear diffusion equation is constructed. Comparative numerical tests with a non-invariant meshless scheme are presented. These tests yield that invariant meshless schemes can lead to substantially improved numerical solutions compared to numerical solutions generated by non-invariant meshless schemes.

Bihlo, Alexander

2012-01-01

38

Invariant meshless discretization schemes

A method is introduced for the construction of meshless discretization schemes which preserve Lie symmetries of the differential equations that these schemes approximate. The method exploits the fact that equivariant moving frames provide a way of associating invariant functions to non-invariant functions. An invariant meshless approximation of a nonlinear diffusion equation is constructed. Comparative numerical tests with a non-invariant meshless scheme are presented. These...

Bihlo, Alexander

2012-01-01

39

A multigrid algorithm for the cell-centered finite difference scheme

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.

Ewing, Richard E.; Shen, Jian

1993-01-01

40

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

Kumar, Vivek; Raghurama Rao, S. V.

2008-04-01

41

A new finite difference scheme for a dissipative cubic nonlinear Schrödinger equation

International Nuclear Information System (INIS)

This paper considers the one-dimensional dissipative cubic nonlinear Schrödinger equation with zero Dirichlet boundary conditions on a bounded domain. The equation is discretized in time by a linear implicit three-level central difference scheme, which has analogous discrete conservation laws of charge and energy. The convergence with two orders and the stability of the scheme are analysed using a priori estimates. Numerical tests show that the three-level scheme is more efficient. (general)

42

A finite difference scheme for a degenerated diffusion equation arising in microbial ecology

A finite difference scheme is presented for a density-dependent diffusion equation that arises in the mathematical modelling of bacterial biofilms. The peculiarity of the underlying model is that it shows degeneracy as the dependent variable vanishes, as well as a singularity as the dependent variable approaches its a priori known upper bound. The first property leads to a finite speed of interface propagation if the initial data have compact support, while the second one introduces counter...

Eberl, Hermann J.; Laurent Demaret

2007-01-01

43

International Nuclear Information System (INIS)

A unified framework is developed for calculating the order of the error for a class of finite-difference approximations to the monoenergetic linear transport equation in slab geometry. In particular, the global discretization errors for the step characteristic, diamond, and linear discontinuous methods are shown to be of order two, while those for the linear moments and linear characteristic methods are of order three, and that for the quadratic method is of order four. A superconvergence result is obtained for the three linear methods, in the sense that the cell-averaged flux approximations are shown to converge at one order higher than the global errors

44

This paper proposes a novel systematic approach for the parallelization of pentadiagonal compact finite-difference schemes and filters based on domain decomposition. The proposed approach allows a pentadiagonal banded matrix system to be split into quasi-disjoint subsystems by using a linear-algebraic transformation technique. As a result the inversion of pentadiagonal matrices can be implemented within each subdomain in an independent manner subject to a conventional halo-exchange process. The proposed matrix transformation leads to new subdomain boundary (SB) compact schemes and filters that require three halo terms to exchange with neighboring subdomains. The internode communication overhead in the present approach is equivalent to that of standard explicit schemes and filters based on seven-point discretization stencils. The new SB compact schemes and filters demand additional arithmetic operations compared to the original serial ones. However, it is shown that the additional cost becomes sufficiently low by choosing optimal sizes of their discretization stencils. Compared to earlier published results, the proposed SB compact schemes and filters successfully reduce parallelization artifacts arising from subdomain boundaries to a level sufficiently negligible for sophisticated aeroacoustic simulations without degrading parallel efficiency. The overall performance and parallel efficiency of the proposed approach are demonstrated by stringent benchmark tests.

Kim, Jae Wook

2013-05-01

45

2D numerical simulation of the MEP energy-transport model with a finite difference scheme

A finite difference scheme of Scharfetter-Gummel type is used to simulate a consistent energy-transport model for electron transport in semiconductors devices, free of any fitting parameters, formulated on the basis of the maximum entropy principle. Simulations of silicon n +-n-n + diodes, 2D-MESFET and 2D-MOSFET and comparisons with the results obtained by a direct simulation of the Boltzmann transport equation and with other energy-transport models, known in the literature, show the validity of the model and the robustness of the numerical scheme.

Romano, V.

2007-02-01

46

A fourth order accurate finite difference scheme for the computation of elastic waves

A finite difference for elastic waves is introduced. The model is based on the first order system of equations for the velocities and stresses. The differencing is fourth order accurate on the spatial derivatives and second order accurate in time. The model is tested on a series of examples including the Lamb problem, scattering from plane interf aces and scattering from a fluid-elastic interface. The scheme is shown to be effective for these problems. The accuracy and stability is insensitive to the Poisson ratio. For the class of problems considered here it is found that the fourth order scheme requires for two-thirds to one-half the resolution of a typical second order scheme to give comparable accuracy.

Bayliss, A.; Jordan, K. E.; Lemesurier, B. J.; Turkel, E.

1986-01-01

47

A study of unstable rock failures using finite difference and discrete element methods

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

Garvey, Ryan J.

48

In order to solve high-resolution 3D problems in computational geodynamics it is crucial to use multigrid solvers in combination with parallel computers. A number of approaches are currently in use in the community, which can broadly be divided into coupled and decoupled approaches. In the decoupled approach, an algebraic or geometric multigrid method is used as a preconditioner for the velocity equations only while an iterative approach such as Schur complement reduction used to solve the outer velocity-pressure equations. In the coupled approach, on the other hand, a multigrid approach is applied to both the velocity and pressure equations. The coupled multigrid approaches are typically employed in combination with staggered finite difference discretizations, whereas the decoupled approach is the method of choice in many of the existing finite element codes. Yet, it is unclear whether there are differences in speed between the two approaches, and if so, how this depends on the initial guess. Here, we implemented both approaches in combination with a staggered finite difference discretization and test the robustness of the two approaches with respect to large jumps in viscosity contrast, as well as their computational efficiency as a function of the initial guess. Acknowledgements. Funding was provided by the European Research Council under the European Community's Seventh Framework Program (FP7/2007-2013) / ERC Grant agreement #258830. Numerical computations have been performed on JUQUEEN of the Jülich high-performance computing center.

Kaus, Boris; Popov, Anton; Püsök, Adina

2014-05-01

49

A 3D staggered-grid finite difference scheme for poroelastic wave equation

Three dimensional numerical modeling has been a viable tool for understanding wave propagation in real media. The poroelastic media can better describe the phenomena of hydrocarbon reservoirs than acoustic and elastic media. However, the numerical modeling in 3D poroelastic media demands significantly more computational capacity, including both computational time and memory. In this paper, we present a 3D poroelastic staggered-grid finite difference (SFD) scheme. During the procedure, parallel computing is implemented to reduce the computational time. Parallelization is based on domain decomposition, and communication between processors is performed using message passing interface (MPI). Parallel analysis shows that the parallelized SFD scheme significantly improves the simulation efficiency and 3D decomposition in domain is the most efficient. We also analyze the numerical dispersion and stability condition of the 3D poroelastic SFD method. Numerical results show that the 3D numerical simulation can provide a real description of wave propagation.

Zhang, Yijie; Gao, Jinghuai

2014-10-01

50

A dynamic grid point allocation scheme for the Characteristic Finite Difference Method

International Nuclear Information System (INIS)

Codes for predicting the events which can occur during a reactor loss-of-coolant accident (LOCA) must be able to cope with the essentially steady flows of normal operation and long-term cooling, as well as with the very severe transients occurring during the blowdown and water injection phases. Although large timesteps and a coarse grid are adequate for steady flows, smaller timesteps and a finer grid are necessary to preserve accuracy during the fast transients. The RAMA code, based on the characteristic finite difference method, has a dynamic grid point allocation scheme which helps to control spatial truncation error. In this scheme, grid points are inserted in regions where large spatial gradients occur in the flow-boiling variables and are deleted when these gradients subside. As well, the mesh of grid points is free to move with the gradients. The algorithm used is similar to that for dynamic timestep control, where large temporal gradients in the flow-boiling variables dictate small timesteps and larger timesteps are used for shallower gradients. The goal is to maintain a prescribed accuracy in the calculation during the entire LOCA prediction while using the minimum number of grid points at each step and, in total, the minimum number of timesteps. Examples are presented which demonstrate the computational efficiency of the scheme, including a benchmark problem involving cold water injection and an experimental case involving both blowdown and cold water injection phases

51

International Nuclear Information System (INIS)

An entirely new discrete levels segment has been created by the Budapest group according to the recommended principles, using the Evaluated Nuclear Structure Data File, ENSDF as a source. The resulting segment contains 96,834 levels and 105,423 gamma rays for 2,585 nuclei, with their characteristics such as energy, spin, parity, half-life as well as gamma-ray energy and branching percentage. Isomer flags for half-lives longer than 1 s have been introduced. For those 1,277 nuclei having at least ten known levels the cutoff level numbers Nm have been determined from fits to the cumulative number of levels. The level numbers Nc associated with the cutoff energies Uc, corresponding to the upper energy limit of levels with unique spin and parity, have been included for each nuclide. The segment has the form of an ASCII file which follows the extended ENEA Bologna convention. For the RIPL Starter File the new Budapest file is recommended as a Discrete Level Schemes Segment because it is most complete, up-to-date, and also well documented. Moreover, the cutoff energies have been determined in a consistent way, giving also hints about basic level density parameters. The recommended files are budapest-levels.dat and budapest-cumulative.dat. As alternative choices, the libraries from Beijing, Bologna, JAERI, Obninsk and Livermore may also be used for special applications. (author)

52

A large class of physical phenomena can be modeled by evolution and wave type Partial Differential Equations (PDE). Few of these equations have known explicit exact solutions. Finite-difference techniques are a popular method for constructing discrete representations of these equations for the purpose of numerical integration. However, the solutions to the difference equations often contain so called numerical instabilities; these are solutions to the difference equations that do not correspond to any solution of the PDE's. For explicit schemes, the elimination of this behavior requires functional relations to exist between the time and space steps-sizes. We show that such functional relations can be obtained for certain PDE's by use of a positivity condition. The PDE's studied are the Burgers, Fisher, and linearized Euler equations.

Mickens, Ronald E.

1996-01-01

53

Information-based complexity applied to one-dimensional finite difference transport schemes

International Nuclear Information System (INIS)

Traditional dimensions for comparing algorithms (or computational procedures) for solving the same class of problems consist of accuracy and computational complexity. A recently developed branch of theoretical computer science, which is termed information-based complexity, adds a third dimension consisting of the type or amount of information regarding the problem data that are used by the computational procedure. Instead of viewing a problem in terms of finding and analyzing a particular algorithm to solve it, information-based complexity addresses the inherent computational characteristics of general problems (as a function of their size or the error of computed solutions). One seeks upper bounds, which emerge from looking at specific algorithms, and the often more important and difficult lower bounds on the complexity of problems. The purpose of this paper is to describe the application of the information-based theory to one-dimensional finite difference schemes in neutron transport. For cell-average information and two different solution operators, the authors obtain the corresponding radius of information and optimal error algorithm. The authors also compute the error of the step-characteristic algorithm

54

A finite difference scheme is presented for the Dirac equation in (1+1)D. It can handle space- and time-dependent mass and potential terms and utilizes exact discrete transparent boundary conditions (DTBCs). Based on a space- and time-staggered leap-frog scheme it avoids fermion doubling and preserves the dispersion relation of the continuum problem for mass zero (Weyl equation) exactly. Considering boundary regions, each with a constant mass and potential term, the associated DTBCs are derived by first applying this finite difference scheme and then using the Z-transform in the discrete time variable. The resulting constant coefficient difference equation in space can be solved exactly on each of the two semi-infinite exterior domains. Admitting only solutions in $l_2$ which vanish at infinity is equivalent to imposing outgoing boundary conditions. An inverse Z-transformation leads to exact DTBCs in form of a convolution in discrete time which suppress spurious reflections at the boundaries and enforce stabi...

Hammer, René; Arnold, Anton

2013-01-01

55

We consider a divergence-free non-dissipative fourth-order explicit staggered finite difference scheme for the hyperbolic Maxwell's equations. Special one-sided difference operators are derived in order to implement the scheme near metal boundaries and dielectric interfaces. Numerical results show the scheme is long-time stable, and is fourth-order convergent over complex domains that include dielectric interfaces and perfectly conducting surfaces. We also examine the scheme's behavior near metal surfaces that are not aligned with the grid axes, and compare its accuracy to that obtained by the Yee scheme.

Yefet, Amir; Petropoulos, Peter G.

1999-01-01

56

Application of the 3D finite difference scheme to the TEXTOR-DED geometry

Energy Technology Data Exchange (ETDEWEB)

In this paper, we use the finite difference code FINITE, developed for the stellarator geometry, to investigate the energy transport in the 3D TEXTOR-DED tokamak configuration. In particular, we concentrate on the comparison between two different algorithms for solving the radial part of the electron energy transport equation. (orig.)

Zagorski, R.; Stepniewski, W. [Institute of Plasma Physics and Laser Microfusion, EURATOM Association, 01-497 Warsaw (Poland); Jakubowski, M. [Institut fuer Plasmaphysik, Forschungszentrum Juelich GmbH, EURATOM Association, Trilateral Euregio Cluster, D-52425 Juelich (Germany); McTaggart, N. [Department of Engineering Materials, University of Sheffield, Sheffield S1 3JD (United Kingdom); Schneider, R.; Xanthopoulos, P. [Max-Planck-Institut fuer Plasmaphysik, Teilinstitut Greifswald, EURATOM Association, Wendelsteinstrasse 1, D-17491 Greifswald (Germany)

2006-09-15

57

Application of the 3D finite difference scheme to the TEXTOR-DED geometry

International Nuclear Information System (INIS)

In this paper, we use the finite difference code FINITE, developed for the stellarator geometry, to investigate the energy transport in the 3D TEXTOR-DED tokamak configuration. In particular, we concentrate on the comparison between two different algorithms for solving the radial part of the electron energy transport equation. (orig.)

58

We present a computational study of the solution of the Falkner-Skan equation (a thirdorder boundary value problem arising in boundary-layer theory) using high-order and high-order-compact finite differences schemes. There are a number of previously reported solution approaches that adopt a reduced-order system of equations, and numerical methods such as: shooting, Taylor series, Runge-Kutta and other semi-analytic methods. Interestingly, though, methods that solve the original non-reduced th...

Carlos Duque-Daza; Duncan Lockerby; Carlos Galeano

2011-01-01

59

Energy Technology Data Exchange (ETDEWEB)

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)

Karlsen, Kenneth Hvistendal; Risebro, Nils Henrik

2000-09-01

60

A staggered mesh finite difference scheme for the computation of compressible flows

A simple high resolution finite difference technique is presented to approximate weak solutions to hyperbolic systems of conservation laws. The method does not rely on Riemann problem solvers and is therefore easy to extend to a wide variety of problems. The overall performance (resolution and CPU requirements) is competitive, with other state-of-the-art techniques offering sharp nonoscillatory shocks and contacts. Theoretical results confirm the reliability of the approach for linear systems and nonlinear scalar equations.

Sanders, Richard

1992-01-01

61

A few families of counterexamples are provided to "A proof that the discrete singular convolution (DSC)/Lagrange-distributed approximation function (LDAF) method is inferior to high order finite differences", Journal of Computational Physics, 214, 538-549 (2006).

Wei, G W; Zhao, Shan

2006-01-01

62

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.

Tan, Sirui; Huang, Lianjie

2014-11-01

63

A staggered mesh finite difference scheme for the computation of hypersonic Euler flows

A shock capturing finite difference method for systems of hyperbolic conservation laws is presented which avoids the need to solve Riemann problems while being competitive in performance with other current methods. A staggered spatial mesh is employed, so that complicated nonlinear waves generated at cell interfaces are averaged over cell interiors at the next time level. The full method combines to form a conservative version of the modified method of characteristics. The advantages of the method are discussed, and numerical results are presented for the two-dimensional double ellipse problem.

Sanders, Richard

1991-01-01

64

Invariant discretization schemes for the shallow-water equations

Invariant discretization schemes are derived for the one- and two-dimensional shallow-water equations with periodic boundary conditions using difference invariants. While originally designed for constructing invariant finite difference schemes, we extend the usage of difference invariants to allow constructing of invariant finite volume methods as well. It is found that the classical invariant schemes converge to the Lagrangian formulation of the shallow-water equations. These schemes require to redistribute the grid points according to the physical fluid velocity, i.e. the mesh cannot remain fixed in the course of the numerical integration. Invariant Eulerian discretization schemes are proposed for the shallow-water equations. Instead of using the fluid velocity as the grid velocity, an invariant moving mesh generator is invoked in order to determine the location of the grid points at the subsequent time level. The numerical conservation of energy and mass is evaluated for the invariant and the non-invariant...

Bihlo, Alexander

2012-01-01

65

On the third-order upwind finite-difference scheme in numerical analysis for initial-value problems

International Nuclear Information System (INIS)

The purpose of this paper is to present highly accurate and stable numerical solutions for the time-dependent Navier-Stokes equations. This numerical method utilizes uniformly third-order finite-difference scheme based on Quadratic Upstream Interpolation for Convective Kinematics with Estimated Streaming Terms(QUICKEST) combined with the Marker and Cell computing technique(QUICKESTMAC) for unsteady convection-dominated flows. The solutions for a time-marching square cavity flow are obtained with Reynolds number 10,000 and the computed results prove the validity of this QUICKESTMAC method. (author)

66

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

Energy Technology Data Exchange (ETDEWEB)

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

Brinkman, D., E-mail: Daniel.Brinkman@asu.edu [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287 (United States); Heitzinger, C., E-mail: Clemens.Heitzinger@asu.edu [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); AIT Austrian Institute of Technology, A-1220 Vienna (Austria); School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287 (United States); Markowich, P.A., E-mail: Peter.Markowich@kaust.edu.sa [Mathematical and Computer Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900 (Saudi Arabia); Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)

2014-01-15

67

We present two finite-difference algorithms for studying the dynamics of spatially extended predator-prey interactions with the Holling type II functional response and logistic growth of the prey. The algorithms are stable and convergent provided the time step is below a (non-restrictive) critical value. This is advantageous as it is well-known that the dynamics of approximations of differential equations (DEs) can differ significantly from that of the underlying DEs themselves. This is particularly important for the spatially extended systems that are studied in this paper as they display a wide spectrum of ecologically relevant behavior, including chaos. Furthermore, there are implementational advantages of the methods. For example, due to the structure of the resulting linear systems, standard direct, and iterative solvers are guaranteed to converge. We also present the results of numerical experiments in one and two space dimensions and illustrate the simplicity of the numerical methods with short programs MATLAB: . Users can download, edit, and run the codes from http://www.uoguelph.ca/~mgarvie/, to investigate the key dynamical properties of spatially extended predator-prey interactions. PMID:17268759

Garvie, Marcus R

2007-04-01

68

Fully Discrete Wavelet Galerkin Schemes

The present paper is intended to give a survey of the developments of the wavelet Galerkin boundary element method. Using appropriate wavelet bases for the discretization of boundary integral operators yields numerically sparse system matrices. These system matrices can be compressed to O(N_j) nonzero matrix entries without loss of accuracy of the underlying Galerkin scheme. Herein, O(N_j) denotes the number of unknowns. As we show in the present paper, the ...

Harbrecht, Helmut; Konik, Michael; Schneider, Reinhold

2006-01-01

69

In this paper, we propose a new WENO finite difference procedure for nonlinear degenerate parabolic equations which may contain discontinuous solutions. Our scheme is based on the method of lines, with a high-order accurate conservative approximation to each of the diffusion terms based on an idea that has been recently presented by Liu et al. [Y. Liu, C.-W. Shu, M. Zhang, High order finite difference WENO schemes for non-linear degenerate parabolic equations, SIAM J. Sci. Comput. 33 (2011) 939-965]. Our scheme tries to circumvent the negative ideal weights that appear when applying the standard WENO idea, as is done in Liu et al. (2011) [13]. In one-dimensional case, first we obtain an optimum polynomial on a six-points stencil. This optimum polynomial is sixth-order accurate in regions of smoothness. Then, we consider this optimum polynomial as a symmetric and convex combination of four polynomials with ideal weights. Following the methodology of the classic WENO procedure, then we calculate the non-oscillatory weights with the ideal weights. Numerical examples are provided to demonstrate the resolution power and accuracy of the scheme. Finally, the new method is extended to multi-dimensional problems by dimension-by-dimension approach. More examples of multi-dimension problems are presented to show that our method remains non-oscillatory while giving good resolution of discontinuities. Finally, we would like to mention that this paper combines and extends the techniques proposed in [13] and Levy et al. (2000) [24].

Abedian, Rooholah; Adibi, Hojatollah; Dehghan, Mehdi

2013-08-01

70

Directory of Open Access Journals (Sweden)

Full Text Available We present a computational study of the solution of the Falkner-Skan equation (a thirdorder boundary value problem arising in boundary-layer theory using high-order and high-order-compact finite differences schemes. There are a number of previously reported solution approaches that adopt a reduced-order system of equations, and numerical methods such as: shooting, Taylor series, Runge-Kutta and other semi-analytic methods. Interestingly, though, methods that solve the original non-reduced third-order equation directly are absent from the literature. Two high-order schemes are presented using both explicit (third-order and implicit compact-difference (fourth-order formulations on a semi-infinite domain; to our knowledge this is the first time that high-order finite difference schemes are presented to find numerical solutions to the non-reduced-order Falkner-Skan equation directly. This approach maintains the simplicity of Taylor-series coefficient matching methods, avoiding complicated numerical algorithms, and in turn presents valuable information about the numerical behaviour of the equation. The accuracy and effectiveness of this approach is established by comparison with published data for accelerating, constant and decelerating flows; excellent agreement is observed. In general, the numerical behaviour of formulations that seek an optimum physical domain size (for a given computational grid is discussed. Based on new insight into such methods, an alternative optimisation procedure is proposed that should increase the range of initial seed points for which convergence can be achieved.

Carlos Duque-Daza

2011-12-01

71

Scientific Electronic Library Online (English)

Full Text Available SciELO Brazil | Language: English Abstract in english We present a computational study of the solution of the Falkner-Skan equation (a thirdorder boundary value problem arising in boundary-layer theory) using high-order and high-order-compact finite differences schemes. There are a number of previously reported solution approaches that adopt a reduced- [...] order system of equations, and numerical methods such as: shooting, Taylor series, Runge-Kutta and other semi-analytic methods. Interestingly, though, methods that solve the original non-reduced third-order equation directly are absent from the literature. Two high-order schemes are presented using both explicit (third-order) and implicit compact-difference (fourth-order) formulations on a semi-infinite domain; to our knowledge this is the first time that high-order finite difference schemes are presented to find numerical solutions to the non-reduced-order Falkner-Skan equation directly. This approach maintains the simplicity of Taylor-series coefficient matching methods, avoiding complicated numerical algorithms, and in turn presents valuable information about the numerical behaviour of the equation. The accuracy and effectiveness of this approach is established by comparison with published data for accelerating, constant and decelerating flows; excellent agreement is observed. In general, the numerical behaviour of formulations that seek an optimum physical domain size (for a given computational grid) is discussed. Based on new insight into such methods, an alternative optimisation procedure is proposed that should increase the range of initial seed points for which convergence can be achieved.

Carlos, Duque-Daza; Duncan, Lockerby; Carlos, Galeano.

2011-12-01

72

Locally exact modifications of discrete gradient schemes

International Nuclear Information System (INIS)

Locally exact integrators preserve linearization of the original system at every point. We construct energy-preserving locally exact discrete gradient schemes for arbitrary multidimensional canonical Hamiltonian systems by modifying classical discrete gradient schemes. Modifications of this kind are found for any discrete gradient.

73

An efficient hybrid pseudospectral/finite-difference scheme for solving the TTI pure P-wave equation

International Nuclear Information System (INIS)

The pure P-wave equation for modelling and migration in tilted transversely isotropic (TTI) media has attracted more and more attention in imaging seismic data with anisotropy. The desirable feature is that it is absolutely free of shear-wave artefacts and the consequent alleviation of numerical instabilities generally suffered by some systems of coupled equations. However, due to several forward–backward Fourier transforms in wavefield updating at each time step, the computational cost is significant, and thereby hampers its prevalence. We propose to use a hybrid pseudospectral (PS) and finite-difference (FD) scheme to solve the pure P-wave equation. In the hybrid solution, most of the cost-consuming wavenumber terms in the equation are replaced by inexpensive FD operators, which in turn accelerates the computation and reduces the computational cost. To demonstrate the benefit in cost saving of the new scheme, 2D and 3D reverse-time migration (RTM) examples using the hybrid solution to the pure P-wave equation are carried out, and respective runtimes are listed and compared. Numerical results show that the hybrid strategy demands less computation time and is faster than using the PS method alone. Furthermore, this new TTI RTM algorithm with the hybrid method is computationally less expensive than that with the FD solution to conventional TTI coupled equations. (paper)

74

Finite-Difference Lattice Boltzmann Methods for binary miscible fluids

Based on a discrete velocity model, two multispeed finite-difference lattice Boltzmann methods for binary miscible fluids are formulated. One is for simulating isothermal systems at the Navier-Stokes level. The other is for simulating thermal and compressible systems at the Euler level. The formulated models are based on a two-fluid kinetic theory. The used finite-difference scheme overcomes defects resulted from the splitting scheme where an evolution step is separated as a propagation and a collision ones.

Xu, A; Xu, Aiguo; Hayakawa, Hisao

2004-01-01

75

The dynamics of the local kinetic energy spectrum of an elastic plate vibrating in a wave turbulence (WT) regime is investigated with a finite difference, energy-conserving scheme. The numerical method allows the simulation of pointwise forcing together with realistic boundary conditions, a set-up which is close to experimental conditions. In the absence of damping, the framework of non-stationary wave turbulence is used. Numerical simulations show the presence of a front propagating to high frequencies, leaving a steady spectrum in its wake. Self-similar dynamics of the spectra are found with and without periodic external forcing. For the periodic forcing, the mean injected power is found to be constant, and the frequency at the cascade front evolves linearly with time resulting in a increase of the total energy. For the free turbulence, the energy contained in the cascade remains constant while the frequency front increases as t. These self-similar solutions are found to be in accordance with the kinetic equation derived from the von Kármán plate equations. The effect of the pointwise forcing is observable and introduces a steeper slope at low frequencies, as compared to the unforced case. The presence of a realistic geometric imperfection of the plate is found to have no effect on the global properties of the spectra dynamics. The steeper slope brought by the external forcing is shown to be still observable in a more realistic case where damping is added.

Ducceschi, Michele; Cadot, Olivier; Touzé, Cyril; Bilbao, Stefan

2014-07-01

76

Split-Field Finite-Difference Time-Domain scheme for Kerr-type nonlinear periodic media

The Split-Field Finite-Difference Time-Domain (SF-FDTD) formulation is extended to periodic structures with Kerr-type nonlinearity. The optical Kerr effect is introduced by an iterative fixed-point procedure for solving the nonlinear system of equations. Using the method, formation of solitons inside homogenous nonlinear media is numerically observed. Furthermore, the performance of the approach with more complex photonic systems, such as high-reflectance coatings and binary phase gratings wi...

France?s Monllor, Jorge; Tervo, Jani; Neipp Lo?pez, Cristian

2012-01-01

77

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.

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

1983-01-01

78

In this paper, the second order of accuracy difference scheme approximately solving the initial-value problem for the integral-differential equation of the hyperbolic type in a Hilbert space H is presented. The stability estimates for the solution of this difference scheme are established. In application, the second order of accuracy difference scheme for solving the local boundary problem for the multidimensional integral-differential equation of the hyperbolic type with two dependent limits is constructed. Theoretical results are supported by numerical examples.

Direk, Zilal; Ashyraliyev, Maksat

2014-08-01

79

We present a quasidiffusion (QD) method for solving neutral particle transport problems in Cartesian XY geometry on unstructured quadrilateral meshes, including local refinement capability. Neutral particle transport problems are central to many applications including nuclear reactor design, radiation safety, astrophysics, medical imaging, radiotherapy, nuclear fuel transport/storage, shielding design, and oil well-logging. The primary development is a new discretization of the low-order QD (LOQD) equations based on cell-local finite differences. The accuracy of the LOQD equations depends on proper calculation of special non-linear QD (Eddington) factors from a transport solution. In order to completely define the new QD method, a proper discretization of the transport problem is also presented. The transport equation is discretized by a conservative method of short characteristics with a novel linear approximation of the scattering source term and monotonic, parabolic representation of the angular flux on incoming faces. Analytic and numerical tests are used to test the accuracy and spatial convergence of the non-linear method. All tests exhibit O(h2) convergence of the scalar flux on orthogonal, random, and multi-level meshes.

Wieselquist, William A.; Anistratov, Dmitriy Y.; Morel, Jim E.

2014-09-01

80

Linearized numerical stability bounds for solving the nonlinear time-dependent Schr\\"odinger equation (NLSE) are shown. The bounds are computed for the fourth-order Runge-Kutta scheme in time and both second-order and fourth-order central differencing in space. Results are given for Dirichlet, modulus-squared Dirichlet, Laplacian-zero, and periodic boundary conditions for one, two, and three dimensions. Our approach is to use standard Runge-Kutta linear stability theory, treating the nonlinearity of the NLSE as a constant. The required bounds on the eigenvalues of the scheme matrices are found analytically when possible, and otherwise estimated using the Gershgorin circle theorem.

Caplan, Ronald M

2011-01-01

81

International Nuclear Information System (INIS)

In this paper, we use the staggered grid, the auxiliary grid, the rotated staggered grid and the non-staggered grid finite-difference methods to simulate the wavefield propagation in 2D elastic tilted transversely isotropic (TTI) and viscoelastic TTI media, respectively. Under the stability conditions, we choose different spatial and temporal intervals to get wavefront snapshots and synthetic seismograms to compare the four algorithms in terms of computational accuracy, CPU time, phase shift, frequency dispersion and amplitude preservation. The numerical results show that: (1) the rotated staggered grid scheme has the least memory cost and the fastest running speed; (2) the non-staggered grid scheme has the highest computational accuracy and least phase shift; (3) the staggered grid has less frequency dispersion even when the spatial interval becomes larger. (paper)

82

In this paper, we use the staggered grid, the auxiliary grid, the rotated staggered grid and the non-staggered grid finite-difference methods to simulate the wavefield propagation in 2D elastic tilted transversely isotropic (TTI) and viscoelastic TTI media, respectively. Under the stability conditions, we choose different spatial and temporal intervals to get wavefront snapshots and synthetic seismograms to compare the four algorithms in terms of computational accuracy, CPU time, phase shift, frequency dispersion and amplitude preservation. The numerical results show that: (1) the rotated staggered grid scheme has the least memory cost and the fastest running speed; (2) the non-staggered grid scheme has the highest computational accuracy and least phase shift; (3) the staggered grid has less frequency dispersion even when the spatial interval becomes larger.

Li, Zhong-sheng; Bai, Chao-ying; Sun, Yao-chong

2013-08-01

83

Synchronisation schemes for two dimensional discrete systems

In this work we consider two models of two dimensional discrete systems subjected to three different types of coupling and analyse systematically the performance of each in realising synchronised states.We find that linear coupling effectively introduce control of chaos along with synchronisation,while synchronised chaotic states are possible with an additive parametric coupling scheme both being equally relevant for specific applications.The basin leading to synchronisation...

Ambika, G.; Ambika, K.

2006-01-01

84

Implicit discretization schemes for Langevin dynamics

We explore here several numerical schemes for Langevin dynamics in the general implicit discretization framework of the Langevin/implicit-Euler scheme, LI. Specifically, six schemes are constructed through different discretization combinations of acceleration, velocity, and position. Among them, the explicit BBK method (LE in our notation) and LI are recovered, and the other four (all implicit) are named LIM1, LIM2, MID1, and MID2. The last two correspond, respectively, to the well-known implicit-midpoint scheme and the trapezoidal rule. LI and LIM1 are first-order accurate and have intrinsic numerical damping. LIM2, MID1, and MID2 appear to have large-timestep stability as LI but overcome numerical damping. However, numerical results reveal limitations on other grounds. From simulations on a model butane, we find that the non-damping methods give similar results when the timestep is small; however, as the timestep increases, LIM2 exhibits a pronounced rise in the potential energy and produces wider distributions for the bond lengths. MID1 and MID2 appear to be the best among those implicit schemes for Langevin dynamics in terms of reasonably reproducing distributions for bond lengths, bond angles and dihedral angles (in comparison to 1 fs timestep explicit simulations), as well as conserving the total energy reasonably. However, the minimization subproblem (due to the implicit formulation) becomes difficult when the timestep increases further. In terms of computational time, all the implicit schemes are very demanding. Nonetheless, we observe that for moderate timesteps, even when the error is large for the fast motions, it is relatively small for the slow motions. This suggests that it is possible by large timestep algorithms to capture the slow motions without resolving accurately the fast motions.

Zhang, Guihua; Schlick, Tamar

85

Finite-difference lattice-Boltzmann methods for binary fluids.

We investigate two-fluid Bhatnagar-Gross-Krook (BGK) kinetic methods for binary fluids. The developed theory works for asymmetric as well as symmetric systems. For symmetric systems it recovers Sirovich's theory and is summarized in models A and B. For asymmetric systems it contributes models C, D, and E which are especially useful when the total masses and/or local temperatures of the two components are greatly different. The kinetic models are discretized based on an octagonal discrete velocity model. The discrete-velocity kinetic models and the continuous ones are required to describe the same hydrodynamic equations. The combination of a discrete-velocity kinetic model and an appropriate finite-difference scheme composes a finite-difference lattice Boltzmann method. The validity of the formulated methods is verified by investigating (i) uniform relaxation processes, (ii) isothermal Couette flow, and (iii) diffusion behavior. PMID:16089910

Xu, Aiguo

2005-06-01

86

Finite-Difference Algorithms For Computing Sound Waves

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

Davis, Sanford

1993-01-01

87

Overestimation of precipitation over steep mountains has been a long-lasting bias in many climate models. After replacing the semi-Lagrangian method with a finite-difference approach for trace transport algorithm (the two-step shape preserving scheme, TSPAS), the modified NCAR CAM5 (M-CAM5) with high horizontal resolution results in a significant improvement of simulation in precipitation over the steep edge of the Tibetan Plateau. The M-CAM5 restrains the "overshoot" of water vapor to the high-altitude region of the windward slopes and significantly reduces the overestimation of precipitation in areas above 2000 m along the southern edge of the Tibetan Plateau. More moisture are left in the low-altitude region on the slope where used to present dry biases in CAM5. The excessive (insufficient) amount of precipitation over the higher (lower) part of the steep slope is partially caused by the multi-grid water vapor transport in CAM5, which leads to spurious accumulation of water vapor at cold and high-altitude grids. Benefited from calculation of transport grid by grid in TSPAS and detailed description of steep mountains by the high-resolution model, M-CAM5 moves water vapor and precipitation downward over windward slopes and presents a more realistic simulation. Results in this study indicate that in addition to the development of physical parameterization schemes, the dynamical process should also be reconsidered in order to improve the climate simulation over steep mountains.

Yu, Rucong; Li, Jian; Zhang, Yi; Chen, Haoming

2015-02-01

88

International Nuclear Information System (INIS)

The results of numerical simulation of fluid flow and heat transfer in rod bundles with geometrical disturbance to the hexagonal rod array configuration are presented. The geometry of the rod bundle was chosen according to the flow and temperature distributions available from the experimental data. Reynolds equation for axial velocity component has been simulated in two dimensions. Turbulent shear stresses have been modeled by the turbulent eddy viscosity with anisotropy defined for radial and azimuthal components. Secondary flows have not been taken into consideration. Also the averaged energy conservation equation closed with anisotropic turbulent conductivity coefficients was simulated. Reynolds and energy conservation equations have been discretizated by the Efficient Finite-Difference (EFD) scheme based on the 'locally exact' analytical solution. The comparison of the accuracy of the EFD method and traditional central-difference scheme has been performed. The benchmark problem has been simulated using components of the Computational Object-Oriented Library for Fluid Dynamics (COOLFD) which is a new-generation porgramming tool aimed to improve the development of the CFD application to complex calculation areas such as rod bundles in nuclear reactors. Comparisons of calculated results and experimental data are presented for the local shear stress, axial velocity and the wall temperature distributions in the 'geometrically disturbed' region around dislocated rodisturbed' region around dislocated rod

89

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

The finite-difference method is widely used for time-domain modelling of the wave equation because of its ease of implementation of high-order spatial discretization schemes, parallelization and computational efficiency. However, finite elements on tetrahedral meshes are more accurate in complex geometries near sharp interfaces. We compared the fourth-order finite-difference method to fourth-order continuous masslumped finite elements in terms of accuracy and computational cost. The results s...

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

2012-01-01

90

Discretized Newton-relaxation solution of high resolution flux-difference split schemes

A method is presented for the implicit solution of high resolution flux-difference split schemes for which it is impractical to obtain the Jacobian matrix analytically. The method is used frequently in numerical schemes for solving nonlinear systems of equations, but apparently has not been used to date for approximating the Jacobian of the Roe numerical flux vectors. The method consists of obtaining a discretized Jacobian by using simple finite-differences of the flux vectors, and then using this discretized Jacobian in a Newton-relaxation solution method. The method is applied to both compressible and incompressible flows. Numerical results are presented that demonstrate the method works for both inviscid and viscous flows.

Whitfield, David L.; Taylor, Lafe K.

1991-01-01

91

Discretized Newton-relaxation solution of high resolution flux-difference split schemes

International Nuclear Information System (INIS)

A method is presented for the implicit solution of high resolution flux-difference split schemes for which it is impractical to obtain the Jacobian matrix analytically. The method is used frequently in numerical schemes for solving nonlinear systems of equations, but apparently has not been used to date for approximating the Jacobian of the Roe numerical flux vectors. The method consists of obtaining a discretized Jacobian by using simple finite-differences of the flux vectors, and then using this discretized Jacobian in a Newton-relaxation solution method. The method is applied to both compressible and incompressible flows. Numerical results are presented that demonstrate the method works for both inviscid and viscous flows. 21 refs

92

Explicit finite-difference lattice Boltzmann method for curvilinear coordinates

In this paper a finite-difference-based lattice Boltzmann method for curvilinear coordinates is proposed in order to improve the computational efficiency and numerical stability of a recent method [R. Mei and W. Shyy, J. Comput. Phys. 143, 426 (1998)] in which the collision term of the Boltzmann Bhatnagar-Gross-Krook equation for discrete velocities is treated implicitly. In the present method, the implicitness of the numerical scheme is removed by introducing a distribution function different from that being used currently. As a result, an explicit finite-difference lattice Boltzmann method for curvilinear coordinates is obtained. The scheme is applied to a two-dimensional Poiseuille flow, an unsteady Couette flow, a lid-driven cavity flow, and a steady flow around a circular cylinder. The numerical results are in good agreement with the results of previous studies. Extensions to other lattice Boltzmann models based on nonuniform meshes are also discussed.

Guo, Zhaoli; Zhao, T. S.

2003-06-01

93

We investigate the connections between several recent methods for the discretization of anisotropic heterogeneous diffusion operators on general grids. We prove that the Mimetic Finite Difference scheme, the Hybrid Finite Volume scheme and the Mixed Finite Volume scheme are in fact identical up to some slight generalizations. As a consequence, some of the mathematical results obtained for each of the method (such as convergence properties or error estimates) may be extended to the unified common framework. We then focus on the relationships between this unified method and nonconforming Finite Element schemes or Mixed Finite Element schemes, obtaining as a by-product an explicit lifting operator close to the ones used in some theoretical studies of the Mimetic Finite Difference scheme. We also show that for isotropic operators, on particular meshes such as triangular meshes with acute angles, the unified method boils down to the well-known efficient two-point flux Finite Volume scheme.

Droniou, Jerome; Gallouët, Thierry; Herbin, Raphaele

2008-01-01

94

Simulating thermohydrodynamics by finite difference solutions of the Boltzmann equation

The formulation of a consistent thermohydrodynamics with a discrete model of the Boltzmann equation requires the representation of the velocity moments up to the fourth order. Space-filling discrete sets of velocities with increasing accuracy were obtained using a systematic approach in accordance with a quadrature method based on prescribed abscissas (Philippi et al., Phys. Rev. E, 73 (5), n. 056702, 2006). These sets of velocities are suitable for collision-propagation schemes, where the discrete velocity and physical spaces are coupled and the Courant number is unitary. The space-filling requirement leads to sets of discrete velocities which can be large in thermal models. In this work, although the discrete sets of velocities are also obtained with a quadrature method based on prescribed abscissas, the lattices are not required to be space-filling. This leads to a reduced number of discrete velocities for the same approximation order but requires the use of an alternative numerical scheme. The use of finite difference schemes for the advection term in the continuous Boltzmann equation has shown to have some advantages with respect to the collision-propagation LBM method by freeing the Courant number from its unitary value and reducing the discretization error. In this work, a second order Runge-Kutta method was used for the simulation of the Sod's shock tube problem, the Couette flow and the Lid-driven cavity flow. Boundary conditions without velocity slip and temperature jumps were written for these discrete Boltzmann equation by splitting the velocity distribution function into an equilibrium and a non-equilibrium part. The equilibrium part was set using the local velocity and temperature at the wall and the non-equilibrium part by extrapolating the non-equilibrium moments to the wall sites.

Surmas, R.; Pico Ortiz, C. E.; Philippi, P. C.

2009-04-01

95

Staggered discretizations, pressure correction schemes and all speed barotropic flows

We present in this paper a class of schemes for the solution of the barotropic Navier- Stokes equations. These schemes work on general meshes, preserve the stability properties of the continuous problem, irrespectively of the space and time steps, and boil down, when the Mach number vanishes, to discretizations which are standard (and stable) in the incompressible framework. Finally, we show that they are able to capture solutions with shocks to the Euler equations

Gastaldo, Laura; Herbin, Raphaele; Kheriji, Walid; Lapuerta, Ce?line; Latche?, Jean-claude

2011-01-01

96

Viscosity of finite difference lattice Boltzmann models

International Nuclear Information System (INIS)

Two-dimensional finite difference lattice Boltzmann models for single-component fluids are discussed and the corresponding macroscopic equations for mass and momentum conservation are derived by performing a Chapman-Enskog expansion. In order to recover the correct mass equation, characteristic-based finite difference schemes should be associated with the forward Euler scheme for the time derivative, while the space centered and second-order upwind schemes should be associated to second-order schemes for the time derivative. In the incompressible limit, the characteristic based schemes lead to spurious numerical contributions to the apparent value of the kinematic viscosity in addition to the physical value that enters the Navier-Stokes equation. Formulae for these spurious numerical viscosities are in agreement with results of simulations for the decay of shear waves

97

Mimetic finite difference methods in image processing

Scientific Electronic Library Online (English)

Full Text Available SciELO Brazil | Language: English Abstract in english We introduce the use of mimetic methods to the imaging community, for the solution of the initial-value problems ubiquitous in the machine vision and image processing and analysis fields. PDE-based image processing and analysis techniques comprise a host of applications such as noise removal and res [...] toration, deblurring and enhancement, segmentation, edge detection, inpainting, registration, motion analysis, etc. Because of their favorable stability and efficiency properties, semi-implicit finite difference and finite element schemes have been the methods of choice (in that order of preference). We propose a new approach for the numerical solution of these problems based on mimetic methods. The mimetic discretization scheme preserves the continuum properties of the mathematical operators often encountered in the image processing and analysis equations. This is the main contributing factor to the improved performance of the mimetic method approach, as compared to both of the aforementioned popular numerical solution techniques. To assess the performance of the proposed approach, we employ the Catté-Lions-Morel-Coll model to restore noisy images, by solving the PDE with the three numerical solution schemes. For all of the benchmark images employed in our experiments, and for every level of noise applied, we observe that the best image restored by using the mimetic method is closer to the noise-free image than the best images restored by the other two methods tested. These results motivate further studies of the application of the mimetic methods to other imaging problems. Mathematical subject classification: Primary: 68U10; Secondary: 65L12.

C., Bazan; M., Abouali; J., Castillo; P., Blomgren.

98

One of the ongoing issues with fractional-order diffusion models is the design of efficient numerical schemes for the space and time discretizations. Until now, most models have relied on a low-order finite difference (FD) method to discretize both the fractional-order space and time derivatives. Some numerical schemes using low-order finite elements (FE) have also been proposed. Both the FD and FE methods have long been used to solve integer-order partial differential equations. These low-or...

Hanert, Emmanuel; Piret, Ce?cile; International Symposium On Fractional Pdes Theory, Numerics And Applications

2013-01-01

99

The coupled double diffusive natural convection and radiation in a tilted and differentially heated square cavity containing a non-gray air-CO2 (or air-H2O) mixtures was numerically investigated. The horizontal walls are insulated and impermeable and the vertical walls are maintained at different temperatures and concentrations. The hybrid lattice Boltzmann method with the multiple-relaxation time model is used to compute the hydrodynamics and the finite difference method to determine temperatures and concentrations. The discrete ordinates method combined to the spectral line-based weighted sum of gray gases model is used to compute the radiative term and its spectral aspect. The effects of the inclination angle on the flow, thermal and concentration fields are analyzed for both aiding and opposing cases. It was found that radiation gas modifies the structure of the velocity and thermal fields by generating inclined stratifications and promoting the instabilities in opposing flows.

Moufekkir, Fayçal; Moussaoui, Mohammed Amine; Mezrhab, Ahmed; Naji, Hassan

2015-04-01

100

We consider an initial-boundary value problem for a generalized 2D time-dependent Schr\\"odinger equation on a semi-infinite strip. For the Crank-Nicolson finite-difference scheme with approximate or discrete transparent boundary conditions (TBCs), the Strang-type splitting with respect to the potential is applied. For the resulting method, the uniform in time $L^2$-stability is proved. Due to the splitting, an effective direct algorithm using FFT is developed to implement the method with the discrete TBC for general potential. Numerical results on the tunnel effect for rectangular barriers are included together with the related practical error analysis.

Ducomet, Bernard; Zlotnik, Ilya

2013-01-01

101

Finite Difference Solution for Precooling Process of Fish Packages

Directory of Open Access Journals (Sweden)

Full Text Available The present work aims at finding an optimized finite difference scheme for the solution of problems involving pure convection heat transfer in slab shaped fresh water fish pieces. A generalized mathematical model was written in dimensionless form and an optimized scheme of the solutions was worked out. A fully explicit finite difference scheme, an implicit finite difference scheme and different combination of the two, with varying values of the weighing factor were thoroughly studied. All the possible options of temperature-time grid sizes were considered. It was found that the simplest explicit finite difference scheme with ten characteristic length division and Fourier number increments one sixth of the square of the space division size gives best convergence and minimal truncation error. Numerically computed and measured temperature-time variations were found to have excellent agreement.

K. A. Abbas

2004-01-01

102

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

DEFF Research Database (Denmark)

The incompressible Euler equations are solved with a free surface, the position of which is captured by applying an Eulerian kinematic boundary condition. The solution strategy follows that of [1, 2], applying a coordinate-transformation to obtain a time-constant spatial computational domain which 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 implicitly, at the end of each time stage, by constructing the pressure from a discrete Poisson equation, derived from the discrete continuity and momentum equations and taking the time-dependent physical domain into account. An efficient preconditionedDefect Correction (DC) solution of the discrete Poisson equation for the pressure is presented, in which the preconditioning step is based on an order-multigrid formulation with a direct solution on the lowest order-level. This ensures fast convergence of the DC method with a computational effort which scales linearly with the problem size. Results obtained with a two-dimensional implementation of the model are compared with highly accurate stream function solutions to the nonlinear wave problem, which show the approximately expected convergence rates and a clear advantage of using high-order finite difference schemes in combination with the Euler equations.

Christiansen, Torben Robert Bilgrav; Bingham, Harry B.

2012-01-01

103

Variationally consistent discretization schemes and numerical algorithms for contact problems

We consider variationally consistent discretization schemes for mechanical contact problems. Most of the results can also be applied to other variational inequalities, such as those for phase transition problems in porous media, for plasticity or for option pricing applications from finance. The starting point is to weakly incorporate the constraint into the setting and to reformulate the inequality in the displacement in terms of a saddle-point problem. Here, the Lagrange multiplier represents the surface forces, and the constraints are restricted to the boundary of the simulation domain. Having a uniform inf-sup bound, one can then establish optimal low-order a priori convergence rates for the discretization error in the primal and dual variables. In addition to the abstract framework of linear saddle-point theory, complementarity terms have to be taken into account. The resulting inequality system is solved by rewriting it equivalently by means of the non-linear complementarity function as a system of equations. Although it is not differentiable in the classical sense, semi-smooth Newton methods, yielding super-linear convergence rates, can be applied and easily implemented in terms of a primal-dual active set strategy. Quite often the solution of contact problems has a low regularity, and the efficiency of the approach can be improved by using adaptive refinement techniques. Different standard types, such as residual- and equilibrated-based a posteriori error estimators, can be designed based on the interpretation of the dual variable as Neumann boundary condition. For the fully dynamic setting it is of interest to apply energy-preserving time-integration schemes. However, the differential algebraic character of the system can result in high oscillations if standard methods are applied. A possible remedy is to modify the fully discretized system by a local redistribution of the mass. Numerical results in two and three dimensions illustrate the wide range of possible applications and show the performance of the space discretization scheme, non-linear solver, adaptive refinement process and time integration.

Wohlmuth, Barbara

104

The computer algebra approach of the finite difference methods for PDEs

International Nuclear Information System (INIS)

In this paper, a first attempt has been made to realize the computer algebra construction of the finite difference methods or the finite difference schemes for constant coefficient partial differential equations. (author). 9 refs, 2 tabs

105

Discrete unified gas kinetic scheme on unstructured meshes

The recently proposed discrete unified gas kinetic scheme (DUGKS) is a finite volume method for deterministic solution of the Boltzmann model equation with asymptotic preserving property. In DUGKS, the numerical flux of the distribution function is determined from a local numerical solution of the Boltzmann model equation using an unsplitting approach. The time step and mesh resolution are not restricted by the molecular collision time and mean free path. To demonstrate the capacity of DUGKS in practical problems, this paper extends the DUGKS to arbitrary unstructured meshes. Several tests of both internal and external flows are performed, which include the cavity flow ranging from continuum to free molecular regimes, a multiscale flow between two connected cavities with a pressure ratio of 10000, and a high speed flow over a cylinder in slip and transitional regimes. The numerical results demonstrate the effectiveness of the DUGKS in simulating multiscale flow problems.

Zhu, Lianhua; Xu, Kun

2015-01-01

106

Discrete unified gas kinetic scheme with force term for incompressible fluid flows

The discrete unified gas kinetic scheme (DUGKS) is a finite-volume scheme with discretization of particle velocity space, which combines the advantages of both lattice Boltzmann equation (LBE) method and unified gas kinetic scheme (UGKS) method, such as the simplified flux evaluation scheme, flexible mesh adaption and the asymptotic preserving properties. However, DUGKS is proposed for near incompressible fluid flows, the existing compressible effect may cause some serious e...

Wu, Chen; Shi, Baochang; Chai, Zhenhua; Wang, Peng

2014-01-01

107

A one dimensional fractional diffusion model with the Riemann-Liouville fractional derivative is studied. First, a second order discretization for this derivative is presented and then an unconditionally stable weighted average finite difference method is derived. The stability of this scheme is established by von Neumann analysis. Some numerical results are shown, which demonstrate the efficiency and convergence of the method. Additionally, some physical properties of this ...

Sousa, Erci?lia; Li, Can

2011-01-01

108

Compatible discrete operator schemes on polyhedral meshes for elliptic and Stokes equations

International Nuclear Information System (INIS)

This thesis presents a new class of spatial discretization schemes on polyhedral meshes, called Compatible Discrete Operator (CDO) schemes and their application to elliptic and Stokes equations In CDO schemes, preserving the structural properties of the continuous equations is the leading principle to design the discrete operators. De Rham maps define the degrees of freedom according to the physical nature of fields to discretize. CDO schemes operate a clear separation between topological relations (balance equations) and constitutive relations (closure laws). Topological relations are related to discrete differential operators, and constitutive relations to discrete Hodge operators. A feature of CDO schemes is the explicit use of a second mesh, called dual mesh, to build the discrete Hodge operator. Two families of CDO schemes are considered: vertex-based schemes where the potential is located at (primal) mesh vertices, and cell-based schemes where the potential is located at dual mesh vertices (dual vertices being in one-to-one correspondence with primal cells). The CDO schemes related to these two families are presented and their convergence is analyzed. A first analysis hinges on an algebraic definition of the discrete Hodge operator and allows one to identify three key properties: symmetry, stability, and P0-consistency. A second analysis hinges on a definition of the discrete Hodge operator using reconstruction operators, and the requirements on these reconstruction operators are identified. In addition, CDO schemes provide a unified vision on a broad class of schemes proposed in the literature (finite element, finite element, mimetic schemes... ). Finally, the reliability and the efficiency of CDO schemes are assessed on various test cases and several polyhedral meshes. (author)

109

Finite difference neuroelectric modeling software.

This paper describes a finite difference neuroelectric modeling software (FNS), written in C and MATLAB, which can be executed as a standalone program or integrated with other packages for electroencephalography (EEG) analysis. The package from the Oxford Center for Functional MRI of the Brain (FMRIB), FMRIB Software Library (FSL), is used to segment the anatomical magnetic resonance (MR) image for realistic head modeling. The EEG electrode array is fitted to the realistic head model using the Bioelectromagnetism MATLAB toolbox. The finite difference formulation for a general inhomogeneous anisotropic body is used to obtain the system matrix equation, which is then solved using the conjugate gradient algorithm. The reciprocity theorem is utilized to limit the number of required forward solutions to N-1, where N is the number of electrodes. Results show that the forward solver only requires 500 MB of random-access memory (RAM) for a realistic 256×256×256 head model and that the software can be conveniently combined with inverse algorithms such as beamformers and MUSIC. The software is freely available under the GNU Public License. PMID:21477619

Dang, Hung V; Ng, Kwong T

2011-06-15

110

An Efficient Elliptic Curve Discrete Logarithm based Trapdoor Hash Scheme without Key Exposure

The trapdoor hash function plays essential role in constructing certain secure digital signature, and signature scheme that composed by trapdoor hash function is widely applied in different fields. However, the key exposure problem of trapdoor hash scheme has brought great distress. In this paper, an efficient trapdoor hash scheme without key exposure based on elliptic curve discrete logarithm is put forward and its security is analyzed, the scheme satisfies the five properties of trapdoor ha...

Yi Sun; Xingyuan Chen; Xuehui Du

2013-01-01

111

A New Signature Scheme Based on Factoring and Discrete Logarithm Problems

Directory of Open Access Journals (Sweden)

Full Text Available In 1994, He and Kiesler proposed a digital signature scheme which was based on the factoring and the discrete logarithm problem both. Same year, Shimin-Wei modi?ed the He-Kiesler signature scheme. In this paper, we propose an improvement of Shimin-Wei signature scheme based on factorization and discrete logarithm problem both with di?erent parameters and using a collision-free one-way hash function. In our opinion, our scheme is more secure than the earlier one.

Swati Verma

2012-07-01

112

Implicit time-dependent finite different algorithm for quench simulation

International Nuclear Information System (INIS)

A magnet in a fusion machine has many difficulties in its application because of requirement of a large operating current, high operating field and high breakdown voltage. A cable-in-conduit (CIC) conductor is the best candidate to overcome these difficulties. However, there remained uncertainty in a quench event in the cable-in-conduit conductor because of a difficulty to analyze a fluid dynamics equation. Several scientists, then, developed the numerical code for the quench simulation. However, most of them were based on an explicit time-dependent finite difference scheme. In this scheme, a discrete time increment is strictly restricted by CFL (Courant-Friedrichs-Lewy) condition. Therefore, long CPU time was consumed for the quench simulation. Authors, then, developed a new quench simulation code, POCHI1, which is based on an implicit time dependent scheme. In POCHI1, the fluid dynamics equation is linearlized according to a procedure applied by Beam and Warming and then, a tridiagonal system can be offered. Therefore, no iteration is necessary to solve the fluid dynamics equation. This leads great reduction of the CPU time. Also, POCHI1 can cope with non-linear boundary condition. In this study, comparison with experimental results was carried out. The normal zone propagation behavior was investigated in two samples of CIC conductors which had different hydraulic diameters. The measured and simulated normal zone propagation length showed relatively good agreement. However, the behavior of the normal voltage shows a little disagreement. These results indicate necessity to improve the treatment of the heat transfer coefficient in the turbulent flow region and the electric resistivity of the copper stabilizer in high temperature and high field region. (author)

113

A coupled discrete unified gas-kinetic scheme for Boussinesq flows

Recently, the discrete unified gas-kinetic scheme (DUGKS) [Z. L. Guo \\emph{et al}., Phys. Rev. E ${\\bf 88}$, 033305 (2013)] based on the Boltzmann equation is developed as a new multiscale kinetic method for isothermal flows. In this paper, a thermal and coupled discrete unified gas-kinetic scheme is derived for the Boussinesq flows, where the velocity and temperature fields are described independently. Kinetic boundary conditions for both velocity and temperature fields are...

Wang, Peng; Tao, Shi; Guo, Zhaoli

2014-01-01

114

Convergence of discrete duality finite volume schemes for the cardiac bidomain model

We prove convergence of discrete duality finite volume (DDFV) schemes on distorted meshes for a class of simplified macroscopic bidomain models of the electrical activity in the heart. Both time-implicit and linearised time-implicit schemes are treated. A short description is given of the 3D DDFV meshes and of some of the associated discrete calculus tools. Several numerical tests are presented.

Andreianov, Boris; Karlsen, Kenneth H; Pierre, Charles

2010-01-01

115

Convergence of discrete duality finite volume schemes for the cardiac bidomain model

We prove convergence of discrete duality finite volume (DDFV) schemes on distorted meshes for a class of simplified macroscopic bidomain models of the electrical activity in the heart. Both time-implicit and linearised time-implicit schemes are treated. A short description is given of the 3D DDFV meshes and of some of the associated discrete calculus tools. Several numerical tests are presented.

Andreianov, Boris; Bendahmane, Mostafa; Karlsen, Kenneth Hvistendahl; Pierre, Charles

2011-01-01

116

This paper is concerned with a few novel RBF-based numerical schemes discretizing partial differential equations. For boundary-type methods, we derive the indirect and direct symmetric boundary knot methods (BKM). The resulting interpolation matrix of both is always symmetric irrespective of boundary geometry and conditions. In particular, the direct BKM applies the practical physical variables rather than expansion coefficients and becomes very competitive to the boundary element method. On the other hand, based on the multiple reciprocity principle, we invent the RBF-based boundary particle method (BPM) for general inhomogeneous problems without a need using inner nodes. The direct and symmetric BPM schemes are also developed. For domain-type RBF discretization schemes, by using the Green integral we develop a new Hermite RBF scheme called as the modified Kansa method (MKM), which differs from the symmetric Hermite RBF scheme in that the MKM discretizes both governing equation and boundary conditions on the...

Chen, W

2001-01-01

117

The theory of viscosity solutions has been effective for representing and approximating weak solutions to fully nonlinear Partial Differential Equations (PDEs) such as the elliptic Monge-Amp\\`ere equation. The approximation theory of Barles-Souganidis [Barles and Souganidis, Asymptotic Anal., 4 (1999) 271-283] requires that numerical schemes be monotone (or elliptic in the sense of [Oberman, SIAM J. Numer. Anal, 44 (2006) 879-895]. But such schemes have limited accuracy. In this article, we establish a convergence result for nearly monotone schemes. This allows us to construct finite difference discretizations of arbitrarily high-order. We demonstrate that the higher accuracy is achieved when solutions are sufficiently smooth. In addition, the filtered scheme provides a natural detection principle for singularities. We employ this framework to construct a formally second-order scheme for the Monge-Amp\\`ere equation and present computational results on smooth and singular solutions.

Froese, Brittany D

2012-01-01

118

Discrete unified gas kinetic scheme with force term for incompressible fluid flows

The discrete unified gas kinetic scheme (DUGKS) is a finite-volume scheme with discretization of particle velocity space, which combines the advantages of both lattice Boltzmann equation (LBE) method and unified gas kinetic scheme (UGKS) method, such as the simplified flux evaluation scheme, flexible mesh adaption and the asymptotic preserving properties. However, DUGKS is proposed for near incompressible fluid flows, the existing compressible effect may cause some serious errors in simulating incompressible problems. To diminish the compressible effect, in this paper a novel DUGKS model with external force is developed for incompressible fluid flows by modifying the approximation of Maxwellian distribution. Meanwhile, due to the pressure boundary scheme, which is wildly used in many applications, has not been constructed for DUGKS, the non-equilibrium extrapolation (NEQ) scheme for both velocity and pressure boundary conditions is introduced. To illustrate the potential of the proposed model, numerical simul...

Wu, Chen; Chai, Zhenhua; Wang, Peng

2014-01-01

119

Directory of Open Access Journals (Sweden)

Full Text Available Problem statement: Here, we develop a discretized scheme using only the penalty method without involving the multiplier parameter to examine the convergence and geometric ratio profiles. Approach: This approach reduces computational time arising from less data manipulation. Objectively, we wish to obtain a numerical solution comparing favourably with the analytic solution.. Methodologically, we discretize the given problem, obtain an unconstrained formulation and construct an operator which sets the stage for the application of the discretized extended conjugate gradient method. Results: We analyse the efficiency of the developed scheme by considering an example and examining the generated sequential approximate solutions and the convergence ratio profile computed quadratically per cycle using the discretized conjugate gradient method. Conclusion/Recommendations: Both results, as shown in the table, look comparably and this suggests that the developed scheme may very well approximate an analytic solution of a given problem to an appreciable level of tolerance without its prior knowledge.

O. Olotu

2011-01-01

120

A free energy satisfying finite difference method for Poisson-Nernst-Planck equations

In this work we design and analyze a free energy satisfying finite difference method for solving Poisson-Nernst-Planck equations in a bounded domain. The algorithm is of second order in space, with numerical solutions satisfying all three desired properties: i) mass conservation, ii) positivity preserving, and iii) free energy satisfying in the sense that these schemes satisfy a discrete free energy dissipation inequality. These ensure that the computed solution is a probability density, and the schemes are energy stable and preserve the equilibrium solutions. Both one- and two-dimensional numerical results are provided to demonstrate the good qualities of the algorithm, as well as effects of relative size of the data given.

Liu, Hailiang; Wang, Zhongming

2014-07-01

121

An energy conserving finite-difference model of Maxwell's equations for soliton propagation

We present an energy conserving leap-frog finite-difference scheme for the nonlinear Maxwell's equations investigated by Hile and Kath [C.V.Hile and W.L.Kath, J.Opt.Soc.Am.B13, 1135 (96)]. The model describes one-dimensional scalar optical soliton propagation in polarization preserving nonlinear dispersive media. The existence of a discrete analog of the underlying continuous energy conservation law plays a central role in the global accuracy of the scheme and a proof of its generalized nonlinear stability using energy methods is given. Numerical simulations of initial fundamental, second and third-order hyperbolic secant soliton pulses of fixed spatial full width at half peak intensity containing as few as 4 and 8 optical carrier wavelengths, confirm the stability, accuracy and efficiency of the algorithm. The effect of a retarded nonlinear response time of the media modeling Raman scattering is under current investigation in this context.

Bachiri, H; Vázquez, L

1997-01-01

122

Original Signer's Forgery Attacks on Discrete Logarithm Based Proxy Signature Schemes

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Full Text Available A proxy signature scheme enables a proxy signer to sign messages on behalf of the original signer. In this paper, we demonstrate that a number of discrete logarithm based proxy signature schemes are vulnerable to an original signer's forgery attack. In this attack, a malicious original signer can impersonate a proxy signer and produce a forged proxy signature on a message. A third party will incorrectly believe that the proxy signer was responsible for generating the proxy signature. This contradicts the strong unforgeability property that is required of proxy signatures schemes. We show six proxy signature schemes vulnerable to this attack including Lu et al.'s proxy blind multi-signature scheme, Xue and Cao's proxy blind signature scheme, Fu et al. and Gu et al.'s anonymous proxy signature schemes, Dai et al. and Huang et al.'s nominative proxy signature schemes are all insecure against the original signer's forgery.

Tianjie Cao

2007-05-01

123

The DFAs of Finitely Different Languages

Two languages are "finitely different" if their symmetric difference is finite. We consider the DFAs of finitely different regular languages and find major structural similarities. We proceed to consider the smallest DFAs that recognize a language finitely different from some given DFA. Such "f-minimal" DFAs are not unique, and this non-uniqueness is characterized. Finally, we offer a solution to the minimization problem of finding such f-minimal DFAs.

Badr, A; Badr, Andrew; Shipman, Ian

2007-01-01

124

Phase-field-based lattice Boltzmann finite-difference model for simulating thermocapillary flows

A phase-field-based hybrid model that combines the lattice Boltzmann method with the finite difference method is proposed for simulating immiscible thermocapillary flows with variable fluid-property ratios. Using a phase field methodology, an interfacial force formula is analytically derived to model the interfacial tension force and the Marangoni stress. We present an improved lattice Boltzmann equation (LBE) method to capture the interface between different phases and solve the pressure and velocity fields, which can recover the correct Cahn-Hilliard equation (CHE) and Navier-Stokes equations. The LBE method allows not only use of variable mobility in the CHE, but also simulation of multiphase flows with high density ratio because a stable discretization scheme is used for calculating the derivative terms in forcing terms. An additional convection-diffusion equation is solved by the finite difference method for spatial discretization and the Runge-Kutta method for time marching to obtain the temperature field, which is coupled to the interfacial tension through an equation of state. The model is first validated against analytical solutions for the thermocapillary driven convection in two superimposed fluids at negligibly small Reynolds and Marangoni numbers. It is then used to simulate thermocapillary migration of a three-dimensional deformable droplet and bubble at various Marangoni numbers and density ratios, and satisfactory agreement is obtained between numerical results and theoretical predictions.

Liu, Haihu; Valocchi, Albert J.; Zhang, Yonghao; Kang, Qinjun

2013-01-01

125

Novel Two-Scale Discretization Schemes for Lagrangian Hydrodynamics

Energy Technology Data Exchange (ETDEWEB)

In this report we propose novel higher order conservative schemes of discontinuous Galerkin (or DG) type for the equations of gas dynamics in Lagrangian coordinates suitable for general unstructured finite element meshes. The novelty of our approach is in the formulation of two-scale non-oscillatory function recovery procedures utilizing integral moments of the quantities of interest (pressure and velocity). The integral moments are computed on a primary mesh (cells or zones) which defines our original scale that governs the accuracy of the schemes. In the non-oscillatory smooth function recovery procedures, we introduce a finer mesh which defines the second scale. Mathematically, the recovery can be formulated as nonlinear energy functional minimization subject to equality and nonlinear inequality constraints. The schemes are highly accurate due to both the embedded (local) mesh refinement features as well as the ability to utilize higher order integral moments. The new DG schemes seem to offer an alternative to currently used artificial viscosity techniques and limiters since the two-scale recovery procedures aim at resolving these issues. We report on some preliminary tests for the lowest order case, and outline some possible future research directions.

Vassilevski, P

2008-05-29

126

An Efficient Elliptic Curve Discrete Logarithm based Trapdoor Hash Scheme without Key Exposure

Directory of Open Access Journals (Sweden)

Full Text Available The trapdoor hash function plays essential role in constructing certain secure digital signature, and signature scheme that composed by trapdoor hash function is widely applied in different fields. However, the key exposure problem of trapdoor hash scheme has brought great distress. In this paper, an efficient trapdoor hash scheme without key exposure based on elliptic curve discrete logarithm is put forward and its security is analyzed, the scheme satisfies the five properties of trapdoor hash functions: effective calculation, trapdoor collision, collision resistance, key exposure resistance and semantic security. Through comparing and analyzing with the existing schemes, it shows that the proposed scheme, which has only multiplicative complexity and removes the operations of computing finite field element inverse, is more advantage in terms of safety and efficiency. Moreover, the scheme supports batch computation that it can greatly improve the efficiency of verification.

Yi Sun

2013-11-01

127

Energy Technology Data Exchange (ETDEWEB)

We present a comprehensive error estimation of four spatial discretization schemes of the two-dimensional Discrete Ordinates (SN) equations on Cartesian grids utilizing a Method of Manufactured Solution (MMS) benchmark suite based on variants of Larsen’s benchmark featuring different orders of smoothness of the underlying exact solution. The considered spatial discretization schemes include the arbitrarily high order transport methods of the nodal (AHOTN) and characteristic (AHOTC) types, the discontinuous Galerkin Finite Element method (DGFEM) and the recently proposed higher order diamond difference method (HODD) of spatial expansion orders 0 through 3. While AHOTN and AHOTC rely on approximate analytical solutions of the transport equation within a mesh cell, DGFEM and HODD utilize a polynomial expansion to mimick the angular flux profile across each mesh cell. Intuitively, due to the higher degree of analyticity, we expect AHOTN and AHOTC to feature superior accuracy compared with DGFEM and HODD, but at the price of potentially longer grind times and numerical instabilities. The latter disadvantages can result from the presence of exponential terms evaluated at the cell optical thickness that arise from the semianalytical solution process. This work quantifies the order of accuracy and the magnitude of the error of all four discretization methods for different optical thicknesses, scattering ratios and degrees of smoothness of the underlying exact solutions in order to verify or contradict the aforementioned intuitive expectation.

Sebastian Schunert; Yousry Y. Azmy; Damien Fournier

2011-05-01

128

Energy Technology Data Exchange (ETDEWEB)

In this work, we develop a new spatial discretization scheme that may be used to numerically solve the neutron transport equation. This new discretization extends the family of corner balance spatial discretizations to include spatial grids of arbitrary polyhedra. This scheme enforces balance on subcell volumes called corners. It produces a lower triangular matrix for sweeping, is algebraically linear, is non-negative in a source-free absorber, and produces a robust and accurate solution in thick diffusive regions. Using an asymptotic analysis, we design the scheme so that in thick diffusive regions it will attain the same solution as an accurate polyhedral diffusion discretization. We then refine the approximations in the scheme to reduce numerical diffusion in vacuums, and we attempt to capture a second order truncation error. After we develop this Upstream Corner Balance Linear (UCBL) discretization we analyze its characteristics in several limits. We complete a full diffusion limit analysis showing that we capture the desired diffusion discretization in optically thick and highly scattering media. We review the upstream and linear properties of our discretization and then demonstrate that our scheme captures strictly non-negative solutions in source-free purely absorbing media. We then demonstrate the minimization of numerical diffusion of a beam and then demonstrate that the scheme is, in general, first order accurate. We also note that for slab-like problems our method actually behaves like a second-order method over a range of cell thicknesses that are of practical interest. We also discuss why our scheme is first order accurate for truly 3D problems and suggest changes in the algorithm that should make it a second-order accurate scheme. Finally, we demonstrate 3D UCBL's performance on several very different test problems. We show good performance in diffusive and streaming problems. We analyze truncation error in a 3D problem and demonstrate robustness in a coarsely discretized problem that contains sharp boundary layers. We also examine eigenvalue and fixed source problems with mixed-shape meshes, anisotropic scattering and multi-group cross sections. Finally, we simulate the MOX fuel assembly in the Advance Test Reactor.

Thompson, K.G.

2000-11-01

129

Discrete unified gas kinetic scheme for all Knudsen number flows: Low-speed isothermal case

Based on the Boltzmann-BGK (Bhatnagar-Gross-Krook) equation, in this paper a discrete unified gas kinetic scheme (DUGKS) is developed for low-speed isothermal flows. The DUGKS is a finite-volume scheme with the discretization of particle velocity space. After the introduction of two auxiliary distribution functions with the inclusion of collision effect, the DUGKS becomes a fully explicit scheme for the update of distribution function. Furthermore, the scheme is an asymptotic preserving method, where the time step is only determined by the Courant-Friedricks-Lewy condition in the continuum limit. Numerical results demonstrate that accurate solutions in both continuum and rarefied flow regimes can be obtained from the current DUGKS. The comparison between the DUGKS and the well-defined lattice Boltzmann equation method (D2Q9) is presented as well.

Guo, Zhaoli; Xu, Kun; Wang, Ruijie

2013-09-01

130

A parallel adaptive finite difference algorithm for petroleum reservoir simulation

Energy Technology Data Exchange (ETDEWEB)

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)

Hoang, Hai Minh

2005-07-01

131

Total internal reflection microscopy: examination of competitive schemes via discrete sources method

International Nuclear Information System (INIS)

The discrete sources method has been applied to perform a computer simulation analysis of different total internal reflection microscopy schemes. It has been found that the positioning of the objective lens beneath a glass prism can provide a considerable advantage for determination of the particle–film distance

132

A unified formalism for spatial discretization schemes of transport equations in slab geometry

International Nuclear Information System (INIS)

It is shown that most of the spatial discretization schemes of transport equations in slab geometry which have been developed recently are particular applications of a general finite element oriented formalism developed by this author and his collaborators for the numerical integration of systems of stiff ordinary differential equations. (author)

133

Weighted Average Finite Difference Methods for Fractional Reaction-Subdiffusion Equation

Directory of Open Access Journals (Sweden)

Full Text Available In this article, a numerical study for fractional reaction-subdiffusion equations is introduced using a class of finite difference methods. These methods are extensions of the weighted average methods for ordinary (non-fractional reaction-subdiffusion equations. A stability analysis of the proposed methods is given by a recently proposed procedure similar to the standard John von Neumann stability analysis. Simple and accurate stability criterion valid for different discretization schemes of the fractional derivative, arbitrary weight factor, and arbitrary order of the fractional derivative, are given and checked numerically. Numerical test examples, figures, and comparisons have been presented for clarity.doi:10.14456/WJST.2014.50

Nasser Hassen SWEILAM

2014-04-01

134

Finite-difference seismic wave modeling including surface topography

I present synthetics of seismic wave propagation near free surface topography. The velocity-stress formulations of both the full elastic and viscoelastic wave equations are used, and I have derived exact boundary conditions for any arbitrary, smooth topography in terms of the particle velocities. Program codes are developed for 2 and 3 dimensions (2-D and 3-D) using finite-difference (F-D) methods for both spatial and temporal numerical discretizations. An 8th order F-D method is used inside the physical model space, and the spatial F-D order decreases gradually towards the free surface topography. The discretization of the medium equations along the side and bottom boundaries, the free surface topography boundary conditions, and the forward time stepping, are all by 2nd order F-D methods. The leap-frog technique is used for time stepping everywhere except for the memory variable equations in the viscoelastic cases, where an explicit version of the unconditionally stable Crank-Nicholson method is used. I show synthetics applying the schemes to isotropic 2-D and 3-D media covered by topographies that are either described by analytic expressions or by real elevation data. These data are taken from an area in South-Eastern Norway that contains the NORESS seismic receiver array. Domains up to 60 x 60 kilometers are used in 3-D simulations, and the applied sources are plane waves generated by a plane of Ricker type point sources. These sources represent earthquakes or teleseismic explosions. For 2-D simulations I have used both plane waves and point sources, since the larger models permissible in 2-D allow for point sources to represent earthquakes or teleseismic explosions quite well. For 2-D simulations I have also included examples using layered media with randomization by a 2-D von Karman function with and without apparent anisotropy. Synthetic snapshots and seismograms show Rayleigh (Rg)-waves emanating from areas of prominent topography as well as strong surface wave directivity from some topographic features. Full viscoelastic modeling with relatively low Q-values, describing near-surface sedimentary layers, exhibit intrinsic attenuation and physical dispersion of the wavefield. Results coincide with numerous observations. 3-D simulations are performed using domain decomposition parallelization implemented by Message Passing Interface (MPI).

Hestholm, Stig Ottar

135

A Finite Difference-Based Modeling Approach for Prediction of Steel Hardenability

In this research work an independent finite difference-based modeling approach was adopted for determination of the hardenability of steels. In this model, at first, cooling curves were generated by solving transient heat transfer equation through discretization with pure explicit finite difference scheme coupled with MATLAB-based programing in view of variable thermo-physical properties of 1080 steel. The cooling curves were solved against 50% transformation nose of TTT diagram in order to predict hardening behavior of 1080 steel in terms of hardenability parameters (Grossmann critical diameter, D C; and ideal critical diameter, D I) and the variation of the unhardened core diameter ( D u) to diameter of steel bar ( D) ratio with diameter of steel bar ( D). The experiments were also performed to determine actual D C value of 1080 steel for still water quenching. The D C value obtained by the developed model was found to match the experimental D C value with only 6% deviation. Therefore, the model developed in the present work can be used for direct determination of D I, D C, and D u without resorting to any rigorous experimentation.

Sushanthi, Neethi; Maity, Joydeep

2014-06-01

136

International Nuclear Information System (INIS)

We present the sublattice approach, a procedure to generate, from a given integrable lattice, a sublattice which inherits its integrability features. We consider, as illustrative example of this approach, the discrete Moutard 4-point equation and its sublattice, the self-adjoint 5-point scheme on the star of the square lattice, which are relevant in the theory of the integrable discrete geometries and in the theory of discrete holomorphic and harmonic functions (in this last context, the discrete Moutard equation is called discrete Cauchy-Riemann equation). Therefore an integrable, at one energy, discretization of elliptic two-dimensional operators is considered. We use the sublattice point of view to derive, from the Darboux transformations and superposition formulas of the discrete Moutard equation, the Darboux transformations and superposition formulas of the self-adjoint 5-point scheme. We also construct, from algebro-geometric solutions of the discrete Moutard equation, algebro-geometric solutions of the self-adjoint 5-point scheme. In particular, we show that the corresponding restrictions on the finite-gap data are of the same type as those for the fixed energy problem for the two-dimensional Schroedinger operator. We finally use these solutions to construct explicit examples of discrete holomorphic and harmonic functions, as well as examples of quadrilateral surfaces in R3

137

High Order Finite Difference Methods in Space and Time

In this thesis, high order accurate discretization schemes for partial differential equations are investigated. In the first paper, the linearized two-dimensional Navier-Stokes equations are considered. A special formulation of the boundary conditions is used and estimates for the solution to the continuous problem in terms of the boundary conditions are derived using a normal mode analysis. Similar estimates are achieved for the discretized equations. For the discretization, a second order f...

Kress, Wendy

2003-01-01

138

Error Estimate for a Fully Discrete Spectral Scheme for Korteweg-de Vries-Kawahara Equation

We are concerned with the convergence of spectral method for the numerical solution of the initial-boundary value problem associated to the Korteweg-de Vries-Kawahara equation (in short Kawahara equation), which is a transport equation perturbed by dispersive terms of 3rd and 5th order. This equation appears in several fluid dynamics problems. It describes the evolution of small but finite amplitude long waves in various problems in fluid dynamics. These equations are discretized in space by the standard Fourier- Galerkin spectral method and in time by the explicit leap-frog scheme. For the resulting fully discrete, conditionally stable scheme we prove an L2-error bound of spectral accuracy in space and of second-order accuracy in time.

Koley, U

2011-01-01

139

Finite Difference Migration Imaging of Magnetotellurics

Directory of Open Access Journals (Sweden)

Full Text Available we put forward a new migration imaging technique of Magnetotellurics (MT data based on improved finite difference method, which increased the accuracy of difference equation and imaging resolution greatly. We also discussed the determination of background resistivity and reimaging. The processing results of theoretical model and case study indicated that this method was a more practical and effective for MT imaging. Finally the characteristics of finite difference migration imaging were summarized and the factors which can affect the migration imaging were analyzed.

Runlin Du

2013-10-01

140

A coupled discrete unified gas-kinetic scheme for Boussinesq flows

Recently, the discrete unified gas-kinetic scheme (DUGKS) [Z. L. Guo \\emph{et al}., Phys. Rev. E ${\\bf 88}$, 033305 (2013)] based on the Boltzmann equation is developed as a new multiscale kinetic method for isothermal flows. In this paper, a thermal and coupled discrete unified gas-kinetic scheme is derived for the Boussinesq flows, where the velocity and temperature fields are described independently. Kinetic boundary conditions for both velocity and temperature fields are also proposed. The proposed model is validated by simulating several canonical test cases, including the porous plate problem, the Rayleigh-b\\'{e}nard convection, and the natural convection with Rayleigh number up to $10^{10}$ in a square cavity. The results show that the coupled DUGKS is of second order accuracy in space and can well describe the convection phenomena from laminar to turbulent flows. Particularly, it is found that this new scheme has better numerical stability in simulating high Rayleigh number flows compared with the pre...

Wang, Peng; Guo, Zhaoli

2014-01-01

141

A scheme for rapidly and accurately computing solutions to boundary integral equations (BIEs) on rotationally symmetric surfaces in R^3 is presented. The scheme uses the Fourier transform to reduce the original BIE defined on a surface to a sequence of BIEs defined on a generating curve for the surface. It can handle loads that are not necessarily rotationally symmetric. Nystrom discretization is used to discretize the BIEs on the generating curve. The quadrature is a high-order Gaussian rule that is modified near the diagonal to retain high-order accuracy for singular kernels. The reduction in dimensionality, along with the use of high-order accurate quadratures, leads to small linear systems that can be inverted directly via, e.g., Gaussian elimination. This makes the scheme particularly fast in environments involving multiple right hand sides. It is demonstrated that for BIEs associated with the Laplace and Helmholtz equations, the kernel in the reduced equations can be evaluated very rapidly by exploiting...

Young, P; Martinsson, P G

2012-01-01

142

Finite-difference migration to zero offset

Energy Technology Data Exchange (ETDEWEB)

Migration to zero offset (MZO), also called dip moveout (DMO) or prestack partial migration, transforms prestack offset seismic data into approximate zero-offset data so as to remove reflection point smear and obtain quality stacked results over a range of reflector dips. MZO has become an important step in standard seismic data processing, and a variety of frequency-wavenumber (f-k) and integral MZO algorithms have been used in practice to date. Here, I present a finite-difference MZO algorithm applied to normal-moveout (NMO)-corrected, common-offset sections. This algorithm employs a traditional poststack 15-degree finite-difference migration algorithm and a special velocity function rather than the true migration velocity. This paper shows results of implementation of this MZO algorithm when velocity varies with depth, and discusses the possibility of applying this algorithm to cases where velocity varies with both depth and horizontal distance.

Li, Jianchao.

1992-01-01

143

Finite-difference migration to zero offset

Energy Technology Data Exchange (ETDEWEB)

Migration to zero offset (MZO), also called dip moveout (DMO) or prestack partial migration, transforms prestack offset seismic data into approximate zero-offset data so as to remove reflection point smear and obtain quality stacked results over a range of reflector dips. MZO has become an important step in standard seismic data processing, and a variety of frequency-wavenumber (f-k) and integral MZO algorithms have been used in practice to date. Here, I present a finite-difference MZO algorithm applied to normal-moveout (NMO)-corrected, common-offset sections. This algorithm employs a traditional poststack 15-degree finite-difference migration algorithm and a special velocity function rather than the true migration velocity. This paper shows results of implementation of this MZO algorithm when velocity varies with depth, and discusses the possibility of applying this algorithm to cases where velocity varies with both depth and horizontal distance.

Li, Jianchao

1992-07-01

144

Polarizable continuum models (PCMs) are a widely used family of implicit solvent models based on reaction-field theory and boundary-element discretization of the solute/continuum interface. An often overlooked aspect of these theories is that discretization of the interface typically does not afford a continuous potential energy surface for the solute. In addition, we show that discretization can lead to numerical singularities and violations of exact variational conditions. To fix these problems, we introduce the switching/Gaussian (SWIG) method, a discretization scheme that overcomes several longstanding problems with PCMs. Our approach generalizes a procedure introduced by York and Karplus [J. Phys. Chem. A 103, 11060 (1999)], extending it beyond the conductor-like screening model. Comparison to other purportedly smooth PCM implementations reveals certain artifacts in these alternative approaches, which are avoided using the SWIG methodology. The versatility of our approach is demonstrated via geometry optimizations, vibrational frequency calculations, and molecular dynamics simulations, for solutes described using quantum mechanics and molecular mechanics.

Lange, Adrian W.; Herbert, John M.

2010-12-01

145

Elementary introduction to finite difference equations

International Nuclear Information System (INIS)

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

146

A spherical higher-order finite-difference time-domain algorithm with perfectly matched layer

A higher-order finite-difference time-domain (HO-FDTD) in the spherical coordinate is presented in this paper. The stability and dispersion properties of the proposed scheme are investigated and an air-filled spherical resonator is modeled in order to demonstrate the advantage of this scheme over the finite-difference time-domain (FDTD) and the multiresolution time-domain (MRTD) schemes with respect to memory requirements and CPU time. Moreover, the Berenger's perfectly matched layer (PML) is derived for the spherical HO-FDTD grids, and the numerical results validate the efficiency of the PML.

Liu, Ya-Wen; Chen, Yi-Wang; Zhang, Pin; Liu, Zong-Xin

2014-12-01

147

The numerical solution of problems in calculus of variation using Chebyshev finite difference method

International Nuclear Information System (INIS)

The Chebyshev finite difference method is used for finding the solution of the ordinary differential equations which arise from problems of calculus of variations. Our approach consists of reducing the problem to a set of algebraic equations. This method can be regarded as a non-uniform finite difference scheme. Some numerical results are also given to demonstrate the validity and applicability of the presented technique. The method is easy to implement and yields very accurate results

148

Finite difference approximations for a fractional diffusion/anti-diffusion equation

A class of finite difference schemes for solving a fractional anti-diffusive equation, recently proposed by Andrew C. Fowler to describe the dynamics of dunes, is considered. Their linear stability is analyzed using the standard Von Neumann analysis: stability criteria are found and checked numerically. Moreover, we investigate the consistency and convergence of these schemes.

Azerad, Pascal

2011-01-01

149

Let $p$ be a prime. Let $V$ be a discrete valuation ring of mixed characteristic $(0,p)$ and index of ramification $e$. Let $f: G \\rightarrow H$ be a homomorphism of finite flat commutative group schemes of $p$ power order over $V$ whose generic fiber is an isomorphism. We provide a new proof of a result of Bondarko and Liu that bounds the kernel and the cokernel of the special fiber of $f$ in terms of $e$. For $e < p-1$ this reproves a result of Raynaud. Our bounds are shar...

Vasiu, Adrian; Zink, Thomas

2009-01-01

150

The dimensionally split reconstruction method as described by Kurganov et al.\\cite{kurganov-2000} is revisited for better understanding and a simple fourth order scheme is introduced to solve 3D hyperbolic conservation laws following dimension by dimension approach. Fourth order central weighted essentially non-oscillatory (CWENO) reconstruction methods have already been proposed to study multidimensional problems \\cite{lpr4,cs12}. In this paper, it is demonstrated that a simple 1D fourth order CWENO reconstruction method by Levy et al.\\cite{lpr7} provides fourth order accuracy for 3D hyperbolic nonlinear problems when combined with the semi-discrete scheme by Kurganov et al.\\cite{kurganov-2000} and fourth order Runge-Kutta method for time integration.

Verma, Prabal Singh

2015-01-01

151

International Nuclear Information System (INIS)

A domain decomposition scheme for the analytical reconstruction of the dominant solution of one-speed slab-geometry discrete ordinates (SN) eigenvalue problems is described. This reconstruction scheme uses the dominant numerical solution generated by the hybrid Spectral Diamond-Spectral Green's Function (SD-SGF) nodal method for SN eigenvalue problems and a basis for the Kernel of the local one-speed slab-geometry discrete ordinates operator. In order to illustrate the positive features of this domain decomposition scheme, numerical results for a typical one-speed slab-geometry model problem are presented

152

TUNED FINITE-DIFFERENCE DIFFUSION OPERATORS

International Nuclear Information System (INIS)

Finite-difference simulations of fluid dynamics and magnetohydrodynamics generally require an explicit diffusion operator, either to maintain stability by attenuating grid-scale structure, or to implement physical diffusivities such as viscosity or resistivity. If the goal is stability only, the diffusion must act at the grid scale, but should affect structure at larger scales as little as possible. For physical diffusivities the diffusion scale depends on the problem, and diffusion may act at larger scales as well. Diffusivity can undesirably limit the computational time step in both cases. We construct tuned finite-difference diffusion operators that minimally limit the time step while acting as desired near the diffusion scale. Such operators reach peak values at the diffusion scale rather than at the grid scale, but behave as standard operators at larger scales. These operators will be useful for simulations with high magnetic diffusivity or kinematic viscosity such as in the simulation of astrophysical dynamos with magnetic Prandtl number far from unity, or for numerical stabilization using hyperdiffusivity.

153

Practical approach to finite-difference resistivity modeling

Energy Technology Data Exchange (ETDEWEB)

Highly efficient finite-difference resistivity modeling algorithms that yield accurate results are put forward. The given medium is discretized and divided into rectangular blocks by using a very coarse system of vertical and horizontal grid lines, whose distance from the source(s) increases logarithmically. Expressions are derived to compute the longitudinal conductance and transverse resistance associated with each of these blocks for a parallel-layer medium followed by a generalized treatment to accommodate arbitrarily shaped structures. Since the values of Dar Zarrouk parameters are derived from the exact resistivity distribution of the given medium, fine features such as a thin but anomalously resistive bed that ordinarily would be missed entirely in coarse discretization can be taken into account. Further reduction in the size of the model is achieved by making use of a symmetry wherever possible. In most cases the computation of the potential field that involves the inversion of a small sparse matrix requires about 0.5 s of computer time. Moreover, changes in geology affect neither the size nor the zero structure of the matrix. Therefore, when more than one model is to be computed, the factorization of the matrix can be done symbolically only once for all models, followed by numeric factorization for each individual model. The coarse grid algorithm was applied to a number of horizontally layered models involving a point source. The results obtained for each model were in excellent agreement with the corresponding analytical data. Finite-difference investigation of the potential field for two-dimensional structures and a line source dipole indicates that as long as one is interested only in the evaluation of the Schlumberger-type apparent resistivity curves, the line-source results may be a much better approximation to the corresponding point-source data than is commonly believed. 7 figures. 2 tables.

Mufti, I.R.

1978-08-01

154

Discrete unified gas kinetic scheme for all Knudsen number flows: II. Compressible case

This paper is a continuation of our earlier work [Z.L. Guo {\\it et al.}, Phys. Rev. E {\\bf 88}, 033305 (2013)] where a multiscale numerical scheme based on kinetic model was developed for low speed isothermal flows with arbitrary Knudsen numbers. In this work, a discrete unified gas-kinetic scheme (DUGKS) for compressible flows with the consideration of heat transfer and shock discontinuity is developed based on the Shakhov model with an adjustable Prandtl number. The method is an explicit finite-volume scheme where the transport and collision processes are coupled in the evaluation of the fluxes at cell interfaces, so that the nice asymptotic preserving (AP) property is retained, such that the time step is limited only by the CFL number, the distribution function at cell interface recovers to the Chapman-Enskog one in the continuum limit while reduces to that of free-transport for free-molecular flow, and the time and spatial accuracy is of second-order accuracy in smooth region. These features make the DUGK...

Guo, Zhaoli; Xu, Kun

2014-01-01

155

For radiative transfer in complex geometries, Sakami and his co-workers have developed a discrete ordinates method (DOM) exponential scheme for unstructured meshes which was mainly applied to gray media. The present study investigates the application of the unstructured exponential scheme to a wider range of non-gray scenarios found in fire and combustion applications, with the goal to implement it in an in-house Computational Fluid Dynamics (CFD) code for fire simulations. The original unstructured gray exponential scheme is adapted to non-gray applications by employing a statistical narrow-band/correlated-k (SNB-CK) gas model and meshes generated using the authors' own mesh generator. Different non-gray scenarios involving spectral gas absorption by H2O and CO2 are investigated and a comparative analysis is carried out between heat flux and radiative source terms predicted and literature data based on ray-tracing and Monte Carlo methods. The maximum discrepancies for total radiative heat flux do not typically exceed 5%.

Dembele, S.; Lima, K. L. M.; Wen, J. X.

2011-11-01

156

Comparative study of numerical schemes of TVD3, UNO3-ACM and optimized compact scheme

Three different schemes are employed to solve the benchmark problem. The first one is a conventional TVD-MUSCL (Monotone Upwind Schemes for Conservation Laws) scheme. The second scheme is a UNO3-ACM (Uniformly Non-Oscillatory Artificial Compression Method) scheme. The third scheme is an optimized compact finite difference scheme modified by us: the 4th order Runge Kutta time stepping, the 4th order pentadiagonal compact spatial discretization with the maximum resolution characteristics. The problems of category 1 are solved by using the second (UNO3-ACM) and third (Optimized Compact) schemes. The problems of category 2 are solved by using the first (TVD3) and second (UNO3-ACM) schemes. The problem of category 5 is solved by using the first (TVD3) scheme. It can be concluded from the present calculations that the Optimized Compact scheme and the UN03-ACM show good resolutions for category 1 and category 2 respectively.

Lee, Duck-Joo; Hwang, Chang-Jeon; Ko, Duck-Kon; Kim, Jae-Wook

1995-05-01

157

Digital Waveguides versus Finite Difference Structures: Equivalence and Mixed Modeling

Directory of Open Access Journals (Sweden)

Full Text Available Digital waveguides and finite difference time domain schemes have been used in physical modeling of spatially distributed systems. Both of them are known to provide exact modeling of ideal one-dimensional (1D band-limited wave propagation, and both of them can be composed to approximate two-dimensional (2D and three-dimensional (3D mesh structures. Their equal capabilities in physical modeling have been shown for special cases and have been assumed to cover generalized cases as well. The ability to form mixed models by joining substructures of both classes through converter elements has been proposed recently. In this paper, we formulate a general digital signal processing (DSP-oriented framework where the functional equivalence of these two approaches is systematically elaborated and the conditions of building mixed models are studied. An example of mixed modeling of a 2D waveguide is presented.

Matti Karjalainen

2004-06-01

158

A Novel Robust Zero-Watermarking Scheme Based on Discrete Wavelet Transform

Directory of Open Access Journals (Sweden)

Full Text Available In traditional watermarking algorithms, the insertion of watermark into the original signal inevitably introduces some perceptible quality degradation. Another problem is the inherent conflict between imperceptibility and robustness. Zero-watermarking technique can solve these problems successfully. But most existing zero-watermarking algorithm for audio and image cannot resist against some signal processing manipulations or malicious attacks. In the paper, a novel audio zero-watermarking scheme based on discrete wavelet transform (DWT is proposed, which is more efficient and robust. The experiments show that the algorithm is robust against the common audio signal processing operations such as MP3 compression, re-quantization, re-sampling, low-pass filtering, cutting-replacement, additive white Gaussian noise and so on. These results demonstrate that the proposed watermarking method can be a suitable candidate for audio copyright protection.

Yu Yang

2012-08-01

159

Let p be a prime. Let V be a discrete valuation ring of mixed characteristic (0,p) and index of ramification e. Let f: G \\to H be a homomorphism of finite flat commutative group schemes of p power order over V whose generic fiber is an isomorphism. We bound the kernel and the cokernel of the special fiber of f in terms of e. For e < p-1 this reproves a result of Raynaud. As an application we obtain an extension theorem for homomorphisms of truncated Barsotti--Tate groups which strengthens Tate's extension theorem for homomorphisms of p-divisible groups. In particular, our method provides short new proofs of the theorems of Tate and Raynaud.

Vasiu, Adrian

2009-01-01

160

A finite-difference method is used to prove the completeness of the eigenfunctions of the Sturm-Liouville operator in conservative form. The finite-difference schemes corresponding to the conservative Sturm-Liouville equation with various boundary conditions are shown to be self-adjoint. The accuracy and convergence of the method are analyzed, and the properties of eigenvalues and eigenvectors of the difference scheme approximating the differential equation and the boundary conditions are examined.

Aliev, A. R.; Eyvazov, E. H.

2015-01-01

161

Finite Difference Method of the Study on Radioactivities DispersionModeling in Environment of Ground

International Nuclear Information System (INIS)

It has been resulted the mathematics equation as model of constructingthe computer algorithm deriving from the transport equation having been theform of radionuclides dispersion in the environment of ground as a result ofdiffusion and advection process. The derivation of mathematics equation usedthe finite difference method into three schemes, the explicit scheme,implicit scheme and Crank-Nicholson scheme. The computer algorithm then wouldbe used as the basic of making the software in case of making a monitoringsystem of automatic radionuclides dispersion on the area around the nuclearfacilities. By having the three schemes, so it would be, in choosing thesoftware system, able to choose the more approximate with the fact. (author)

162

The discrete variational derivative method based on discrete differential forms

As is well known, for PDEs that enjoy a conservation or dissipation property, numerical schemes that inherit this property are often advantageous in that the schemes are fairly stable and give qualitatively better numerical solutions in practice. Lately, Furihata and Matsuo have developed the so-called “discrete variational derivative method” that automatically constructs energy preserving or dissipative finite difference schemes. Although this method was originally developed on uniform meshes, the use of non-uniform meshes is of importance for multi-dimensional problems. On the other hand, the theories of discrete differential forms have received much attention recently. These theories provide a discrete analogue of the vector calculus on general meshes. In this paper, we show that the discrete variational derivative method and the discrete differential forms by Bochev and Hyman can be combined. Applications to the Cahn-Hilliard equation and the Klein-Gordon equation on triangular meshes are provided as demonstrations. We also show that the schemes for these equations are H1-stable under some assumptions. In particular, one for the nonlinear Klein-Gordon equation is obtained by combination of the energy conservation property and the discrete Poincaré inequality, which are the temporal and spacial structures that are preserved by the above methods.

Yaguchi, Takaharu; Matsuo, Takayasu; Sugihara, Masaaki

2012-05-01

163

Calculating photonic Green's functions using a non-orthogonal finite difference time domain method

In this paper we shall propose a simple scheme for calculating Green's functions for photons propagating in complex structured dielectrics or other photonic systems. The method is based on an extension of the finite difference time domain (FDTD) method, originally proposed by Yee, also known as the Order-N method, which has recently become a popular way of calculating photonic band structures. We give a new, transparent derivation of the Order-N method which, in turn, enables us to give a simple yet rigorous derivation of the criterion for numerical stability as well as statements of charge and energy conservation which are exact even on the discrete lattice. We implement this using a general, non-orthogonal co-ordinate system without incurring the computational overheads normally associated with non-orthogonal FDTD. We present results for local densities of states calculated using this method for a number of systems. Firstly, we consider a simple one dimensional dielectric multilayer, identifying the suppres...

Ward, A J

1998-01-01

164

Finite difference analysis of the transient temperature profile within GHARR-1 fuel element

International Nuclear Information System (INIS)

Highlights: • Transient heat conduction for GHARR-1 fuel was developed and simulated by MATLAB. • The temperature profile after shutdown showed parabolic decay pattern. • The recorded temperature of about 411.6 K was below the melting point of the clad. • The fuel is stable and no radioactivity will be released into the coolant. - Abstract: Mathematical model of the transient heat distribution within Ghana Research Reactor-1 (GHARR-1) fuel element and related shutdown heat generation rates have been developed. The shutdown heats considered were residual fission and fission product decay heat. A finite difference scheme for the discretization by implicit method was used. Solution algorithms were developed and MATLAB program implemented to determine the temperature distributions within the fuel element after shutdown due to reactivity insertion accident. The simulations showed a steady state temperature of about 341.3 K which deviated from that reported in the GHARR-1 safety analysis report by 2% error margin. The average temperature obtained under transient condition was found to be approximately 444 K which was lower than the melting point of 913 K for the aluminium cladding. Thus, the GHARR-1 fuel element was stable and there would be no release of radioactivity in the coolant during accident conditions

165

An Efficient Discretization Scheme to Solve the Spatially Inhomogeneous Electron Boltzmann Equation

The steady-state radially inhomogeneous electron Boltzmann equation (EBE) is solved for a cylindrical dc positive column in He, at intermediate pressures. The EBE is written using the classical two-term approximation in (r,u) phase space, where r is the radial position and u the electron kinetic energy. The numerical treatment of the space boundary conditions was improved(L.L. Alves, G. Gousset and C.M. Ferreira, J. Phys. IV 7), 143 (1997) in order to satisfy the electron continuity equation in the vicinity of the discharge boundaries. This correction can change the eigenvalue solution NR by about 50%. The EBE is discretized in energy following Rockwood(S.D. Rockwood, Phys. Rev. A 8), 2348 (1973), and in space by adopting an exponential scheme(D.L. Scharfetter, H.K. Gummel, IEEE Trans. ED-16), 64 (1969)^,(J.S. Chang and G. Cooper, J. Comp. Phys. 6), 1 (1970). The latter scheme is especially well suited to support large space-charge field gradients at the discharge wall, which permits to obtain a self-consistent solution, by coupling the EBE with the ion transport equations and Poisson's equation.

Punset, C.; Alves, L. L.; Gousset, G.; Ferreira, C. M.

1999-10-01

166

TWO STAGE DISCRETE TIME EXTENDED KALMAN FILTER SCHEME FOR MICRO AIR VEHICLE

Directory of Open Access Journals (Sweden)

Full Text Available Navigation of Micro Air Vehicle (MAV is one of the most challenging areas of twenty first century’s research. Micro Air Vehicle (MAV is the miniaturized configuration of aircraft with a size of six inches in length and below the weight of hundred grams, which includes twenty grams of payload as well. Due to its small size, MAV is highly affected by the wind gust and therefore the navigation of Micro Air Vehicle (MAV is very important because precise navigation is a very basic step for the control of the Micro Air Vehicle (MAV. This paper presents two stage cascaded discrete time Extended Kalman Filter while using INS/GPS based navigation. First stage of this scheme estimates the Euler angles of Micro Air Vehicle (MAV whereas the second stage of this scheme estimates the position of Micro Air Vehicle (MAV in terms of height, longitude and latitude. As the system is considered as non-linear, so Extended Kalman Filter is used. On-board sensors in first stage included MEMS Gyro, MEMS Accelerometer, MEMS Magnetometer whereas second stage includes GPS.

Ali Usman

2012-03-01

167

The reliability of finite difference and particle methods for fragmentation problems

International Nuclear Information System (INIS)

The authors reply to criticisms made by Boss and Bodenheimer of the use of their particle method for fragmentation problems. A new calculation with their particle scheme is discussed, which indicates that, in the event of drastic angular momentum loss, the particle method results resemble more closely those from the finite difference calculations. (U.K.)

168

Finite-difference field calculations for two-dimensionally confined x-ray waveguides

International Nuclear Information System (INIS)

A numerical method for calculation of the electromagnetic field in two-dimensionally confined x-ray waveguides is presented. It is based on the parabolic wave equation, which is solved by means of a finite-difference scheme. The results are verified by a comparison to analytical theory, namely,Fresnel reflectivity and the weakly guiding optical fiber

169

ON FINITE DIFFERENCES ON A STRING PROBLEM

Directory of Open Access Journals (Sweden)

Full Text Available This study presents an analysis of a one-Dimensional (1D time dependent wave equation from a vibrating guitar string. We consider the transverse displacement of a plucked guitar string and the subsequent vibration motion. Guitars are known for production of great sound in form of music. An ordinary string stretched between two points and then plucked does not produce quality sound like a guitar string. A guitar string produces loud and unique sound which can be organized by the player to produce music. Where is the origin of guitar sound? Can the contribution of each part of the guitar to quality sound be accounted for, by mathematically obtaining the numerical solution to wave equation describing the vibration of the guitar string? In the present sturdy, we have solved the wave equation for a vibrating string using the finite different method and analyzed the wave forms for different values of the string variables. The results show that the amplitude (pitch or quality of the guitar wave (sound vary greatly with tension in the string, length of the string, linear density of the string and also on the material of the sound board. The approximate solution is representative; if the step width; ?x and ?t are small, that is <0.5.

J. M. Mango

2014-01-01

170

Energy Technology Data Exchange (ETDEWEB)

The problem of radiation heat transfer coupled with other modes of heat transfer is important in many engineering applications. Some examples are the heat transfer in glass fabrication and in thermal isolation materials. The angular and spatial discretization of the radiative transport equation in the discrete ordinates method (DOM) plays an important role to obtain accurate numerical results. Two high order spatial discretization schemes are used and compared. One spatial discretization scheme is unidirectional and the other is multidimensional interpolating scheme. Different angular quadratures are selected and tested to obtain accurate results with less computational time. The radiative heat transport equation is solved using the conventional procedure of solution for DOM and the algorithm is validated by comparison with literature exact solutions for different two-dimensional cases. The radiative source term in the energy equation is computed from intensities field. The radiative conductive model is validated by comparison with test cases solutions from the literature. Non-uniform grids are implemented for multidimensional spatial scheme and the results are compared with the result of uniform grid showing agreement. Also, the non-uniform grids are tested in cases of high temperature gradients. To accelerate convergence an adequate relaxation factors in radiative heat transport equation and in energy equation are used. The method can be used to handle cases with reflecting boundaries. (author)

Ismail, Kamal A.R.; Salinas, Carlos T.S. [Department of Thermal and Fluids Engineering, Faculty of Mechanical Engineering, PO Box 6122, State University of Campinas, 13083-970 Campinas SP (Brazil)

2006-07-15

171

We present an abstract framework for analyzing the weak error of fully discrete approximation schemes for linear evolution equations driven by additive Gaussian noise. First, an abstract representation formula is derived for sufficiently smooth test functions. The formula is then applied to the wave equation, where the spatial approximation is done via the standard continuous finite element method and the time discretization via an I-stable rational approximation to the exponential function. It is found that the rate of weak convergence is twice that of strong convergence. Furthermore, in contrast to the parabolic case, higher order schemes in time, such as the Crank-Nicolson scheme, are worthwhile to use if the solution is not very regular. Finally we apply the theory to parabolic equations and detail a weak error estimate for the linearized Cahn-Hilliard-Cook equation as well as comment on the stochastic heat equation.

Kovács, M; Lindgren, F

2012-01-01

172

Stochastic finite-difference time-domain

This dissertation presents the derivation of an approximate method to determine the mean and the variance of electro-magnetic fields in the body using the Finite-Difference Time-Domain (FDTD) method. Unlike Monte Carlo analysis, which requires repeated FDTD simulations, this method directly computes the variance of the fields at every point in space at every sample of time in the simulation. This Stochastic FDTD simulation (S-FDTD) has at its root a new wave called the Variance wave, which is computed in the time domain along with the mean properties of the model space in the FDTD simulation. The Variance wave depends on the electro-magnetic fields, the reflections and transmission though the different dielectrics, and the variances of the electrical properties of the surrounding materials. Like the electro-magnetic fields, the Variance wave begins at zero (there is no variance before the source is turned on) and is computed in the time domain until all fields reach steady state. This process is performed in a fraction of the time of a Monte Carlo simulation and yields the first two statistical parameters (mean and variance). The mean of the field is computed using the traditional FDTD equations. Variance is computed by approximating the correlation coefficients between the constituitive properties and the use of the S-FDTD equations. The impetus for this work was the simulation time it takes to perform 3D Specific Absorption Rate (SAR) FDTD analysis of the human head model for cell phone power absorption in the human head due to the proximity of a cell phone being used. In many instances, Monte Carlo analysis is not performed due to the lengthy simulation times required. With the development of S-FDTD, these statistical analyses could be performed providing valuable statistical information with this information being provided in a small fraction of the time it would take to perform a Monte Carlo analysis.

Smith, Steven Michael

2011-12-01

173

Skew-symmetric convection form and secondary conservative finite difference methods for moving grids

The secondary conservative finite difference method for the convective term is recognized as a useful tool for unsteady flow simulations. However, the secondary conservative convection scheme and associated skew-symmetric form have not been extended to those for moving grids. In this study, the skew-symmetric form and the secondary conservative convection schemes for ALE type moving grid simulations are proposed. For the moving grid simulations, the geometric conservation law (GCL) for metrics and the Jacobian is known as a mathematical constraint for capturing a uniform flow. A new role of the GCL is revealed in association with the commutability and conservation properties of the convection schemes. The secondary conservative convection schemes for moving grids are then constructed for compressible and incompressible flows, respectively. For compressible flows, it is necessary to introduce a shock capturing method to resolve discontinuities. However, the shock capturing methods do not work well for turbulent flow simulations because of their excessive numerical dissipation. On the other hand, the secondary conservative finite difference method does not work well for flows with discontinuities. In this study, we also present a computational technique that combines the shock capturing and the secondary conservative finite difference methods. In order to check the commutability and conservation properties of the convection schemes, numerical tests are done for compressible and incompressible inviscid periodic flows on moving grids. Then, the reliabilities of the schemes are demonstrated on the piston problem, the flow around pitching airfoil, and the flow around an oscillating square cylinder.

Morinishi, Yohei; Koga, Kazuki

2014-01-01

174

International Nuclear Information System (INIS)

High order resolution schemes based on the NVD and TVD boundedness criteria are applied to radiative transfer problems using the DOM in two-dimensional unstructured triangular grids. The implementation of these schemes in unstructured grids requires approximations, and two implementations reported in the literature are compared with a new one. Three different methods have been used to calculate the gradient of the radiation intensity at the center of the control volumes. The various schemes are applied to several test problems, the results are compared with those obtained using the step scheme, the mean flux interpolation scheme and another high order scheme based on a truncated Taylor series expansion, and the most accurate implementations are identified. It is concluded that although the high order schemes perform much better than the others, they are not as accurate as in Cartesian coordinates, and their order of convergence is lower than in that case. - Highlights: • The radiative transfer equation is solved in unstructured grids using the DOM. • Discretization schemes based on the NVD and TVD boundedness criteria are used. • Several implementations relying on different approximations are compared. • The order of convergence in unstructured grids is lower than in Cartesian grids. • The most accurate and the fastest implementations of the schemes were identified

175

This paper proposes a blind multi-watermarking scheme based on designing two back-to-back encoders. The first encoder is implemented to embed a robust watermark into remote sensing imagery by applying a Discrete Cosine Transform (DCT) approach. Such watermark is used in many applications to protect the copyright of the image. However, the second encoder embeds a fragile watermark using `SHA-1' hash function. The purpose behind embedding a fragile watermark is to prove the authenticity of the image (i.e. tamper-proof). Thus, the proposed technique was developed as a result of new challenges with piracy of remote sensing imagery ownership. This led researchers to look for different means to secure the ownership of satellite imagery and prevent the illegal use of these resources. Therefore, Emirates Institution for Advanced Science and Technology (EIAST) proposed utilizing existing data security concept by embedding a digital signature, "watermark", into DubaiSat-1 satellite imagery. In this study, DubaiSat-1 images with 2.5 meter resolution are used as a cover and a colored EIAST logo is used as a watermark. In order to evaluate the robustness of the proposed technique, a couple of attacks are applied such as JPEG compression, rotation and synchronization attacks. Furthermore, tampering attacks are applied to prove image authenticity.

Al-Mansoori, Saeed; Kunhu, Alavi

2013-10-01

176

Dynamic Rupture Simulation of Bending Faults With a Finite Difference Approach

Many questions about physical parameters governing the rupture propagation of earthquakes seem to find their answers within realistic dynamic considerations. Sophisticated constitutive relations based in laboratory experiments have lead to a better understanding of rupture evolution from its very beginning to its arrest. On the other hand, large amount of field observations as well as recent numerical simulations have also demonstrated the importance, in rupture growing, of considering more reasonable geological settings (e.g., bending and step-over fault geometries; heterogeneous surrounding media). So far, despite the development of powerful numerical tools, there still exist some numerical considerations that overstep their possibilities. Authors have solved the dynamic problem by applying the boundary integral equations method (BIEM) in order to explore the influence of fault geometry. This can be possible because of the fact that only the rupture path must be discretized, reducing the impact of numerical discretization. However, the BIEM needs the analytical solution of Green functions that can only be computed for a homogeneous space. Up to date, no interaction with heterogeneous structures can be taken in to account. In contrast, finite difference (FD) approaches have been widely used. In this case, due to the specific discretization of the elastodynamic equations through the entire domain, and the azimuthal anisotropy intrinsic to differential operators, only planar faults have been considered and numerical artefacts have to be carefully checked. In this work, we have used a recently proposed four-order staggered grid finite difference scheme to model in-plane (mode II) dynamic shear fracturing propagation with any pre-established geometry. In contrast with the classical 2-D staggered grid elementary cell in which all the elastic fields are defined in different positions (except the normal stresses), the stencil used here consider the velocity and stress fields separately in only two staggered grids. This permit an efficient treatment of boundary conditions to impose the shear stress drop in the nodes where the stresses are located. On the other hand, the stencil allows the four order Cartesian differential operators being decoupled into two different 45 degrees rotated operators. This procedure reduces numerical anisotropy along preferred directions and provides stable solutions for any fault orientation. Numerical solutions of dynamical fracture still exhibit large oscillations coming from local discretization effects and integration procedures. These perturbations can strongly alter the rupture front velocity and the average slip rate behind the crack tip. We controlled this phenomenon by applying a smoothing Laplacian operator to velocity equations. Such a mathematical tool, provided that suitable input parameters are supplied, helps to vanish these oscillations. Specifying a fault thickness in simulations yields similar results as we scale down numerical parameters, if the same fault geometry is kept. A simple definition of the fault is done placing it in the middle of the grid without using any adhoc numerical ghost plane often used in FD approaches. The fault is a sum of source points taken as close as possible to the hypothetical fault line. Simulations of irregular fault geometry (e.g., bending faults) are possible using the superposition technique. Spontaneous and velocity fixed rupture propagation will be presented with abrupt stress drop, as well as with time- and slip- weakening constitutive laws. Analysis of arbitrarily heterogeneous media surrounding the fault region in the dynamics of seismic sources evolution is possible.

Cruz-Atienza, V. M.; Virieux, J.; Operto, S.

2002-12-01

177

Improving sub-grid scale accuracy of boundary features in regional finite-difference models

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

Panday, Sorab; Langevin, Christian D.

2012-01-01

178

Mixed-grid and staggered-grid finite-difference methods for frequency-domain acoustic wave modelling

We compare different finite-difference schemes for two-dimensional (2-D) acoustic frequency-domain forward modelling. The schemes are based on staggered-grid stencils of various accuracy and grid rotation strategies to discretize the derivatives of the wave equation. A combination of two staggered-grid stencils on the classical Cartesian coordinate system and the 45° rotated grid is the basis of the so-called mixed-grid stencil. This method is compared with a parsimonious staggered-grid method based on a fourth-order approximation of the first derivative operator. Averaging of the mass acceleration can be incorporated in the two stencils. Sponge-like perfectly matched layer absorbing boundary conditions are also examined for each stencil and shown to be effective. The deduced numerical stencils are examined for both the wavelength content and azimuthal variation. The accuracy of the fourth-order staggered-grid stencil is slightly superior in terms of phase velocity dispersion to that of the mixed-grid stencil when averaging of the mass acceleration term is applied to the staggered-grid stencil. For fourth-order derivative approximations, the classical staggered-grid geometry leads to a stencil that incorporates 13 grid nodes. The mixed-grid approach combines only nine grid nodes. In both cases, wavefield solutions are computed using a direct matrix solver based on an optimized multifrontal method. For this 2-D geometry, the staggered-grid strategy is significantly less efficient in terms of memory and CPU time requirements because of the enlarged bandwidth of the impedance matrix and increased number of coefficients in the discrete stencil. Therefore, the mixed-grid approach should be suggested as the routine scheme for 2-D acoustic wave propagation modelling in the frequency domain.

Hustedt, Bernhard; Operto, Stéphane; Virieux, Jean

2004-06-01

179

Efficient architectures for two-dimensional discrete wavelet transform using lifting scheme.

Novel architectures for 1-D and 2-D discrete wavelet transform (DWT) by using lifting schemes are presented in this paper. An embedded decimation technique is exploited to optimize the architecture for 1-D DWT, which is designed to receive an input and generate an output with the low- and high-frequency components of original data being available alternately. Based on this 1-D DWT architecture, an efficient line-based architecture for 2-D DWT is further proposed by employing parallel and pipeline techniques, which is mainly composed of two horizontal filter modules and one vertical filter module, working in parallel and pipeline fashion with 100% hardware utilization. This 2-D architecture is called fast architecture (FA) that can perform J levels of decomposition for N * N image in approximately 2N2(1 - 4(-J))/3 internal clock cycles. Moreover, another efficient generic line-based 2-D architecture is proposed by exploiting the parallelism among four subband transforms in lifting-based 2-D DWT, which can perform J levels of decomposition for N * N image in approximately N2(1 - 4(-J))/3 internal clock cycles; hence, it is called high-speed architecture. The throughput rate of the latter is increased by two times when comparing with the former 2-D architecture, but only less additional hardware cost is added. Compared with the works reported in previous literature, the proposed architectures for 2-D DWT are efficient alternatives in tradeoff among hardware cost, throughput rate, output latency and control complexity, etc. PMID:17357722

Xiong, Chengyi; Tian, Jinwen; Liu, Jian

2007-03-01

180

On nonlinear finite difference inequalities in two independent variables

The aim of the present paper is to establish some new finite difference inequalities involving functions of two independent variables which provide explicit bounds on unknown functions. The inequalities given here can be used as tools in the qualitative theory of certain partial finite difference equations.

Pachpatte, B. G.

2002-01-01

181

International Nuclear Information System (INIS)

A novel approach is presented in this paper for improving anisotropic diffusion PDE models, based on the Perona–Malik equation. A solution is proposed from an engineering perspective to adaptively estimate the parameters of the regularizing function in this equation. The goal of such a new adaptive diffusion scheme is to better preserve edges when the anisotropic diffusion PDE models are applied to image enhancement tasks. The proposed adaptive parameter estimation in the anisotropic diffusion PDE model involves self-organizing maps and Bayesian inference to define edge probabilities accurately. The proposed modifications attempt to capture not only simple edges but also difficult textural edges and incorporate their probability in the anisotropic diffusion model. In the context of the application of PDE models to image processing such adaptive schemes are closely related to the discrete image representation problem and the investigation of more suitable discretization algorithms using constraints derived from image processing theory. The proposed adaptive anisotropic diffusion model illustrates these concepts when it is numerically approximated by various discretization schemes in a database of magnetic resonance images (MRI), where it is shown to be efficient in image filtering and restoration applications

182

Explicit Finite Difference Solution of Heat Transfer Problems of Fish Packages in Precooling

Directory of Open Access Journals (Sweden)

Full Text Available The present work aims at finding an optimized explicit finite difference scheme for the solution of problems involving pure heat transfer from the surfaces of Pangasius Sutchi fish samples suddenly exposed to a cooling environment. Regular shaped packages in the form of an infinite slab were considered and a generalized mathematical model was written in dimensionless form. An accurate sample of the data set was chosen from the experimental work and was used to seek an optimized scheme of solutions. A fully explicit finite difference scheme has been thoroughly studied from the viewpoint of stability, the required time for execution and precision. The characteristic dimension (half thickness was divided into a number of divisions; n = 5, 10, 20, 50 and 100 respectively. All the possible options of dimensionless time (the Fourier number increments were taken one by one to give the best convergence and truncation error criteria. The simplest explicit finite difference scheme with n = (10 and stability factor (Î?X2/Î?Ï? = 2 was found to be reliable and accurate for prediction purposes."

A. S. Mokhtar

2004-01-01

183

International Nuclear Information System (INIS)

The suitability of high-order accurate, centered and upwind-biased compact difference schemes for large eddy simulation (LES) is evaluated through the static and dynamic analyses. For the static error analysis, the power spectra of the finite-differencing and aliasing errors are evaluated in the discrete Fourier space, and for the dynamic error analysis LES of isotropic turbulence is performed with various dissipative and non-dissipative schemes. Results from the static analysis give a misleading conclusion that both the aliasing and finite-differencing errors increase as the numerical dissipation increases. The dynamic analysis, however, shows that the aliasing error decreases as the dissipation increases and the finite-differencing error overweighs the aliasing error. It is also shown that there exists an optimal upwind scheme of minimizing the total discretization error because the dissipative schemes decrease the aliasing error but increase the finite-differencing error. In addition, a classical issue on the treatment of nonlinear term in the Navier-Stokes equation is revisited to show that the skew-symmetric form minimizes both the finite-differencing and aliasing errors. The findings from the dynamic analysis are confirmed by the physical space simulations of turbulent channel flow at Re=23000 and flow over a circular cylinder at Re=3900

184

International Nuclear Information System (INIS)

This report presents comparisons of results of five implicit and explicit finite difference recession computation techniques with results from a more accurate ''benchmark'' solution applied to a simple one-dimensional nonlinear ablation problem. In the comparison problem a semi-infinite solid is subjected to a constant heat flux at its surface and the rate of recession is controlled by the solid material's latent heat of fusion. All thermal properties are assumed constant. The five finite difference methods include three front node dropping schemes, a back node dropping scheme, and a method in which the ablation problem is embedded in an inverse heat conduction problem and no nodes are dropped. Constancy of thermal properties and the semiinfinite and one-dimensional nature of the problem at hand are not necessary assumptions in applying the methods studied to more general problems. The best of the methods studied will be incorporated into APL's Standard Heat Transfer Program

185

Optimal variable-grid finite-difference modeling for porous media

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.

Liu, Xinxin; Yin, Xingyao; Li, Haishan

2014-12-01

186

Finite difference lattice Boltzmann model with flux limiters for liquid-vapor systems

In this paper we apply a finite difference lattice Boltzmann model to study the phase separation in a two-dimensional liquid-vapor system. Spurious numerical effects in macroscopic equations are discussed and an appropriate numerical scheme involving flux limiter techniques is proposed to minimize them and guarantee a better numerical stability at very low viscosity. The phase separation kinetics is investigated and we find evidence of two different growth regimes depending ...

Sofonea, V.; Lamura, A.; Gonnella, G.; Cristea, A.

2004-01-01

187

The origin of the spurious interface velocity in finite difference lattice Boltzmann models for liquid - vapor systems is related to the first order upwind scheme used to compute the space derivatives in the evolution equations. A correction force term is introduced to eliminate the spurious velocity. The correction term helps to recover sharp interfaces and sets the phase diagram close to the one derived using the Maxwell construction.

Cristea, A; Cristea, Artur; Sofonea, Victor

2003-01-01

188

This paper is concerned with moving mesh finite difference solution of partial differential equations. It is known that mesh movement introduces an extra convection term and its numerical treatment has a significant impact on the stability of numerical schemes. Moreover, many implicit second and higher order schemes, such as the Crank-Nicolson scheme, will loss their unconditional stability. A strategy is presented for developing temporally high order, unconditionally stable...

Huang, Weizhang

2013-01-01

189

Stability analysis of single-phase thermosyphon loops by finite difference numerical methods

International Nuclear Information System (INIS)

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

190

C3: A finite volume-finite difference hybrid model for tsunami propagation and runup

A numerical model that couples Finite Difference and Finite Volume schemes has been developed for tsunami propagation and runup study. An explicit leap-frog scheme and a first order upwind scheme has been considered in the Finite Difference module, while in the Finite Volume scheme a Godunov Type method based on the f-waves approach has been used. The Riemann solver included in the model corresponds to an approximate augmented solver for the Shallow Water Equations (SWE) in the presence of variable bottom surface. With this hybrid model some of the problems inherent to the Godunov type schemes are avoided in the offshore region, while in the coastal area the use of a conservative method ensures the correct computation of the runup and wave breaking. The model has been tested and validated using different problems with a known analytical solution and also with laboratory experiments, considering both non breaking and breaking waves. The results are very satisfactory, showing that the hybrid approach is a useful technique for practical usages.

Olabarrieta, M.; Medina, R.; Gonzalez, M.; Otero, L.

2011-08-01

191

In engineering fields there have recently been a number of studies that have applied the finite-difference time-domain (FDTD) numerical method to elastodynamic problems. These studies include those of ultrasonic transducers and electro-mechanical devices. In FDTD formulations, the first-order set of partial differential equations given by the constitutive equations are discretized using a leap-frog finite-difference scheme. When a high-contrast discontinuity, especially a free surface, is present, some difficulties arise due to the spatially staggered nature of the grid of the FDTD approach, with neither all the velocity variables nor all the stress variables appearing on the same grid lines. The present study considers the following modifications to the FDTD approach: a standard staggered grid for anisotropic elastic wave fields is rotated so that the diagonal directions of the standard grid lie parallel to the axes of the analysis region. This configuration, called the diagonally staggered grid (DSG), improves the accuracy of the implementation of free boundaries without requiring virtual grids in a vacuum area. The effectiveness of DSG was verified by applying this method to model problems of isotropic and anisotropic solid materials.

Sato, Masahiro

2008-05-01

192

Improvement of the finite difference lattice Boltzmann method for low mach number flows

International Nuclear Information System (INIS)

This paper presents a numerical method to compute flow-acoustic resonance at low Mach number within a reasonable computing time. Light water reactors have experienced flow-acoustic resonance which is attributed to unsteady compressible flows at low Mach number. This phenomenon is undesirable because the induced sound causes loud noise and vibrations of the mechanical structures. However, a numerical simulation of this flow-acoustic resonance at low Mach number requires a large computing time and a highly accurate method in order to simultaneously compute flows and acoustic waves. The finite difference lattice Boltzmann method which is a powerful tool for obtaining computational fluid dynamics has high accuracy for simultaneous calculation of flows and acoustic waves. It becomes an efficient method to compute low Mach number flow if the computing time is shortened. In this paper, the finite difference lattice Boltzmann method was sped up. Three improvements were proposed: development of a new particle model, modification of the governing equation, and employment of an efficient time marching scheme. The computing time of the proposed finite difference lattice Boltzmann model was compared with the conventional finite difference lattice Boltzmann model for the calculation of the cubic cavity flow. The results showed that the computing time of the proposed model is 30% of the time needed by the conventional finite difference lattice Boltzmann model. The flow-acoustic resoce Boltzmann model. The flow-acoustic resonance at low Mach number at the side branch was calculated using the proposed model. The numerical results showed quantitative agreement with the experimental data. (author)

193

Finite difference analysis of laminar free convection flow past a non isothermal vertical cone

A finite-difference analysis for the transient free convection flow of an incompressible viscous fluid past a vertical cone with variable wall surface temperature T {w/'} ( x) = T {?/'} + a x n varying as power function of distance from the apex ( x = 0) is presented here. The dimensionless governing equations of the flow that are unsteady, coupled and non-linear partial differential equations are solved by an efficient, accurate and unconditionally stable finite difference scheme of Crank-Nicolson type. The velocity and temperature fields have been studied for various parameters such as Prandtl number and n (exponent in power law variation in surface temperature). The local as well as average skin-friction and Nusselt number are also presented and analyzed graphically. The present results are compared with available results in literature and are found to be in good agreement.

Bapuji, Pullepu; Ekambavanan, K.; Pop, I.

2008-03-01

194

Analysis of guided polarization modes in multimode rib waveguide by finite difference method

The multimode devices, which are also polarization-sensitive, have been widely used in modern optical communication system. In some cases, the modal properties, including the modal propagation constants and the modal fields of every order, must be given for the device design. The scalar finite difference beam propagation method (FD-BPM) is extended to solve this polarization-related problem. The different finite difference schemes corresponding to different polarized directions, which satisfy different boundary continual conditions, are formulized and the alternate directions implicit (ADI) FD-BPM were used to deal with the three dimensional (3D) waveguide. The guided modal properties of a 3D rib waveguide including the propagation constants and modal field distributions up to ten ranks were obtained and illustrated as an example.

Yan, ChaoJun; Liu, Xiang; Jiang, Binghua; Wan, Junli

2008-12-01

195

Stable discontinuous staggered grid in the finite-difference modelling of seismic motion

We present an algorithm of the spatial discontinuous grid for the 3-D fourth-order velocity-stress staggered-grid finite-difference modelling of seismic wave propagation and earthquake motion. The ratio between the grid spacing of the coarser and finer grids can be an arbitrary odd number. The algorithm allows for large numbers of time levels without inaccuracy and eventual instability due to numerical noise inevitably generated at the contact of two grids with different spatial grid spacings. The key feature of the algorithm is the application of the Lanczos downsampling filter. The algorithm of the discontinuous grid is directly applicable also to the displacement-stress staggered-grid finite-difference scheme.

Kristek, Jozef; Moczo, Peter; Galis, Martin

2010-12-01

196

To make the application of the finite-element method practical in semiconductor device simulation, the authors have applied the Scharfetter-Gummel (S-G) scheme in conjunction with an accurate seven-point Gaussian quadrature rule to the assembly of the finite-element stiffness matrices and right-hand-side vector of the semiconductor equations. The key of this method lies in accurate interpolation rules, which are derived on the basis of simple device physics considerations. The inherent simplicity and flexibility in the finite element formulation make the new method applicable to multidimensional problems. The simplicity of embedding the S-G scheme in the quadrature of finite-element assembly lends itself to all kinds of finite-element methods using various elements, shape functions, and weightings. The resultant exponential functional fitting avoids high discretization errors usually incurred by the classical finite-element discretization method. Solutions with high accuracy, even on coarse mesh, and a significant speed-up of convergence rate are obtained.

Tan, Gen-Lin; Yuan, Xiao-Li; Zhang, Qi-Ming; Ku, Walter H.; Shey, An-Jui

1989-05-01

197

Some Experiences with High Order Discretization Schemes for Compressible Fluid Flow

It is widely recognized that the structure and complexity of compressible fluid flow places high demands on numerical discretization techniques for the fluid flow equations. Fluid flows arising in external aerodynamics often contain both flow field discontinuities and fluid boundary-layers. Both must be accurately resolved to provide useful information to aerodynamic design and analysis engineers. These accuracy requirements motivated the present author to examine a class of finite-volume techniques on arbitrary triangulated domains based on linear or quadratic reconstruction of integral-averaged data followed by upwind flux function evaluation and small time evolution. More recently, we have considered some new upwind techniques which yield compact discretizations while maintaining higher order accuracy. In the mini-symposium talk we will discuss both of these techniques as well as demonstrate the relative merits of each method by computing a number of aerodynamic flows containing shock waves and boundary-layers.

Barth, Timothy J.; Chancellor, Marisa K. (Technical Monitor)

1997-01-01

198

Identification of a discrete memory constitutive scheme for mild steel type materials

International Nuclear Information System (INIS)

The aim of this paper is to define a tensorial constitutive scheme available for annealed mild steel type materials; the mechanical behavior is then remarkable for both peak effect associated with the plateau along the first loading and rapid hardening leading to non symmetrical cycles when cycling with a rather limited given strain amplitude. The proposed scheme is based on the additivity of three kinds of intrinsic dissipations and is suitable for irrotational and rotational, monotonic and cyclic evolutions. Furthermore, second order effects are at least qualitatively described. (orig./RF)

199

An analytical discrete ordinates solution for two-dimensional problems based on nodal schemes

International Nuclear Information System (INIS)

In this work, the ADO method is used to solve the integrated one dimensional equations generated by the application of a nodal scheme on the two dimensional transport problem in cartesian geometry. Particularly, relations between the averaged fluxes and the unknown fluxes at the boundary are introduced as the usually needed auxiliary equations. The ADO approach, along with a level symmetric quadrature scheme, lead to an important reduction in the order of the associated eigenvalue systems. Numerical results are presented for a two dimensional problem in order to compare with available results in the literature. (author)

200

Replica-symmetry breaking: discrete and continuous schemes in the Sherrington-Kirkpatrick model.

Czech Academy of Sciences Publication Activity Database

Ro?. 41, ?. 32 (2008), 324004/1-324004/14. ISSN 1751-8113 Institutional research plan: CEZ:AV0Z10100520 Keywords : replica-symmetry breaking * hierarchical solution * Parisi continuous scheme * expansion near de Almeida-Thouless line Subject RIV: BE - Theoretical Physics Impact factor: 1.540, year: 2008

Janiš, Václav; Klí?, Antonín; Ringel, Matouš

2008-01-01

201

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

Energy Technology Data Exchange (ETDEWEB)

Wave propagation phenomena are important in many DOE applications such as nuclear explosion monitoring, geophysical exploration, estimating ground motion hazards and damage due to earthquakes, non-destructive testing, underground facilities detection, and acoustic noise propagation. There are also future applications that would benefit from simulating wave propagation, such as geothermal energy applications and monitoring sites for carbon storage via seismic reflection techniques. In acoustics and seismology, it is of great interest to increase the frequency bandwidth in simulations. In seismic exploration, greater frequency resolution enables shorter wave lengths to be included in the simulations, allowing for better resolution in the seismic imaging. In nuclear explosion monitoring, higher frequency seismic waves are essential for accurate discrimination between explosions and earthquakes. When simulating earthquake induced motion of large structures, such as nuclear power plants or dams, increased frequency resolution is essential for realistic damage predictions. Another example is simulations of micro-seismic activity near geothermal energy plants. Here, hydro-fracturing induces many small earthquakes and the time scale of each event is proportional to the square root of the moment magnitude. As a result, the motion is dominated by higher frequencies for smaller seismic events. The above wave propagation problems are all governed by systems of hyperbolic partial differential equations in second order differential form, i.e., they contain second order partial derivatives of the dependent variables. Our general research theme in this project has been to develop numerical methods that directly discretize the wave equations in second order differential form. The obvious advantage of working with hyperbolic systems in second order differential form, as opposed to rewriting them as first order hyperbolic systems, is that the number of differential equations in the second order system is significantly smaller. Another issue with re-writing a second order system into first order form is that compatibility conditions often must be imposed on the first order form. These (Saint-Venant) conditions ensure that the solution of the first order system also satisfies the original second order system. However, such conditions can be difficult to enforce on the discretized equations, without introducing additional modeling errors. This project has previously developed robust and memory efficient algorithms for wave propagation including effects of curved boundaries, heterogeneous isotropic, and viscoelastic materials. Partially supported by internal funding from Lawrence Livermore National Laboratory, many of these methods have been implemented in the open source software WPP, which is geared towards 3-D seismic wave propagation applications. This code has shown excellent scaling on up to 32,768 processors and has enabled seismic wave calculations with up to 26 Billion grid points. TheWPP calculations have resulted in several publications in the field of computational seismology, e.g.. All of our current methods are second order accurate in both space and time. The benefits of higher order accurate schemes for wave propagation have been known for a long time, but have mostly been developed for first order hyperbolic systems. For second order hyperbolic systems, it has not been known how to make finite difference schemes stable with free surface boundary conditions, heterogeneous material properties, and curvilinear coordinates. The importance of higher order accurate methods is not necessarily to make the numerical solution more accurate, but to reduce the computational cost for obtaining a solution within an acceptable error tolerance. This is because the accuracy in the solution can always be improved by reducing the grid size h. However, in practice, the available computational resources might not be large enough to solve the problem with a low order method.

Petersson, N A; Sjogreen, B

2012-03-26

202

An assessment of semi-discrete central schemes for hyperbolic conservation laws

International Nuclear Information System (INIS)

High-resolution finite volume methods for solving systems of conservation laws have been widely embraced in research areas ranging from astrophysics to geophysics and aero-thermodynamics. These methods are typically at least second-order accurate in space and time, deliver non-oscillatory solutions in the presence of near discontinuities, e.g., shocks, and introduce minimal dispersive and diffusive effects. High-resolution methods promise to provide greatly enhanced solution methods for Sandia's mainstream shock hydrodynamics and compressible flow applications, and they admit the possibility of a generalized framework for treating multi-physics problems such as the coupled hydrodynamics, electro-magnetics and radiative transport found in Z pinch physics. In this work, we describe initial efforts to develop a generalized 'black-box' conservation law framework based on modern high-resolution methods and implemented in an object-oriented software framework. The framework is based on the solution of systems of general non-linear hyperbolic conservation laws using Godunov-type central schemes. In our initial efforts, we have focused on central or central-upwind schemes that can be implemented with only a knowledge of the physical flux function and the minimal/maximal eigenvalues of the Jacobian of the flux functions, i.e., they do not rely on extensive Riemann decompositions. Initial experimentation with high-resolution central schemes suggests that contact discontinuitiesemes suggests that contact discontinuities with the concomitant linearly degenerate eigenvalues of the flux Jacobian do not pose algorithmic difficulties. However, central schemes can produce significant smearing of contact discontinuities and excessive dissipation for rotational flows. Comparisons between 'black-box' central schemes and the piecewise parabolic method (PPM), which relies heavily on a Riemann decomposition, shows that roughly equivalent accuracy can be achieved for the same computational cost with both methods. However, PPM clearly outperforms the central schemes in terms of accuracy at a given grid resolution and the cost of additional complexity in the numerical flux functions. Overall we have observed that the finite volume schemes, implemented within a well-designed framework, are extremely efficient with (potentially) very low memory storage. Finally, we have found by computational experiment that second and third-order strong-stability preserving (SSP) time integration methods with the number of stages greater than the order provide a useful enhanced stability region. However, we observe that non-SSP and non-optimal SSP schemes with SSP factors less than one can still be very useful if used with time-steps below the standard CFL limit. The 'well-designed' integration schemes that we have examined appear to perform well in all instances where the time step is maintained below the standard physical CFL limit

203

Finite difference time domain modelling of particle accelerators

International Nuclear Information System (INIS)

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

204

Continuous dependence and differentiation of solutions of finite difference equations

Directory of Open Access Journals (Sweden)

Full Text Available Conditions are given for the continuity and differentiability of solutions of initial value problems and boundary value problems for the nth order finite difference equation, u(m+n=f(m,u(m,u(m+1,Ã¢Â€Â¦,u(m+nÃ¢ÂˆÂ’1,mÃ¢ÂˆÂˆÃ¢Â„Â¤.

Linda Lee

1991-01-01

205

Staggered Finite Difference Stencils In Frequency Domain Modelling

Seismic forward modelling in the frequency domain is of special interest because of its computational efficiency for multisource experiments. Moreover, realistic rheology is easily incorporated in the modelling by introducing complex velocities. Standard frequency domain modelling is performed using the star geometry. The second-order hyperbolic partial differential equation is discretized using second-order derivative approximations on a Cartesian grid (5-points star strategy). The 9-points star strategy incorpoartes an additional numerical grid that is rotated by 45 degrees. Both grids are combined by averaging coefficients to give the 9-points star geometry. Numerical accuarcy is guaranteed by an optimization technique that determines the averaging coefficients such that the velocity dispersion is minimized. We investigate effects of FD staggered cross stencils instead of directly constructing star stencils through grid rotations. We consider a frequency-space FD scheme with PML conditions where derivatives are discretized using either second-order or fourth- order staggered difference stencils. As for the star strategy, staggered stencils com- bine neighbouring points for derivative approximations, though now the combination comes automatically with the staggered stencil interpolation. Still one may perform a staggered stencil optimization to further enhance numerical accuracy as suggested by Holberg (1987). We show the equivalence of the second-order FD staggered cross stencil and the 5- points star stencil. Further, we analyze fourth-order centered FD derivative approxi- mations that leads to a 13-points staggered cross stencil. We shall compare the deduced new staggered cross stencil with the usual 9-points star stencil. Numerical dispersion is investigated for both the wavelength content and azimuthal variation. We illustrate the results on two examples of frequency domain seismic wave propagation in 2D homogeneous and heterogeneous media. References: Holberg, O. 1987, Computational Aspects of Choice of Operator and Sampling In- terval for Numerical Differentiation in Large-Scale Simulation of Wave Phenomena, Geophysical Prospecting 35, 629-655.

Hustedt, B.; Operto, S.; Virieux, J.

206

Finite-difference time-domain simulation of GPR data

Simulation of digital ground penetrating radar (GPR) wave propagation in two-dimensional (2-D) media is developed, tested, implemented, and applied using a time-domain staggered-grid finite-difference (FD) numerical method. Three types of numerical algorithms for constructing synthetic common-shot, constant-offset radar profiles based on an actual transmitter-to-receiver configuration and based on the exploding reflector concept are demonstrated to mimic different types of radar survey geometries. Frequency-dependent attenuation is also incorporated to account for amplitude decay and time shift in the recorded responses. The algorithms are based on an explicit FD solution to Maxwell's curl equations. In addition, the first-order TE mode responses of wave propagation phenomena are considered due to the operating frequency of current GPR instruments. The staggered-grid technique is used to sample the fields and approximate the spatial derivatives with fourth-order FDs. The temporal derivatives are approximated by an explicit second-order difference time-marching scheme. By combining paraxial approximation of the one-way wave equation ( A2) and the damping mechanisms (sponge filter), we propose a new composite absorbing boundary conditions (ABC) algorithm that effectively absorb both incoming and outgoing waves. To overcome the angle- and frequency-dependent characteristic of the absorbing behaviors, each ABC has two types of absorption mechanism. The first ABC uses a modified Clayton and Enquist's A2 condition. Moreover, a fixed and a floating A2 ABC that operates at one grid point is proposed. The second ABC uses a damping mechanism. By superimposing artificial damping and by alternating the physical attenuation properties and impedance contrast of the media within the absorbing region, those waves impinging on the boundary can be effectively attenuated and can prevent waves from reflecting back into the grid. The frequency-dependent characteristic of the damping mechanism can be used to adjust the width of the absorbing zone around the computational domain. By applying any combination of absorbing mechanism, non-physical reflections from the computation domain boundary can be effectively minimized. The algorithm enables us to use very thin absorbing boundaries. The model can be parameterized through velocity, relative electrical permittivity (dielectric constants), electrical conductivity, magnetic permeability, loss tangent, Q values, and attenuation. According to this scheme, widely varying electrical properties of near-surface earth materials can be modeled. The capability of simulating common-source, constant-offset and zero-offset gathers is also demonstrated through various synthetic examples. The synthetic cases for typical GPR applications include buried objects such as pipes of different materials, AVO analysis for ground water exploration, archaeological site investigation, and stratigraphy studies. The algorithms are also applied to iterative modeling of GPR data acquired over a gymnasium construction site on the NCCU campus.

Chen, How-Wei; Huang, Tai-Min

1998-10-01

207

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

International Nuclear Information System (INIS)

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

208

Replica-symmetry breaking: discrete and continuous schemes in the Sherrington-Kirkpatrick model

We study hierarchies of replica-symmetry-breaking solutions of the Sherrington-Kirkpatrick model. Stationarity equations for order parameters of solutions with an arbitrary number of hierarchies are set and the limit to infinite number of hierarchical levels is discussed. In particular, we demonstrate how the continuous replica-symmetry breaking scheme of Parisi emerges and how the limit to infinite-many hierarchies leads to equations for the order-parameter function of the ...

Janis, V.; Klic, A.; Ringel, M.

2007-01-01

209

A multigrid semi-implicit finite difference method for the two-dimensional shallow water equations

A multigrid semi-implicit finite difference method is presented to solve the two-dimensional shallow water equations which describe the behaviour of basin water under the influence of the Coriolis force, atmospheric pressure gradients and tides. The semi-implicit finite difference method discretizes implicitly both the gradient of the water elevation in the momentum equations and the velocity divergence in the continuity equations and explicitly the convective terms using an Eulerian-Lagrangian approach. At each time step we apply the multigrid computation to solve the resulting linear, symmetric, pentadiagonal system of discrete equations. The multigrid algorithm, defined on staggered grids, provides accelerated convergence histories. We numerically simulate the water circulation in a closed rectangular basin, centrally crossed by a deeper channel. Moreover, simulation of the circulation in San Pablo Bay shows the high flexibility and applicability of this method to concrete problems. Visualizations of the computed variables, water depth and velocity, are shown by figures. Displays of convergence histories show promising multigrid acceleration.

Spitaleri, R. M.; Corinaldesi, L.

1997-12-01

210

Finite-difference lattice Boltzmann model with flux limiters for liquid-vapor systems.

In this paper we apply a finite difference lattice Boltzmann model to study the phase separation in a two-dimensional liquid-vapor system. Spurious numerical effects in macroscopic equations are discussed and an appropriate numerical scheme involving flux limiter techniques is proposed to minimize them and guarantee a better numerical stability at very low viscosity. The phase separation kinetics is investigated and we find evidence of two different growth regimes depending on the value of the fluid viscosity as well as on the liquid-vapor ratio. PMID:15600560

Sofonea, V; Lamura, A; Gonnella, G; Cristea, A

2004-10-01

211

Numerical simulation of shock wake propagation using the finite difference lattice Boltzmann method

International Nuclear Information System (INIS)

The shock wave process represents an abrupt change in fluid properties, in which finite variations in pressure, temperature, and density occur over the shock thickness which is comparable to the mean free path of the gas molecules involved. This shock wave fluid phenomenon is simulated by using the Finite Difference Lattice Boltzmann Method (FDLBM). In this paper, a new model is proposed using the lattice BGK compressible fluid model in FDLBM for the purpose of speeding up the calculation as well as stabilizing the numerical scheme. The numerical results of the proposed model show good agreement with the theoretical predictions

212

Finite difference lattice Boltzmann model with flux limiters for liquid-vapor systems

In this paper we apply a finite difference lattice Boltzmann model to study the phase separation in a two-dimensional liquid-vapor system. Spurious numerical effects in macroscopic equations are discussed and an appropriate numerical scheme involving flux limiter techniques is proposed to minimize them and guarantee a better numerical stability at very low viscosity. The phase separation kinetics is investigated and we find evidence of two different growth regimes depending on the value of the fluid viscosity as well as on the liquid-vapor ratio.

Sofonea, V; Gonnella, G; Cristea, A

2004-01-01

213

Finite difference analysis for Navier-Stokes and energy equations of Couette-Poiseuille flow

International Nuclear Information System (INIS)

Numerical results for the problem of combined convective heat transfer in a vertical annular gap between two concentric Isothermal cylinders, are presented. Emphasis was given to the effects of the inlet temperature, flow direction and the inner cylinder rotation on hydrodynamic and heat transfer characteristics. The boundary layer simplifications of the Navier-Stokes equations and the energy equation were solved by means of an extension of the linearized finite difference scheme used previously by Coney and El-Shaarawi (1975). The results were obtained for Re of 100, 200 and 250, 04 and -2x1044. 14 refs.; 11 figs

214

Staircase-free finite-difference time-domain formulation for general materials in complex geometries

DEFF Research Database (Denmark)

A stable Cartesian grid staircase-free finite-difference time-domain formulation for arbitrary material distributions in general geometries is introduced. It is shown that the method exhibits higher accuracy than the classical Yee scheme for complex geometries since the computational representation of physical structures is not of a staircased nature, Furthermore, electromagnetic boundary conditions are correctly enforced. The method significantly reduces simulation times as fewer points per wavelength are needed to accurately resolve the wave and the geometry. Both perfect electric conductors and dielectric structures have been investigated, Numerical results are presented and discussed.

Dridi, Kim; Hesthaven, J.S.

2001-01-01

215

An exact expression of steady discrete shocks was recently obtained by the author in [9] for a class of residual-based compact schemes (RBC) applied to the inviscid Bürgers equation in a finite domain. Following the same lines, the analysis is extended to an infinite domain for a scalar conservation law with a general convex flux. For the dissipative high-order schemes considered, discrete shocks in infinite domain or with boundary conditions at short distance (Rankine-Hugoniot relations) are found to be very close. Besides, the present analytical description of shock capturing in infinite domain is explicit and so simple that it could lead to a new approach for correcting parasitic oscillations of high order RBC schemes. In a second part of the paper, exact solutions are also derived for equivalent differential equations (EDE) approximating RBC2p-1 schemes (subscript denotes the accuracy order) at orders 2p and 2p+1. Although EDE involves Taylor expansions around steep structures, agreement between the exact EDE shock-profiles and the discrete shocks is remarkably good for RBC5 and RBC7 schemes. In addition, a strong similarity is demonstrated between the analytical expressions of discrete shocks and EDE shock profiles.

Lerat, Alain

2014-09-01

216

Finite-difference modeling with variable grid-size and adaptive time-step in porous media

Forward modeling of elastic wave propagation in porous media has great importance for understanding and interpreting the influences of rock properties on characteristics of seismic wavefield. However, the finite-difference forward-modeling method is usually implemented with global spatial grid-size and time-step; it consumes large amounts of computational cost when small-scaled oil/gas-bearing structures or large velocity-contrast exist underground. To overcome this handicap, combined with variable grid-size and time-step, this paper developed a staggered-grid finite-difference scheme for elastic wave modeling in porous media. Variable finite-difference coefficients and wavefield interpolation were used to realize the transition of wave propagation between regions of different grid-size. The accuracy and efficiency of the algorithm were shown by numerical examples. The proposed method is advanced with low computational cost in elastic wave simulation for heterogeneous oil/gas reservoirs.

Liu, Xinxin; Yin, Xingyao; Wu, Guochen

2014-04-01

217

Directory of Open Access Journals (Sweden)

Full Text Available Watermarking represents a potentially effective tool for the protection and verification of ownership rights in remote sensing images. Multispectral images (MSIs are the main type of images acquired by remote sensing radiometers. In this paper, a robust multispectral image watermarking technique based on the discrete wavelet transform (DWT and the tucker decomposition (TD is proposed. The core idea behind our proposed technique is to apply TD on the DWT coefficients of spectral bands of multispectral images. We use DWT to effectively separate multispectral images into different sub-images and TD to efficiently compact the energy of sub-images. Then watermark is embedded in the elements of the last frontal slices of the core tensor with the smallest absolute value. The core tensor has a good stability and represents the multispectral image properties. The experimental results on LANDSAT images show the proposed approach is robust against various types of attacks such as lossy compression, cropping, addition of noise etc.

Hai Fang

2013-11-01

218

Replica-symmetry breaking: discrete and continuous schemes in the Sherrington-Kirkpatrick model

International Nuclear Information System (INIS)

We study hierarchies of replica-symmetry-breaking solutions of the Sherrington-Kirkpatrick model. Stationarity equations for order parameters of solutions with an arbitrary number of hierarchies are set and the limit to infinite number of hierarchical levels is discussed. In particular, we demonstrate how the continuous replica-symmetry breaking scheme of Parisi emerges and how the limit to infinite-many hierarchies leads to equations for the order-parameter function of the continuous solution. The general analysis is accompanied by an explicit asymptotic solution near the de Almeida-Thouless instability line in the nonzero magnetic field

219

A new and innovative method for solving the 1D Poisson Equation is presented, using the finite differences method, with Robin Boundary conditions. The exact formula of the inverse of the discretization matrix is determined. This is the first time that this famous matrix is inverted explicitly, without using the right hand side. Thus, the solution is determined in a direct, very accurate (O(h2)), and very fast (O(N)) manner. This new approach treats all cases of boundary c...

Serigne Bira Gueye; Kharouna Talla; Cheikh Mbow

2014-01-01

220

Least-Squares Image Resizing Using Finite Differences

We present an optimal spline-based algorithm for the enlargement or reduction of digital images with arbitrary (noninteger) scaling factors. This projection-based approach can be realized thanks to a new finite difference method that allows the computation of inner products with analysis functions that are B-splines of any degree n. A noteworthy property of the algorithm is that the computational complexity per pixel does not depend on the scaling factor a. For a given choice of basis functio...

Mun?oz Barrutia, A.; Blu, T.; Unser, M.

2001-01-01

221

Some remarks on finite-difference equations of physical interest

Energy Technology Data Exchange (ETDEWEB)

In this paper, the properties of mixed finite-difference and differential equations arising in various physical problems are investigated. First, a prescription for the correct transition to the continuum limit is given and illustrated in some concrete cases. It is further found that, by introducing a suitable generating function associated with a mixed equation, Cauchy's problem for a class of partial differential operators can be solved in a quite simple way.

Casagrande, F.; Montaldi, E. (Milan Univ. (Italy). Ist. di Fisica)

1977-08-21

222

Some remarks on finite-difference equations of physical interest

International Nuclear Information System (INIS)

In this paper, the properties of mixed finite-difference and differential equations arising in various physical problems are investigated. First, a prescription for the correct transition to the continuum limit is given and illustrated in some concrete cases. It is further found that, by introducing a suitable generating function associated with a mixed equation, Cauchy's problem for a class of partial differential operators can be solved in a quite simple way. (author)

223

Using finite difference method to simulate casting thermal stress

Thermal stress simulation can provide a scientific reference to eliminate defects such as crack, residual stress centralization and deformation etc., caused by thermal stress during casting solidification. To study the thermal stress distribution during casting process, a unilateral thermal-stress coupling model was employed to simulate 3D casting stress using Finite Difference Method (FDM), namely all the traditional thermal-elastic-plastic equations are numerically and differentially discre...

Liao Dunming; Zhang Bin; Zhou Jianxin

2011-01-01

224

A simple finite difference procedure for the vortex controlled diffuser

A simple prediction procedure for sudden expansion incompressible flows is developed and applied to the vortex controlled diffuser. Transient Navier-Stokes equations of an incompressible fluid are solved by means of their associated finite difference equations in terms of the primitive pressure velocity variables. A computer code is developed using a laminar flow simulation with free slip or no slip wall boundary conditions. In addition, predicted results confirm that effectiveness increases with increases in duct length and bleed flow rate

Busnaina, A. A.; Lilley, D. G.

1982-01-01

225

This paper proposes a Model Predictive Control (MPC) strategy to address regulation problems for constrained polytopic Linear Parameter Varying (LPV) systems subject to input and state constraints in which both plant measurements and command signals in the loop are sent through communication channels subject to time-varying delays (Networked Control System (NCS)). The results here proposed represent a significant extension to the LPV framework of a recent Receding Horizon Control (RHC) scheme developed for the so-called robust case. By exploiting the parameter availability, the pre-computed sequences of one- step controllable sets inner approximations are less conservative than the robust counterpart. The resulting framework guarantees asymptotic stability and constraints fulfilment regardless of plant uncertainties and time-delay occurrences. Finally, experimental results on a laboratory two-tank test-bed show the effectiveness of the proposed approach.

Franzè, Giuseppe; Lucia, Walter; Tedesco, Francesco

2014-12-01

226

Discrete Wavelet Transform Method: A New Optimized Robust Digital Image Watermarking Scheme

Directory of Open Access Journals (Sweden)

Full Text Available In this paper, a wavelet-based logo watermarking scheme is presented. The logo watermark is embedded into all sub-blocks of the LLn sub-band of the transformed host image, using quantization technique. Extracted logos from all sub-blocks are mixed to make the extracted watermark from distorted watermarked image. Knowing the quantization step-size, dimensions of logo and the level of wavelet transform, the watermark is extracted, without any need to have access to the original image. Robustness of the proposed algorithm was tested against the following attacks: JPEG2000 and old JPEG compression, adding salt and pepper noise, median filtering, rotating, cropping and scaling. The promising experimental results are reported and discussed.

Hassan Talebi

2012-11-01

227

Comparison of Green and Lowtran radiation schemes with a discrete ordinate method UV model

International Nuclear Information System (INIS)

Using the same input parameters for the calculations, the Green and Lowtran codes for calculating UV irradiances were compared to the discrete ordinate method (DOM) model by Stamnes et al., which was used as a reference. The comparisons were performed at 305 and 380 nm for different ozone concentrations, aerosol optical depths and aerosol absorption characteristics. No obvious dependencies on optical depth, single scattering albedo or column ozone were found for the ratio of the Green and the Lowtran code to the DOM model. At 380 nm the Green model agrees with DOM within 10%, whereas the Lowtran code shows discrepancies of ±25%. At 305 nm the Green model shows 10% higher values than the DOM model at low zenith angles and up to 80% lower values for zenith angles between 60 and 80o. The Lowtran code shows 60% higher values than DOM at small zenith angles and 60% lower values at large zenith angles. When the spectra from each model were weighted with the erythemal action spectrum the Green model overestimated the DOM results by less than 10% for zenith angles less than 50o. Discrepancies between DOM and Lowtran models exceeded 10% except for a small range of zenith angles. (Author)

228

A Skin Tone Based Stenographic Scheme using Double Density Discrete Wavelet Transforms.

Directory of Open Access Journals (Sweden)

Full Text Available Steganography is the art of concealing the existence of data in another transmission medium i.e. image, audio, video files to achieve secret communication. It does not replace cryptography but rather boosts the security using its obscurity features. In the proposed method Biometric feature (Skin tone region is used to implement Steganography[1]. In our proposed method Instead of embedding secret data anywhere in image, it will be embedded in only skin tone region. This skin region provides excellent secure location for data hiding. So, firstly skin detection is performed using, HSV (Hue, Saturation, Value color space in cover images. Thereafter, a region from skin detected area is selected, which is known as the cropped region. In this cropped region secret message is embedded using DD-DWT (Double Density Discrete Wavelet Transform. DD-DWT overcomes the intertwined shortcomings of DWT (like poor directional selectivity, Shift invariance, oscillations and aliasing[2].optimal pixel adjustment process (OPA is used to enhance the image quality of the stego-image. Hence the image obtained after embedding secret message (i.e. Stego image is far more secure and has an acceptable range of PSNR. The proposed method is much better than the previous works both in terms of PSNR and robustness against various attacks (like Gaussian Noise, salt and pepper Noise, Speckle Noise, rotation, JPEG Compression, Cropping, and Contrast Adjustment etc.

Varsha Gupta

2013-07-01

229

A finite difference method for the design of gradient coils in MRI--an initial framework.

This paper proposes a finite-difference (FD)-based method for the design of gradient coils in MRI. The design method first uses the FD approximation to describe the continuous current density of the coil space and then employs the stream function method to extract the coil patterns. During the numerical implementation, a linear equation is constructed and solved using a regularization scheme. The algorithm details have been exemplified through biplanar and cylindrical gradient coil design examples. The design method can be applied to unusual coil designs such as ultrashort or dedicated gradient coils. The proposed gradient coil design scheme can be integrated into a FD-based electromagnetic framework, which can then provide a unified computational framework for gradient and RF design and patient-field interactions. PMID:22353392

Zhu, Minhua; Xia, Ling; Liu, Feng; Zhu, Jianfeng; Kang, Liyi; Crozier, Stuart

2012-09-01

230

In this paper we apply the ideas of algebraic topology to the analysis of the finite volume and finite element methods, illuminating the similarity between the discretization strategies adopted by the two methods, in the light of a geometric interpretation proposed for the role played by the weighting functions in finite elements. We discuss the intrinsic discrete nature of some of the factors appearing in the field equations, underlining the exception represented by the constitutive term, the discretization of which is maintained as the key issue for numerical methods devoted to field problems. We propose a systematic technique to perform this task, present a rationale for the adoption of two dual discretization grids and point out some optimization opportunities in the combined selection of interpolation functions and cell geometry for the finite volume method. Finally, we suggest an explanation for the intrinsic limitations of the classical finite difference method in the construction of accurate high order formulas for field problems.

Mattiussi, Claudio

1997-05-01

231

Seismic imaging using finite-differences and parallel computers

Energy Technology Data Exchange (ETDEWEB)

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

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

1997-12-31

232

Directory of Open Access Journals (Sweden)

Full Text Available In this paper, the wave propagation in free space and different dielectric material by using Finite Difference Time Domain (FDTD method has been studied. Among various numerical methods Finite Difference Time Domain method is being used to study the time evolution behavior of electromagnetic field by solving the Maxwell’sequation in time domain. In this paper, FDTD method has been employed to study the wave propagation in free space and different dielectric materials. The wave equations are discretized in time and space as required by this FDTD method and leaf-frog algorithm is used to find the solution. We observed wave propagation for one and two dimensional cases. We also observed wave propagation through lossy medium for one dimensional case. For two dimensional cases the patterns of wave incident on rectangular dielectric slab, square metal, RCC pillar were observed. In order to visualize the wave propagation, the evaluation of the excitation at various locations of problem space is monitored. The numerical results agree with the propagation characteristics as expected.

Md. Kamal Hossain

2010-10-01

233

International Nuclear Information System (INIS)

For analysing the hexagonal reactor by multigroup diffusion theory a two dimensional finite difference code HEXG has been written. Mesh-centred finite difference scheme with hexagonal meshes gives rise to seven point coupling. One can consider 30deg, 60deg, 90deg, 120deg symmetry in addition to a full core treatment. HEXG can be used for analysis of a single fuel assembly with reflective boundary conditions on all sides. One can also perform a detailed core analysis with single fuel pin representation wherein the external boundary condition is either xero flux or vacuum boundary. The solution method is point successive over relaxation (PSOR) with a generalised coarse mesh rebalancing (CMR) acceleration scheme for the inner loop of iterations. HEXG is used for determining the eigenvalue or K-effective, flux, adjoint flux and power distributions in hexagonal lattice/core configurations. (author). 14 refs., 5 tabs., 8 figs

234

Energy conserving and potential-enstrophy dissipating schemes for the shallow water equations

To incorporate potential enstrophy dissipation into discrete shallow water equations with no or arbitrarily small energy dissipation, a family of finite-difference schemes have been derived with which potential enstrophy is guaranteed to decrease while energy is conserved (when the mass flux is nondivergent and time is continuous). Among this family of schemes, there is a member that minimizes the spurious impact of infinite potential vorticities associated with infinitesimal fluid depth. The scheme is, therefore, useful for problems in which the free surface may intersect with the lower boundary.

Arakawa, Akio; Hsu, Yueh-Jiuan G.

1990-01-01

235

Finite difference program for calculating hydride bed wall temperature profiles

International Nuclear Information System (INIS)

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

236

International Nuclear Information System (INIS)

A general adjoint Monte Carlo-forward discrete ordinates radiation transport calculational scheme has been created to study the effects of the radiation environment in Hiroshima and Nagasaki due to the bombing of these two cities. Various such studies for comparison with physical data have progressed since the end of World War II with advancements in computing machinery and computational methods. These efforts have intensified in the last several years with the U.S.-Japan joint reassessment of nuclear weapons dosimetry in Hiroshima and Nagasaki. Three principal areas of investigation are: (1) to determine by experiment and calculation the neutron and gamma-ray energy and angular spectra and total yield of the two weapons; (2) using these weapons descriptions as source terms, to compute radiation effects at several locations in the two cities for comparison with experimental data collected at various times after the bombings and thus validate the source terms; and (3) to compute radiation fields at the known locations of fatalities and surviving individuals at the time of the bombings and thus establish an absolute cause-and-effect relationship between the radiation received and the resulting injuries to these individuals and any of their descendants as indicated by their medical records. It is in connection with the second and third items, the determination of the radiation effects and the dose received by individuals, that the current study is concernede current study is concerned

237

We study effects of both magnetic field and radiation on unsteady free convective magnetohydrodynamic (MHD) flow under the influence of heat and mass transfer. An implicit finite difference scheme of Crank-Nicolson method is used to analyze the results. The governing boundary layer equations along with the initial and boundary conditions are casted into a dimensionless form which results in a more precise solution. We determine the change in velocity under the influence of r...

Ismail, M. N.; Mohamadien, G. F.; Go?ker, U?mit D.

2012-01-01

238

This paper considers the magnetohydrodynamic flow and heat transfer in a viscous incompressible fluid between two parallel porous plates experiencing a discontinuous change in wall temperature. An explicit finite difference scheme has been employed to solve the coupled non-linear equations governing the flow. The flow phenomenon has been characterized by Hartmann number, suction Reynolds number, channel Reynolds number and Prandtl number. The effects of these parameters on the velocity and te...

S S Das, M. Mohanty

2012-01-01

239

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

Lansing, F. L.

1976-01-01

240

Finite difference method to find period-one gait cycles of simple passive walkers

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

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

2015-01-01

241

Using finite difference to solve heat removal in metallic sections industrially produced

This work is dedicated to analyze the heat removal phenomena during the simulation of the continuous casting process of the steel squared sections; it is a useful method to produce big mounts of steel and some other metals such as aluminum. Radiation, forced convection and thermal conduction are the physical phenomena involved. The method used to solve the heat removal and distribution is a finite difference. Steel is discretized using a regular squared mesh. Here a 3D problem is simplified to a 2D in which every node represents a 3D steel volume, but the assumptions are appropriately justified in order to reduce computing time without sacrifice precision on calculation. The efficiency of the method is also evaluated and alternatives to improve the approaching and results are commented.

Ramírez-López, A.; Muñoz-Negron, D.; Palomar-Pardeve, M.; Romero-Romo, M. A.; Cruz-Morales, V.

2012-09-01

242

Dynamic rupture simulation of non-planar faults with a finite-difference approach

Two-dimensional (2-D) modelling of dynamic seismic rupture is performed using a recent staggered-grid finite-difference formulation. Rupture boundary conditions are applied only inside the crack, without assuming any symmetry with respect to the rupture surface. By a simple rotation of the stress tensor, the local orientation of the crack is taken into consideration at each stress point. The grid size is controlled by the source discretization. The greater the number of grid nodes discretizing the finite source, the lower the grid size could be. Below the lower bound value associated with a given discretization, numerical artefacts are not negligible with respect to the spatial frequency content of the dynamic solution. Solutions converge for both point and finite sources by densifying the number of stress points in the source. Numerical scaling of boundary conditions is an important element of this convergence and allows the removal of high-frequency spurious effects of dynamic rupture conditions. For the self-similar crack, a comparison with Kostrov's analytical solution shows that accurate stress singularities are obtained for various crack orientations with respect to the numerical grid. For spontaneous rupture modelling assuming a slip-weakening constitutive law, similar solutions are found for both rupture kinematics and excited wavefield in planar faults with any orientation. Finally, based on these results, rupture propagation over an arbitrary non-planar fault is justified and then performed in the presence of heterogeneous medium.

Cruz-Atienza, V. M.; Virieux, J.

2004-09-01

243

A RBF Based Local Gridfree Scheme for Unsteady Convection-Diffusion Problems

Directory of Open Access Journals (Sweden)

Full Text Available In this work a Radial Basis Function (RBF based local gridfree scheme has been presented for unsteady convection diffusion equations. Numerical studies have been made using multiquadric (MQ radial function. Euler and a three stage Runge-Kutta schemes have been used for temporal discretization. The developed scheme is compared with the corresponding finite difference (FD counterpart and found that the solutions obtained using the former are more superior. As expected, for a fixed time step and for large nodal densities, thought the Runge-Kutta scheme is able to maintain higher order of accuracy over the Euler method, the temporal discretization is independent of the improvement in the solution which in the developed scheme has been achived by optimizing the shape parameter of the RBF.

Sanyasiraju VSS Yedida

2009-12-01

244

Finite difference analysis of curved deep beams on Winkler foundation

Directory of Open Access Journals (Sweden)

Full Text Available This research deals with the linear elastic behavior of curved deep beams resting on elastic foundations with both compressional and frictional resistances. Timoshenko’s deep beam theory is extended to include the effect of curvature and the externally distributed moments under static conditions. As an application to the distributed moment generations, the problems of deep beams resting on elastic foundations with both compressional and frictional restraints have been investigated in detail. The finite difference method was used to represent curved deep beams and the results were compared with other methods to check the accuracy of the developed analysis. Several important parameters are incorporated in the analysis, namely, the vertical subgrade reaction, horizontal subgrade reaction, beam width, and also the effect of beam thickness to radius ratio on the deflections, bending moments, and shear forces. The computer program (CDBFDA (Curved Deep Beam Finite Difference Analysis Program coded in Fortran-77 for the analysis of curved deep beams on elastic foundations was formed. The results from this method are compared with other methods exact and numerical and check the accuracy of the solutions. Good agreements are found, the average percentages of difference for deflections and moments are 5.3% and 7.3%, respectively, which indicate the efficiency of the adopted method for analysis.

Adel A. Al-Azzawi

2011-03-01

245

Arrayed waveguide grating using the finite difference beam propagation method

The purpose of this work is to analyze by simulation the coupling effects occurring in Arrayed Waveguide Grating (AWG) using the finite difference beam propagation method (FD-BPM). Conventional FD-BPM techniques do not immediately lend themselves to the analysis of large structures such as AWG. Cooper et al.1 introduced a description of the coupling between the interface of arrayed waveguides and star couplers using the numerically-assisted coupled-mode theory. However, when the arrayed waveguides are spatially close, such that, there is strong coupling between them, and coupled-mode theory is not adequate. On the other hand, Payne2 developed an exact eigenvalue equation for the super modes of a straight arrayed waveguide which involve a computational overhead. In this work, an integration of both methods is accomplished in order to describe the behavior of the propagation of light in guided curves. This new method is expected to reduce the necessary effort for simulation while also enabling the simulation of large and curved arrayed waveguides using a fully vectorial finite difference technique.

Toledo, M. C. F.; Alayo, M. I.

2013-03-01

246

Finite-Difference Frequency-Domain Method in Nanophotonics

DEFF Research Database (Denmark)

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 in a three-dimensional photonic-crystal membrane-based cavity, a quasi-one-dimensional nanobeam cavity and arrays of side-coupled nanobeam cavities, to modeling light propagation through metal films with single or periodically arranged multiple subwavelength slits.

Ivinskaya, Aliaksandra

2011-01-01

247

Discrete geometric conservation laws (DGCLs) govern the geometric parameters of numerical schemes designed for the solution of unsteady flow problems on moving grids. A DGCL requires that these geometric parameters, which include among others grid positions and velocities, be computed so that the corresponding numerical scheme reproduces exactly a constant solution. Sometimes, this requirement affects the intrinsic design of an arbitrary Lagrangian Eulerian (ALE) solution method. In this paper, we show for sample ALE schemes that satisfying the corresponding DGCL is a necessary and sufficient condition for a numerical scheme to preserve the nonlinear stability of its fixed grid counterpart. We also highlight the impact of this theoretical result on practical applications of computational fluid dynamics.

Farhat, Charbel; Geuzaine, Philippe; Grandmont, Céline

2001-12-01

248

The k-epsilon and direct-stress (DS) turbulence models are applied to two elliptic-flow problems, in order to assess their applicability in an engineering context. Solutions of the model equations are obtained by means of a finite volume method. Accuracy of the numerical solutions is examined with the aid of three discretization schemes: hybrid, QUICK, and a new higher-order, bounded scheme with the acronym CCCT. Numerical experiments indicate that the latter is superior to the former two, for the elliptic-flow problems under consideration. This is because it is free from the effects of first-order numerical diffusion (inherent in the hybrid scheme) and is boundedness preserving (unlike the QUICK scheme). The study suggests that the DS model is more sensitive to capturing streamline curvature effects and corner eddies, than is the k-epsilon model.

Gaskell, P. H.; Lau, A. K. C.

249

Modelling the core convection using finite element and finite difference methods

Applications of both parallel finite element and finite difference methods to thermal convection in a rotating spherical shell modelling the fluid dynamics of the Earth's outer core are presented. The numerical schemes are verified by reproducing the convection benchmark test by Christensen et al. [Christensen, U.R., Aubert, J., Cardin, P., Dormy, E., Gibbons, S., Glatzmaier, G.A., Grote, E., Honkura, Y., Jones, C., Kono, M., Matsushima, M., Sakuraba, A., Takahashi, F., Tilgner, A., Wilcht, J., Zhang, K., 2001. A numerical dynamo benchmark. Phys. Earth Planet. Interiors 128, 25-34.]. Both global average and local characteristics agree satisfactorily with the benchmark solution. With the element-by-element (EBE) parallelization technique, the finite element code demonstrates nearly optimal linear scalability in computational speed. The finite difference code is also efficient and scalable by utilizing a parallel library Aztec [Tuminaro, R.S., Heroux, M., Hutchinson, S.A., Shadid, J.N., 1999. Official AZTEC User's Guide: Version 2.1.].

Chan, K. H.; Li, Ligang; Liao, Xinhao

2006-08-01

250

MasQU: Finite Differences on Masked Irregular Stokes Q,U Grids

The detection of B-mode polarization in the CMB is one of the most important outstanding tests of inflationary cosmology. One of the necessary steps for extracting polarization information in the CMB is reducing contamination from so-called "ambiguous modes" on a masked sky, which contain leakage from the larger E-mode signal. This can be achieved by utilising derivative operators on the real-space Stokes Q and U parameters. This paper presents an algorithm and a software package to perform this procedure on the nearly full sky, i.e., with projects such as the Planck Surveyor and future satellites in mind; in particular, the package can perform finite differences on masked, irregular grids and is applied to a semi-regular spherical pixellization, the HEALPix grid. The formalism reduces to the known finite-difference solutions in the case of a regular grid. We quantify full-sky improvements on the possible bounds on the CMB B-mode signal. We find that in the specific case of E and B-mode separation, there exists a "pole problem" in our formalism which produces signal contamination at very low multipoles l. Several solutions to the "pole problem" are presented; one proposed solution facilitates a calculation of a general Gaussian quadrature scheme, which finds application in calculating accurate harmonic coefficients on the HEALPix sphere. Nevertheless, on a masked sphere the software represents a considerable reduction in B-mode noise from limited sky coverage.

Bowyer, Jude; Jaffe, Andrew H.; Novikov, Dmitri I.

2011-01-01

251

In finite difference time domain simulation of room acoustics, source functions are subject to various constraints. These depend on the way sources are injected into the grid and on the chosen parameters of the numerical scheme being used. This paper addresses the issue of selecting and designing sources for finite difference simulation, by first reviewing associated aims and constraints, and evaluating existing source models against these criteria. The process of exciting a model is generalized by introducing a system of three cascaded filters, respectively, characterizing the driving pulse, the source mechanics, and the injection of the resulting source function into the grid. It is shown that hard, soft, and transparent sources can be seen as special cases within this unified approach. Starting from the mechanics of a small pulsating sphere, a parametric source model is formulated by specifying suitable filters. This physically constrained source model is numerically consistent, does not scatter incoming waves, and is free from zero- and low-frequency artifacts. Simulation results are employed for comparison with existing source formulations in terms of meeting the spectral and temporal requirements on the outward propagating wave. PMID:24437765

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

2014-01-01

252

International Nuclear Information System (INIS)

This paper describes the the next evolution step in development of the direct method for solving systems of Nonlinear Algebraic Equations (SNAE). These equations arise from the finite difference approximation of original nonlinear partial differential equations (PDE). This method has been extended on the SNAE with three variables. The solving SNAE bases on Reiterating General Singular Value Decomposition of rectangular matrix pencils (RGSVD-algorithm). In contrast to the computer algebra algorithm in integer arithmetic based on the reduction to the Groebner's basis that algorithm is working in floating point arithmetic and realizes the reduction to the Kronecker's form. The possibilities of the method are illustrated on the example of solving the one-dimensional diffusion equation for 3-component model isotope mixture in a ga centrifuge. The implicit scheme for the finite difference equations without simplifying the nonlinear properties of the original equations is realized. The technique offered provides convergence to the solution for the single run. The Toolbox SNAE is developed in the framework of the high performance numeric computation and visualization software MATLAB. It includes more than 30 modules in MATLAB language for solving SNAE with two and three variables. (author)

253

In this paper, a novel, unified model-based fault-detection and prediction (FDP) scheme is developed for nonlinear multiple-input-multiple-output (MIMO) discrete-time systems. The proposed scheme addresses both state and output faults by considering separate time profiles. The faults, which could be incipient or abrupt, are modeled using input and output signals of the system. The fault-detection (FD) scheme comprises online approximator in discrete time (OLAD) with a robust adaptive term. An output residual is generated by comparing the FD estimator output with that of the measured system output. A fault is detected when this output residual exceeds a predefined threshold. Upon detecting the fault, the robust adaptive terms and the OLADs are initiated wherein the OLAD approximates the unknown fault dynamics online while the robust adaptive terms help in ensuring asymptotic stability of the FD design. Using the OLAD outputs, a fault diagnosis scheme is introduced. A stable parameter update law is developed not only to tune the OLAD parameters but also to estimate the time to failure (TTF), which is considered as a first step for prognostics. The asymptotic stability of the FDP scheme enhances the detection and TTF accuracy. The effectiveness of the proposed approach is demonstrated using a fourth-order MIMO satellite system. PMID:20106734

Thumati, Balaje T; Jagannathan, S

2010-03-01

254

The discrete energy method in numerical relativity: Towards long-term stability

The energy method can be used to identify well-posed initial boundary value problems for quasi-linear, symmetric hyperbolic partial differential equations with maximally dissipative boundary conditions. A similar analysis of the discrete system can be used to construct stable finite difference equations for these problems at the linear level. In this paper we apply these techniques to some test problems commonly used in numerical relativity and observe that while we obtain convergent schemes, fast growing modes, or ``artificial instabilities,'' contaminate the solution. We find that these growing modes can partially arise from the lack of a Leibnitz rule for discrete derivatives and discuss ways to limit this spurious growth.

Lehner, L; Reula, O; Tiglio, M; Lehner, Luis; Neilsen, David; Reula, Oscar; Tiglio, Manuel

2004-01-01

255

Directory of Open Access Journals (Sweden)

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

Vineet K. Srivastava

2014-03-01

256

Temperature Calculation of Annular Fuel Pellet by Finite Difference Method

International Nuclear Information System (INIS)

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

257

Effects of sources on time-domain finite difference models.

Recent work on excitation mechanisms in acoustic finite difference models focuses primarily on physical interpretations of observed phenomena. This paper offers an alternative view by examining the properties of models from the perspectives of linear algebra and signal processing. Interpretation of a simulation as matrix exponentiation clarifies the separate roles of sources as boundaries and signals. Boundary conditions modify the matrix and thus its modal structure, and initial conditions or source signals shape the solution, but not the modal structure. Low-frequency artifacts are shown to follow from eigenvalues and eigenvectors of the matrix, and previously reported artifacts are predicted from eigenvalue estimates. The role of source signals is also briefly discussed. PMID:24993210

Botts, Jonathan; Savioja, Lauri

2014-07-01

258

Finite-difference modeling of commercial aircraft using TSAR

Energy Technology Data Exchange (ETDEWEB)

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.

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

1994-11-15

259

Visualization of elastic wavefields computed with a finite difference code

Energy Technology Data Exchange (ETDEWEB)

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

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

1994-11-15

260

Computational electrodynamics the finite-difference time-domain method

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.

Taflove, Allen

2005-01-01

261

Preliminary results are presented of a finite element/finite difference method (semidiscrete Galerkin method) used to calculate compressible boundary layer flow about airfoils, in which the group finite element scheme is applied to the Dorodnitsyn formulation of the boundary layer equations. The semidiscrete Galerkin (SDG) method promises to be fast, accurate and computationally efficient. The SDG method can also be applied to any smoothly connected airfoil shape without modification and possesses the potential capability of calculating boundary layer solutions beyond flow separation. Results are presented for low speed laminar flow past a circular cylinder and past a NACA 0012 airfoil at zero angle of attack at a Mach number of 0.5. Also shown are results for compressible flow past a flat plate for a Mach number range of 0 to 10 and results for incompressible turbulent flow past a flat plate. All numerical solutions assume an attached boundary layer.

Strong, Stuart L.; Meade, Andrew J., Jr.

1992-01-01

262

We propose numerical simulations of viscoelastic fluids based on a hybrid algorithm combining Lattice-Boltzmann models (LBM) and Finite Differences (FD) schemes, the former used to model the macroscopic hydrodynamic equations, and the latter used to model the polymer dynamics. The kinetics of the polymers is introduced using constitutive equations for viscoelastic fluids with finitely extensible non-linear elastic dumbbells with Peterlin's closure (FENE-P). The numerical model is first benchmarked by characterizing the rheological behaviour of dilute homogeneous solutions in various configurations, including steady shear, elongational flows, transient shear and oscillatory flows. As an upgrade of complexity, we study the model in presence of non-ideal multicomponent interfaces, where immiscibility is introduced in the LBM description using the "Shan-Chen" model. The problem of a confined viscoelastic (Newtonian) droplet in a Newtonian (viscoelastic) matrix under simple shear is investigated and numerical resu...

Gupta, A; Scagliarini, A

2014-01-01

263

Black-Scholes finite difference modeling in forecasting of call warrant prices in Bursa Malaysia

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

Mansor, Nur Jariah; Jaffar, Maheran Mohd

2014-07-01

264

A full Eulerian finite difference approach for solving fluid-structure coupling problems

A new simulation method for solving fluid-structure coupling problems has been developed. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. A volume-of-fluid formulation (Hirt and Nichols (1981, J. Comput. Phys., 39, 201)), which has been widely used for multiphase flow simulations, is applied to describing the multi-component geometry. The temporal change in the solid deformation is described in the Eulerian frame by updating a left Cauchy-Green deformation tensor, which is used to express constitutive equations for nonlinear Mooney-Rivlin materials. In this paper, various verifications and validations of the present full Eulerian method, which solves the fluid and solid motions on a fixed grid, are demonstrated, and the numerical accuracy involved in the fluid-structure coupling problems is examined.

Sugiyama, Kazuyasu; Takeuchi, Shintaro; Takagi, Shu; Matsumoto, Yoichiro

2010-01-01

265

A full Eulerian finite difference approach for solving fluid-structure coupling problems

A new simulation method for solving fluid-structure coupling problems has been developed. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. A volume-of-fluid formulation [Hirt, Nichols, J. Comput. Phys. 39 (1981) 201], which has been widely used for multiphase flow simulations, is applied to describing the multi-component geometry. The temporal change in the solid deformation is described in the Eulerian frame by updating a left Cauchy-Green deformation tensor, which is used to express constitutive equations for nonlinear Mooney-Rivlin materials. In this paper, various verifications and validations of the present full Eulerian method, which solves the fluid and solid motions on a fixed grid, are demonstrated, and the numerical accuracy involved in the fluid-structure coupling problems is examined.

Sugiyama, Kazuyasu; , Satoshi, Ii; Takeuchi, Shintaro; Takagi, Shu; Matsumoto, Yoichiro

2011-02-01

266

A simple algorithm incorporating with the equivalent heat-capacity model is described for the finite-difference heat-transfer analysis with phase change. The specific heats associated to those nodes adjacent to the fusion front are determined using a linear interpolation of nodal temperatures to properly account for the latent heat effect. Numerical results for both one-dimensional and two-dimensional problems are in good agreement with those existing in the literature. This scheme is proven to be insensitive to the selection of temperature interval 2 delta T assumed for phase change to take place. Therefore, very small or large temperature interval 2 delta T can be used to properly simulate the fusion of pure metal or alloy, respectively. The present algorithm also could be extended to a three-dimensional phase change problem and other nonlinear heat-conduction analyses.

Hsiao, J. S.

1984-12-01

267

GPU Accelerated 2-D Staggered-grid Finite Difference Seismic Modelling

Directory of Open Access Journals (Sweden)

Full Text Available The staggered-grid finite difference (FD method demands significantly computational capability and is inefficient for seismic wave modelling in 2-D viscoelastic media on a single PC. To improve computation speedup, a graphic processing units (GPUs accelerated method was proposed, for modern GPUs have now become ubiquitous in desktop computers and offer an excellent cost-to-performance-ratio parallelism. The geophysical model is decomposed into subdomains for PML absorbing conditions. The vertex and fragment processing are fully used to solve FD schemes in parallel and the latest updated frames are swapped in Framebuffer Object (FBO attachments as inputs for the next simulation step. The seismic simulation program running on modern PCs provides significant speedup over a CPU implementation, which makes it possible to simulate realtime complex seismic propagation in high resolution of 2048*2048 gridsizes on low-cost PCs.

Zhangang Wang

2011-08-01

268

Finite difference preserving the energy properties of a coupled system of diffusion equations

Scientific Electronic Library Online (English)

Full Text Available Neste trabalho, nós provamos a propriedade de decaimento exponencial da energia numérica associada a um particular esquema numérico em diferenças finitas aplicado a um sistema acoplado de equações de difusão. Ao nível da dinâmica do contínuo, é bem conhecido que a energia do sistema é decrescente e [...] exponencialmente estável. Aqui nós apresentamos em detalhes a análise numérica de decaimento exponencial da energia numérica desde que obedecido o critério de estabilidade. Abstract in english In this paper we proved the exponential decay of the energy of a numerical scheme in finite difference applied to a coupled system of diffusion equations. At the continuous level, it is well-known that the energy is decreasing and stable in the exponential sense. We present in detail the numerical a [...] nalysis of exponential decay to numerical energy since holds the stability criterion.

A.J.A., Ramos; D.S., Almeida Jr..

2013-08-01

269

High-order finite difference solution for 3D nonlinear wave-structure interaction

DEFF Research Database (Denmark)

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 OceanWave3D presented in [1, 2]. A nonlinear decomposition of the solution into incident and scattered fields is used to increase the efficiency of the wave-structure interaction problem resolution. Application of the method to the diffraction of nonlinear waves around a fixed, bottom mounted circular cylinder are presented and compared to the fully nonlinear potential code XWAVE as well as to experiments.

Ducrozet, Guillaume; Bingham, Harry B.

2010-01-01

270

A New Time-Dependent Finite Difference Method for Relativistic Shock Acceleration

We present a new approach to calculate the particle distribution function about relativistic shocks including synchrotron losses using the method of lines with an explicit finite difference scheme. A steady, continuous, one dimensional plasma flow is considered to model thick (modified) shocks, leading to a calculation in three dimensions plus time, the former three being momentum, pitch angle and position. The method accurately reproduces the expected power law behaviour in momentum at the shock for upstream flow speeds ranging from 0.1c to 0.995c (1 < \\Gamma < 10). It also reproduces approximate analytical results for the synchrotron cutoff shape for a non-relativistic shock, demonstrating that the loss process is accurately represented. The algorithm has been implemented as a hybrid OpenMP--MPI parallel algorithm to make efficient use of SMP cluster architectures and scales well up to many hundreds of CPUs.

Delaney, Sean; Duffy, Peter; Downes, Turlough P

2011-01-01

271

Computational Electromagnetism with Variational Integrators and Discrete Differential Forms

In this paper, we introduce a general family of variational, multisymplectic numerical methods for solving Maxwell's equations, using discrete differential forms in spacetime. In doing so, we demonstrate several new results, which apply both to some well-established numerical methods and to new methods introduced here. First, we show that Yee's finite-difference time-domain (FDTD) scheme, along with a number of related methods, are multisymplectic and derive from a discrete Lagrangian variational principle. Second, we generalize the Yee scheme to unstructured meshes, not just in space, but in 4-dimensional spacetime. This relaxes the need to take uniform time steps, or even to have a preferred time coordinate at all. Finally, as an example of the type of methods that can be developed within this general framework, we introduce a new asynchronous variational integrator (AVI) for solving Maxwell's equations. These results are illustrated with some prototype simulations that show excellent energy and conservatio...

Stern, Ari; Desbrun, Mathieu; Marsden, Jerrold E

2007-01-01

272

Energy Technology Data Exchange (ETDEWEB)

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

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

1994-12-31

273

Systematic split-step finite difference time domain (SS-FDTD) formulations, based on the general Lie-Trotter-Suzuki product formula, are presented for solving the time-dependent Maxwell equations in double-dispersive electromagnetic materials. The proposed formulations provide a unified tool for constructing a family of unconditionally stable algorithms such as the first order split-step FDTD (SS1-FDTD), the second order split-step FDTD (SS2-FDTD), and the second order alternating direction implicit FDTD (ADI-FDTD) schemes. The theoretical stability of the formulations is included and it has been demonstrated that the formulations are unconditionally stable by construction. Furthermore, the dispersion relation of the formulations is derived and it has been found that the proposed formulations are best suited for those applications where a high space resolution is needed. Two-dimensional (2-D) and 3-D numerical examples are included and it has been observed that the SS1-FDTD scheme is computationally more efficient than the ADI-FDTD counterpart, while maintaining approximately the same numerical accuracy. Moreover, the SS2-FDTD scheme allows using larger time step than the SS1-FDTD or ADI-FDTD and therefore necessitates less CPU time, while giving approximately the same numerical accuracy.

Ramadan, Omar

2014-12-01

274

In this paper a high-order implicit multi-step method, known in the literature as Two Implicit Advanced Step-point (TIAS) method, has been implemented in a high-order Discontinuous Galerkin (DG) solver for the unsteady Euler and Navier-Stokes equations. Application of the absolute stability condition to this class of multi-step multi-stage time discretization methods allowed to determine formulae coefficients which ensure A-stability up to order 6. The stability properties of such schemes have been verified by considering linear model problems. The dispersion and dissipation errors introduced by TIAS method have been investigated by looking at the analytical solution of the oscillation equation. The performance of the high-order accurate, both in space and time, TIAS-DG scheme has been evaluated by computing three test cases: an isentropic convecting vortex under two different testing conditions and a laminar vortex shedding behind a circular cylinder. To illustrate the effectiveness and the advantages of the proposed high-order time discretization, the results of the fourth- and sixth-order accurate TIAS schemes have been compared with the results obtained using the standard second-order accurate Backward Differentiation Formula, BDF2, and the five stage fourth-order accurate Strong Stability Preserving Runge-Kutta scheme, SSPRK4.

Nigro, Alessandra; De Bartolo, Carmine; Bassi, Francesco; Ghidoni, Antonio

2014-11-01

275

3D anisotropic modeling for airborne EM systems using finite-difference method

Most current airborne EM data interpretations assume an isotropic model, which is sometimes inappropriate, especially in regions with distinct dipping anisotropy due to strong layering and stratifications. In this paper, we investigate airborne EM modeling and interpretation for a 3D earth with arbitrarily electrical anisotropy. We implement the staggered finite-difference algorithm to solve the coupled partial differential equations for the scattered electrical fields. Whereas the current density that is connected to the diagonal elements of the anisotropic conductivity tensor is discretized by using the volume weighted average, the current density that is connected to the non-diagonal elements is discretized by using the volume current density average. Further, we apply a divergence correction technique designed specifically for 3D anisotropic models to speed up the modeling process. For numerical experiments, we take both VMD and HMD transmitting dipoles for two typical anisotropic cases: 1) anisotropic anomalous inhomogeneities embedded in an isotropic half-space; and 2) isotropic anomalous inhomogeneities embedded in an anisotropic host rock. Model experiments show that our algorithm has high calculation accuracy, the divergence correction technique used in the modeling can greatly improve the convergence of the solutions, accelerating the calculation speed up to 2 times for the model presented in the paper. The characteristics inside the anisotropic earth, like the location of the anomalous body and the principal axis orientations, can also be clearly identified from AEM area surveys.

Liu, Yunhe; Yin, Changchun

2014-10-01

276

FLUOMEG: a planar finite difference mesh generator for fluid flow problems with parallel boundaries

International Nuclear Information System (INIS)

A two- or three-dimensional finite difference mesh generator capable of discretizing subrectangular flow regions (planar coordinates) with arbitrarily shaped bottom contours (vertical dimension) was developed. This economical, interactive computer code, written in FORTRAN IV and employing DISSPLA software together with graphics terminal, generates first a planar rectangular grid of variable element density according to the geometry and local kinematic flow patterns of a given fluid flow problem. Then subrectangular areas are deleted to produce canals, tributaries, bays, and the like. For three-dimensional problems, arbitrary bathymetric profiles (river beds, channel cross section, ocean shoreline profiles, etc.) are approximated with grid lines forming steps of variable spacing. Furthermore, the code works as a preprocessor numbering the discrete elements and the nodal points. Prescribed values for the principal variables can be automatically assigned to solid as well as kinematic boundaries. Cabinet drawings aid in visualizing the complete flow domain. Input data requirements are necessary only to specify the spacing between grid lines, determine land regions that have to be excluded, and to identify boundary nodes. 15 figures, 2 tables

277

In this paper, we propose an effective numerical method for solving nonlinear Volterra partial integro-differential equations. These equations include the partial differentiations of an unknown function and the integral term containing the unknown function as the "memory" of system. Radial basis functions and finite difference method as the main techniques play the important role to reduce a nonlinear partial integro-differential equation to a linear system of equations. Some examples are demonstrated to describe the method. Numerical results confirm the validity and efficiency of the presented method.

Avazzadeh, Z.; Rizi, Z. Beygi; Ghaini, F. M. Maalek; Loghmani, G. B.

2011-06-01

278

In this paper, a three-dimensional (3D) finite-difference lattice Boltzmann model for simulating compressible flows with shock waves is developed in the framework of the double-distribution-function approach. In the model, a density distribution function is adopted to model the flow field, while a total energy distribution function is adopted to model the temperature field. The discrete equilibrium density and total energy distribution functions are derived from the Hermite expansions of the continuous equilibrium distribution functions. The discrete velocity set is obtained by choosing the abscissae of a suitable Gauss-Hermite quadrature with sufficient accuracy. In order to capture the shock waves in compressible flows and improve the numerical accuracy and stability, an implicit-explicit finite-difference numerical technique based on the total variation diminishing flux limitation is introduced to solve the discrete kinetic equations. The model is tested by numerical simulations of some typical compressible flows with shock waves ranging from 1D to 3D. The numerical results are found to be in good agreement with the analytical solutions and/or other numerical results reported in the literature.

He, Ya-Ling; Liu, Qing; Li, Qing

2013-10-01

279

Directory of Open Access Journals (Sweden)

Full Text Available Results of a sensitivity study are presented from various configurations of the NEMO ocean model in the Black Sea. The standard choices of vertical discretization, viz. z levels, s coordinates and enveloped s coordinates, all show their limitations in the areas of complex topography. Two new hybrid vertical coordinate schemes are presented: the "s-on-top-of-z" and its enveloped version. The hybrid grids use s coordinates or enveloped s coordinates in the upper layer, from the sea surface to the depth of the shelf break, and z-coordinates are set below this level. The study is carried out for a number of idealised and real world settings. The hybrid schemes help reduce errors generated by the standard schemes in the areas of steep topography. Results of sensitivity tests with various horizontal diffusion formulations are used to identify the optimum value of Smagorinsky diffusivity coefficient to best represent the mesoscale activity.

G. Shapiro

2013-03-01

280

A mixed finite difference method for calculating the external and internal flow field around inlet with centerbody is presented. First, calculation by mixed finite difference method of the velocity potential equation with small disturbance in the transverse direction using Cartesian mesh, irrotational schemes, and exact body surface boundary conditions is carried out to obtain a basic field solution including the shape and location of the shock and the sonic line. Then, the full potential equation is used to improve the accuracy of the computed value of field variables. The use of multi-layer line relaxations along the radial lines is effective for inlet with centerbody, and in this case, more relaxation sweeps are carried out (with smaller relaxation factor) inside the inlet than outside. Computations were made for axisymmetric inlet with different freestream Mach numbers M (infinity) = 1.04 to approximately 1.27. Computation results show that the method is promising.

Luo, S.; Shen, H.; Ji, M.; Xing, Z.; Dong, S.; Han, A.

1984-09-01

281

Kelvin wave propagation along straight boundaries in C-grid finite-difference models

Discrete solutions for the propagation of coastally-trapped Kelvin waves are studied, using a second-order finite-difference staggered grid formulation that is widely used in geophysical fluid dynamics (the Arakawa C-grid). The fundamental problem of linear, inviscid wave propagation along a straight coastline is examined, in a fluid of constant depth with uniform background rotation, using the shallow-water equations which model either barotropic (surface) or baroclinic (internal) Kelvin waves. When the coast is aligned with the grid, it is shown analytically that the Kelvin wave speed and horizontal structure are recovered to second-order in grid spacing h. When the coast is aligned at 45° to the grid, with the coastline approximated as a staircase following the grid, it is shown analytically that the wave speed is only recovered to first-order in h, and that the horizontal structure of the wave is infected by a thin computational boundary layer at the coastline. It is shown numerically that such first-order convergence in h is attained for all other orientations of the grid and coastline, even when the two are almost aligned so that only occasional steps are present in the numerical coastline. Such first-order convergence, despite the second-order finite differences used in the ocean interior, could degrade the accuracy of numerical simulations of dynamical phenomena in which Kelvin waves play an important role. The degradation is shown to be particularly severe for a simple example of near-resonantly forced Kelvin waves in a channel, when the energy of the forced response can be incorrect by a factor of 2 or more, even with 25 grid points per wavelength.

Griffiths, Stephen D.

2013-12-01

282

A 3D Mimetic Finite Difference Method for Rupture Dynamics

We are developing a method for solving earthquake rupture dynamics problems on structured curvilinear meshes. The advantage of a curvilinear mesh over a rectangular mesh is that it can accommodate free-surface topography as well as non-planar fault geometry. The advantages of using a structured mesh over an unstructured mesh (as used in many finite element methods) is simplicity and computational efficiency. Structured meshes also make a number of computational tasks easier, such as parallelization, or coupling with other codes that use similar structured meshes. To build the discretized equations of motion on a structured, yet non Cartesian mesh, we use a mimetic method, so named because it takes special care to mimic the important conservation properties of the original equations of motion. We begin by writing the equations of motion in terms of gradient and divergence operators. We then derive a discrete grad (or div) operator by differentiating an interpolation function of the discrete variable. Next, that grad (or div) operator is plugged into a discrete analog of Gauss' Identity and manipulated to find the adjoint div (or grad) operator. We use a computer algebra system to handle the manipulations, which is practically essential for the 3D case because of the extreme lengths of the expressions to be coded. The code is currently implemented as a "rapid prototype" in MATLAB and undergoing validation prior to conversion to a high performance language. We compare results for simple types of rupture that have analytical solutions.

Ely, G.; Minster, J.; Day, S.

2004-12-01

283

Finite Element - Finite Difference Coupling for Elastodynamic Rupture Propagation

On one hand, the classical finite element (FE) method on triangular unstructured mesh provides a robust and highly adaptive geometrical description of fault interfaces, but implies the resolution of a costly non-linear system of equations at each time step. On the other hand, the finite difference (FD) method is a low-cost and accurate method for wave propagation but cannot handle complex fault geometries. To cumulate both methods' advantages, FE and FD are coupled as follows. The FE domain, which includes faults, is embedded in a surrounding velocity-stress FD domain. On the FE mesh, an iterative domain decomposition technique is used to solve the non-linear problem. Both 2D SH and PSV configurations are considered. In SH, various coupling strategies are compared: coupling by the velocity field, by the stress field or both; with fully staggered FD grid or rotated staggered FD grid; with FD of order 2 or 4; with or without interpolation of the coupled field. Results are very comparable but it turns out that the simplest method is the coupling by velocity. In PSV, it comes out that the rotated staggered grid is the best option. To conclude, some simulations of rupture propagation on discontinuous faults are presented.

Wolf, S.; Favreau, P.; Ionescu, I. R.

2006-12-01

284

A finite difference model for free surface gravity drainage

Energy Technology Data Exchange (ETDEWEB)

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

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

1993-09-01

285

Finite Difference Simulation and Imaging of Seismic Waves in Complex Media.

Seismic wave propagation in two-dimensional non -homogeneous porous media is simulated with a finite difference method which solves the first order hyperbolic systems based on the theories developed by Biot, and de la Cruz and Spanos. Original solutions for a P-wave point or line source in a uniform porous medium are derived for the purposes of source implementation and algorithm testing. The existence of seismically observable differences due to the presence of pores has been examined through synthetic examples, which indicate that amplitude versus offset variations may be observed on receivers at increasing distance and could be diagnostic of the matrix and fluid parameters. These methods are applied in simulating seismic wave propagation over an expanded steam heated zone in Cold Lake Alberta area in enhanced oil recovery processing. New approaches are developed to construct absorbing boundaries in wave modeling problems. A wave propagation modification technique and one-way sponge filter technique are developed. Either of these approaches, when combined with the one-dimensional absorbing boundary conditions, absorbs not only the body waves but also surface waves effectively even in the poroelastic wave modeling where three types of waves may be present. A velocity-pressure finite difference method is developed for modeling viscoacoustic wave propagation in heterogeneous media. A viscoacoustic medium is approximated by a generalized Maxwell body and a first order hyperbolic system is formulated to describe the wave motion. Viscoacoustic synthetic seismograms have been computed and compared with data from crosshole seismic experiments for monitoring steam injection projects in the Cold Lake area. An original first order hyperbolic system is formulated for one-way waves in heterogeneous media. This system is used in implementing absorbing boundaries and extrapolating wave field in the space-time domain. A back-propagation method is developed to implement seismic depth migration with an explicit finite difference scheme at a reduced computational cost. A number of examples illustrate the application of the one-way wave system in modelling, in absorbing reflections from the computational boundaries and in migrating pre-stack and post-stack synthetic seismic data.

Dai, Nanxun

286

Finite-difference time-domain simulations of metamaterials

Metamaterials are periodic structures created by many identical scattering objects which are stationary and small compared to the wavelength of electromagnetic wave applied to it so that when combined with different elements, these materials have the potential to be coupled to the applied electromagnetic wave without modifying the structure. Due to their unusual properties that are not readily available in nature, metamaterials have been drawing significant attentions in many research areas, including theoretical, experimental as well as numerical investigations. As one of the major computational electromagnetic modeling methods, finite-difference time-domain (FDTD) technique tackles problems by providing a full wave solution. FDTD, which is able to show transient evolution of interactions between electromagnetic wave and physical objects, not only has the advantage in dispersive and nonlinear material simulations, but also has the ability to model circuit elements including semiconductor devices. All these features make FDTD a competitive candidate in numerical methods of metamaterial simulations. This dissertation presents the implementation of FDTD technique to deal with three dimensional (3D) problems characterized with metamaterial structures. We endeavor to make the FDTD engine multi-functional and fast, as depicted in the following three efforts: (1) We incorporated FDTD engine with the stable and highly efficient model for materials with dispersion, nonlinearity and gain properties. (2) We coupled FDTD engine with SPICE, the general-purpose and powerful analog electronic circuit simulator. This makes FDTD ready to simulate complex semiconductor devices and provides a variety of possibilities for novel metamaterials. (3) We investigated the cutting-edge area of Graphics Processing Units (GPU) computing module to speed up the FDTD engine, and implemented subgridding system to target more efficient modeling for metamaterial applications with embedded fine structures. The contribution of this work is toward the development of a powerful FDTD engine for modern metamaterial analysis. Our implementation could be used to improve the analysis of a number of electromagnetic problems.

Hao, Zhengwei

287

In this paper we propose a fundamentally different conjugate gradient method, in which the well-known parameter [beta]k is computed by an approximation of the Hessian/vector product through finite differences. For search direction computation, the method uses a forward difference approximation to the Hessian/vector product in combination with a careful choice of the finite difference interval. For the step length computation we suggest an acceleration scheme able to improve the efficiency of the algorithm. Under common assumptions, the method is proved to be globally convergent. It is shown that for uniformly convex functions the convergence of the accelerated algorithm is still linear, but the reduction in function values is significantly improved. Numerical comparisons with conjugate gradient algorithms including CONMIN by Shanno and Phua [D.F. Shanno, K.H. Phua, Algorithm 500, minimization of unconstrained multivariate functions, ACM Trans. Math. Softw. 2 (1976) 87-94], SCALCG by Andrei [N. Andrei, Scaled conjugate gradient algorithms for unconstrained optimization, Comput. Optim. Appl. 38 (2007) 401-416; N. Andrei, Scaled memoryless BFGS preconditioned conjugate gradient algorithm for unconstrained optimization, Optim. Methods Softw. 22 (2007) 561-571; N. Andrei, A scaled BFGS preconditioned conjugate gradient algorithm for unconstrained optimization, Appl. Math. Lett. 20 (2007) 645-650], and new conjugacy condition and related new conjugate gradient by Li, Tang and Wei [G. Li, C. Tang, Z. Wei, New conjugacy condition and related new conjugate gradient methods for unconstrained optimization, J. Comput. Appl. Math. 202 (2007) 523-539] or truncated Newton TN by Nash [S.G. Nash, Preconditioning of truncated-Newton methods, SIAM J. on Scientific and Statistical Computing 6 (1985) 599-616] using a set of 750 unconstrained optimization test problems show that the suggested algorithm outperforms these conjugate gradient algorithms as well as TN.

Andrei, Neculai

2009-08-01

288

International Nuclear Information System (INIS)

Seismic waves radiated from an earthquake propagate in the Earth and the ground shaking is felt and recorded at (or near) the ground surface. Understanding the wave propagation with respect to the Earth's structure and the earthquake mechanisms is one of the main objectives of seismology, and predicting the strong ground shaking for moderate and large earthquakes is essential for quantitative seismic hazard assessment. The finite difference scheme for solving the wave propagation problem in elastic (sometimes anelastic) media has been more widely used since the 1970s than any other numerical methods, because of its simple formulation and implementation, and its easy scalability to large computations. This paper briefly overviews the advances in finite difference simulations, focusing particularly on earthquake mechanics and the resultant wave radiation in the near field. As the finite difference formulation is simple (interpolation is smooth), an easy coupling with other approaches is one of its advantages. A coupling with a boundary integral equation method (BIEM) allows us to simulate complex earthquake source processes

289

International Nuclear Information System (INIS)

Heat pipes are being considered as a part of the thermal management system of many space crafts due to the fact that heat pipes are capable of passively transporting large amounts of thermal energy over considerable distances with essentially no temperature drop. Mathematical modeling of heat pipe performance has been developed for both transient and steady state modes: however, existing transient heat pipe models are of limited accuracy during vary rapid transients. The modeling of the response of the vapor region in the event of rapid transients (including frozen start-ups) has not been investigated fully. The purpose of this study is to model the performance of a screened wick heat pipe in rapid transient modes and to determine the limiting conditions under which the heat pipe will operate

290

Mixed convection heat transfer in two-dimensional lid-driven rectangular cavity filled with air (Pr=0.71) is studied numerically. A hybrid scheme with multiple relaxation time lattice Boltzmann method (MRT-LBM) is used to obtain the velocity field while the temperature field is deduced from energy balance equation by using the finite difference method (FDM). The main objective of this work is to investigate the model effectiveness for mixed convection flow simulation. Results are presented in terms of streamlines, isotherms and Nusselt numbers. Excellent agreement is obtained between our results and previous works. The different comparisons demonstrate the robustness and the accuracy of our proposed approach.

Bettaibi, Soufiene; Kuznik, Frédéric; Sediki, Ezeddine

2014-06-01

291

International Nuclear Information System (INIS)

The use of the albedo boundary conditions for multigroup one-dimensional neutron transport eigenvalue problems in the discrete ordinates (SN) formulation is described. The hybrid spectral diamond-spectral Green's function (SD-SGF) nodal method that is completely free from all spatial truncation errors, is used to determine the multigroup albedo operator. In the inner iteration it is used the 'one-node block inversion' (NBI) iterative scheme, which has convergence rate greater than the modified source iteration (SI) scheme. The power method for convergence of the dominant numerical solution is accelerated by the Tchebycheff method. Numerical results are given to illustrate the method's efficiency. (author). 7 refs, 4 figs, 3 tabs

292

Finite-difference numerical simulations of underground explosion cavity decoupling

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 source located at the center of a spherical cavity generates only diverging compressional waves. However, we find that shear waves are generated by an off-center source, or by a non-spherical cavity (e.g. a tunnel). Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

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

2012-12-01

293

Finite-Difference Numerical Simulation of Seismic Gradiometry

We use the phrase seismic gradiometry to refer to the developing research area involving measurement, modeling, analysis, and interpretation of spatial derivatives (or differences) of a seismic wavefield. In analogy with gradiometric methods used in gravity and magnetic exploration, seismic gradiometry offers the potential for enhancing resolution, and revealing new (or hitherto obscure) information about the subsurface. For example, measurement of pressure and rotation enables the decomposition of recorded seismic data into compressional (P) and shear (S) components. Additionally, a complete observation of the total seismic wavefield at a single receiver (including both rectilinear and rotational motions) offers the possibility of inferring the type, speed, and direction of an incident seismic wave. Spatially extended receiver arrays, conventionally used for such directional and phase speed determinations, may be dispensed with. Seismic wave propagation algorithms based on the explicit, time-domain, finite-difference (FD) numerical method are well-suited for investigating gradiometric effects. We have implemented in our acoustic, elastic, and poroelastic algorithms a point receiver that records the 9 components of the particle velocity gradient tensor. Pressure and particle rotation are obtained by forming particular linear combinations of these tensor components, and integrating with respect to time. All algorithms entail 3D O(2,4) FD solutions of coupled, first- order systems of partial differential equations on uniformly-spaced staggered spatial and temporal grids. Numerical tests with a 1D model composed of homogeneous and isotropic elastic layers show isolation of P, SV, and SH phases recorded in a multiple borehole configuration, even in the case of interfering events. Synthetic traces recorded by geophones and rotation receivers in a shallow crosswell geometry with randomly heterogeneous poroelastic models also illustrate clear P (fast and slow) and S separation. Finally, numerical tests of the "point seismic array" concept are oriented toward understanding its potential and limitations. Sandia National Laboratories is a multiprogram science and engineering facility operated by Sandia Corporation, a Lockheed-Martin company, for the United States Department of Energy under contract DE- AC04-94AL85000.

Aldridge, D. F.; Symons, N. P.; Haney, M. M.

2006-12-01

294

Dynamic ultimate load analysis using a finite difference method

International Nuclear Information System (INIS)

The method of numerical integration is explained on a one-degree-of-freedom system. A generalization to systems with several degrees of freedom is given. The conditions for numerical stability and for getting a sufficient approximation to the exact solution of the differential equations are dealt with. Not only a time discretization but also a geometric discretization is necessary. This may be anticipated by a lumped-mass dynamic model, or, with continuous bodies, it could be performed, e.g., by a mesh pattern of finite coordinate differences. Examples are given for the numerical treatment especially of beams and plates. Starting from the corresponding differential equations describing a process of wave propagation, the rotational inertia of single beam or plate elements as well as the transverse shear deformations are included. By this numerical method of dynamic analysis suitable for computer programming, point-by-point time-history solutions are obtained for deterministic excitations and for material properties, both varying arbitrarily with time and space. Applications for practical dynamic problems of nuclear structural design taking into account a defined material ductility are discussed. (orig./HP)

295

Dynamic Rupture Simulation of Bent Faults with a New Finite Difference Approach

Many questions about physical parameters governing the rupture propagation of earthquakes find their answers within realistic dynamic considerations. For instance, sophisticated constitutive relations based on laboratory experiments have led to a better understanding of rupture evolution from its very beginning to its arrest. In fact, large amount of field observations as well as recent simulations have shown the importance of considering more reasonable geological settings (e.g., bent and step-over fault geometries; heterogeneous surrounding media). However, despite the development of powerful numerical tools, one important question remains unanswered. How important is in rupture process the feedback coming from a heterogeneous structure if the fault geometry is complex? To start answering this question, we propose a numerical approach based in a new staggered-grid finite-difference technique. In this work, we use a recently proposed four-order staggered-grid finite-difference scheme to dynamically model in-plane (mode II) shear fracturing propagation in faults with any pre-established geometry. In contrast with the classical 2-D staggered grid elementary cell in which all the elastic fields are defined in different positions (except the normal stresses), the stencil used here considers the velocity and stress fields separately in only two staggered grids. Such an elementary structure is a straightforward consequence of a new definition of the four-order spatial differential operators: they are decoupled into two 45-degree rotated operators. This approach permits efficient treatment of boundary conditions to impose the shear stress drop in the nodes where the entire stress tensor is located. Furthermore, this procedure reduces numerical anisotropy along preferred directions and provides stable solutions for any fault orientation. The fault is defined as a set of point sources placed in the middle of the grid without using any ad hoc numerical ghost plane often used in finite-difference approaches. Thus, the fault is a sum of point sources that are taken as close as possible from the given analytical fault line. One point source is defined as a cluster of stress-grid points. Numerically, there exist different point-source configurations that are equivalent. However, configurations with more stress-grid points allow better rupture simulations for any fault geometry. Simulations with the standard slip-weakening constitutive law are presented. To quantify the slip upon every point source having any fault orientation, we define a slip function which depends on the displacement field around every point source but not in the fault plane orientation. We also present spontaneous and velocity fixed self-similar simulations. As we are dealing with a finite-difference approach, the proposed methodology makes possible to analyze the effect of arbitrary heterogeneous media surrounding the fault region in the dynamics of seismic sources evolution.

Cruz-Atienza, V. M.; Virieux, J.; Operto, S.

2003-04-01

296

Finite difference modelling of bulk high temperature superconducting cylindrical hysteresis machines

International Nuclear Information System (INIS)

A mathematical model of the critical state based on averaged fluxon motion has been implemented to solve for the current and field distributions inside a high temperature superconducting hysteresis machine. The machine consists of a rotor made from a solid cylindrical single domain HTS placed in a perpendicular rotating field. The solution technique uses the finite difference approximation for a two-dimensional domain, discretized in cylindrical polar co-ordinates. The torque generated or equivalently the hysteresis loss in such a machine has been investigated using the model. It was found that to maximize the efficiency, the field needs to penetrate the rotor such that B0/?0JcR=0.56, where B0 is the applied field amplitude, Jc is the critical current density and R is the rotor radius. This corresponds to a penetration that is 27% greater than that which reaches the centre of the rotor. An examination of the torque density distributions across the rotor reveal that for situations where the field is less than optimal, a significant increase in the performance can be achieved by removing an inner cylinder from the rotor. (author)

297

International Nuclear Information System (INIS)

The lowest order Nodal Integral Method (NIM) which belongs to a large class of nodal methods, the Lawrence-Dorning class, is written in a five-point, weighted-difference form and contrasted against the edge-centered Finite Difference Method (FDM). The final equations for the two methods exhibit three differences: the NIM employs almost three times as many discrete-variables (which are node- and surface-averaged values of the flux) as the FDM; the spatial weights in the NIM include hyperbolic functions opposed to the algebraic weights in the FDM; the NIM explicitly imposes continuity of the net current across cell edges. A homogeneous model problem is devised to enable an analytical study of the numerical solutions accuracy. The analysis shows that on a given mesh the FDM calculated fundamental mode eigenvalue is more accurate than that calculated by the NIM. However, the NIM calculated flux distribution is more accurate, especially when the problem size is several times as thick as the diffusion length. Numerical results for a nonhomogeneous test problem indicate the very high accuracy of the NIM for fixed source problems in such cases. 18 refs., 1 fig., 1 tab

298

Energy Technology Data Exchange (ETDEWEB)

The isotropic elastic wave equation governs the propagation of seismic waves caused by earthquakes and other seismic events. It also governs the propagation of waves in solid material structures and devices, such as gas pipes, wave guides, railroad rails and disc brakes. In the vast majority of wave propagation problems arising in seismology and solid mechanics there are free surfaces. These free surfaces have, in general, complicated shapes and are rarely flat. Another feature, characterizing problems arising in these areas, is the strong heterogeneity of the media, in which the problems are posed. For example, on the characteristic length scales of seismological problems, the geological structures of the earth can be considered piecewise constant, leading to models where the values of the elastic properties are also piecewise constant. Large spatial contrasts are also found in solid mechanics devices composed of different materials welded together. The presence of curved free surfaces, together with the typical strong material heterogeneity, makes the design of stable, efficient and accurate numerical methods for the elastic wave equation challenging. Today, many different classes of numerical methods are used for the simulation of elastic waves. Early on, most of the methods were based on finite difference approximations of space and time derivatives of the equations in second order differential form (displacement formulation), see for example [1, 2]. The main problem with these early discretizations were their inability to approximate free surface boundary conditions in a stable and fully explicit manner, see e.g. [10, 11, 18, 20]. The instabilities of these early methods were especially bad for problems with materials with high ratios between the P-wave (C{sub p}) and S-wave (C{sub s}) velocities. For rectangular domains, a stable and explicit discretization of the free surface boundary conditions is presented in the paper [17] by Nilsson et al. In summary, they introduce a discretization, that use boundary-modified difference operators for the mixed derivatives in the governing equations. Nilsson et al. show that the method is second order accurate for problems with smoothly varying material properties and stable under standard CFL constraints, for arbitrarily varying material properties. In this paper we generalize the results of Nilsson et al. to curvilinear coordinate systems, allowing for simulations on non-rectangular domains. Using summation by parts techniques, we show that there exists a corresponding stable discretization of the free surface boundary condition on curvilinear grids. We also prove that the discretization is stable and energy conserving both in semi-discrete and fully discrete form. As for the Cartesian method in, [17], the stability and conservation results holds for arbitrarily varying material properties. By numerical experiments it is established that the method is second order accurate.

Appelo, D; Petersson, N A

2007-12-17

299

Vertical Discretization of Hydrostatic Primitive Equations with Finite Element Method

A vertical finite element (VFE) discretization of hydrostatic primitive equations is developed for the dynamical core of a numerical weather prediction (NWP) system at KIAPS, which is horizontally discretized by a spectral element on a cubed-sphere grid. The governing equations are discretized on a hybrid pressure-based vertical coordinate [1]. Compared with a vertical finite difference (VFD) discretization, which is only first order accurate for non-uniform grids, the VFE has many advantages such that it gives more accurate results, all variables are defined in the same full level, the level of vertical noise might be reduced [2], and it is easily coupled with existing physics packages, developed for a Lorentz staggering grid system. Due to these reasons, we adopted the VFE scheme presented by Untch [2] for the vertical discretization. Instead of using semi-Lagrangian and semi-implicit schemes of ECMWF, we use the Eulerian equations and second-order Runge-Kutta scheme as the first step in implementing the VFE for the dynamical core of the KIAPS's NWP model. Since the Eulerian hydrostatic equations are used in this study, both integral and derivative operators are required to implement the VFE using the Galerkin method with b-splines as basis functions. To compare the accuracy of the VFE with the VFD, the two-dimensional test case of mountain waves is used where physical configuration and initial conditions are the same as that of Durran [3]. In this case, the horizontal and vertical velocities obtained by the analytical solution, VFD, VFE-linear and VFE-cubic are compared to understand their numerical features and the vertical flux of horizontal momentum is also presented as the measurement of solution accuracy since it is sensitive to errors in a solution [3]. It is shown that the VFE with a cubic b-spline function is more accurate than the VFD and VFE with a linear b-spline function as the vertical flux is closer to unity, which will be presented in the conference. Reference Simmons, A. J., Burridge, D. M., 1981: An energy and angular momentum conserving vertical finite difference scheme and hybrid vertical coordinates. Mon. Wea. Rev., 109, 758-766. Untch, A., Hortal, M., 2004: A finite-element schemes for the vertical discretization of the semi-Lagrangian version of the ECMWF forecast model. Q. J. R. Meteorol. Soc., 130, 1505-1530. Durran, D. R., Klemp, J. B., 1983: A compressible model for the simulation of moist mountain waves. Mon. Wea. Rev., 111, 2341-2361.

Yi, Tae-Hyeong; Park, Ja-Rin

2014-05-01

300

Accurate 3-D finite difference computation of traveltimes in strongly heterogeneous media

Seismic traveltimes and their spatial derivatives are the basis of many imaging methods such as pre-stack depth migration and tomography. A common approach to compute these quantities is to solve the eikonal equation with a finite-difference scheme. If many recently published algorithms for resolving the eikonal equation do now yield fairly accurate traveltimes for most applications, the spatial derivatives of traveltimes remain very approximate. To address this accuracy issue, we develop a new hybrid eikonal solver that combines a spherical approximation when close to the source and a plane wave approximation when far away. This algorithm reproduces properly the spherical behaviour of wave fronts in the vicinity of the source. We implement a combination of 16 local operators that enables us to handle velocity models with sharp vertical and horizontal velocity contrasts. We associate to these local operators a global fast sweeping method to take into account all possible directions of wave propagation. Our formulation allows us to introduce a variable grid spacing in all three directions of space. We demonstrate the efficiency of this algorithm in terms of computational time and the gain in accuracy of the computed traveltimes and their derivatives on several numerical examples.

Noble, M.; Gesret, A.; Belayouni, N.

2014-12-01

301

Treatment of late time instabilities in finite difference EMP scattering codes

International Nuclear Information System (INIS)

Time-domain solutions to the finite-differenced Maxwell's equations give rise to several well-known nonphysical propagation anomalies. In particular, when a radiative electric-field look back scheme is employed to terminate the calculation, a high-frequency, growing, numerical instability is introduced. This paper describes the constraints made on the mesh to minimize this instability, and a technique of applying an absorbing sheet to damp out this instability without altering the early time solution. Also described are techniques to extend the data record in the presence of high-frequency noise through application of a low-pass digital filter and the fitting of a damped sinusoid to the late-time tail of the data record. An application of these techniques is illustrated with numerical models of the FB-111 aircraft and the B-52 aircraft in the in-flight refueling configuration using the THREDE finite difference computer code. Comparisons are made with experimental scale model measurements with agreement typically on the order of 3 to 6 dB near the fundamental resonances

302

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

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

Bollig, Evan F.; Flyer, Natasha; Erlebacher, Gordon

2012-08-01

303

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

International Nuclear Information System (INIS)

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

304

Rigorous interpolation near tilted interfaces in 3-D finite-difference EM modelling

We present a rigorous method for interpolation of electric and magnetic fields close to an interface with a conductivity contrast. The method takes into account not only a well-known discontinuity in the normal electric field, but also discontinuity in all the normal derivatives of electric and magnetic tangential fields. The proposed method is applied to marine 3-D controlled-source electromagnetic modelling (CSEM) where sources and receivers are located close to the seafloor separating conductive seawater and resistive formation. For the finite-difference scheme based on the Yee grid, the new interpolation is demonstrated to be much more accurate than alternative methods (interpolation using nodes on one side of the interface or interpolation using nodes on both sides, but ignoring the derivative jumps). The rigorous interpolation can handle arbitrary orientation of interface with respect to the grid, which is demonstrated on a marine CSEM example with a dipping seafloor. The interpolation coefficients are computed by minimizing a misfit between values at the nearest nodes and linear expansions of the continuous field components in the coordinate system aligned with the interface. The proposed interpolation operators can handle either uniform or non-uniform grids and can be applied to interpolation for both sources and receivers.

Shantsev, Daniil V.; Maaø, Frank A.

2015-02-01

305

Finite difference modeling of coherent wave amplification in the Earth's radiation belts

Modeling of gyroresonant wave-particle interactions in the radiation belts requires solving the Vlasov-Maxwell system of equations in an inhomogenous background geomagnetic field. Previous works have employed particle-in-cell methods or Eulerian solvers (such as the Vlasov Hybrid Simulation code) to provide numerical solutions to the problem. In this report, we provide an alternative numerical approach by utilizing a first order finite difference upwind scheme. When coupled to the narrowband Maxwell's equations, the model reproduces linear as well as nonlinear wave growth of coherent signals. Wave growth is nonlinear growth when the wave amplitude exceeds the minimum value for phase trapping of counterstreaming particles and is linear otherwise. The model also demonstrates free-running frequency variation for a case with a high linear growth rate. In addition, the model confirms the theoretical prediction of a stable "phase-space hole" during the nonlinear growth process. The plasma parameters and L shell used in this study are typical of those associated with the Siple Station wave injection experiment.

Harid, V.; Go?kowski, M.; Bell, T.; Li, J. D.; Inan, U. S.

2014-12-01

306

Spatial Coupling of a Lattice Boltzmann fluid model with a Finite Difference Navier-Stokes solver

In multiscale, multi-physics applications, there is an increasing need for coupling numerical solvers that are each applied to a different part of the problem. Here we consider the case of coupling a Lattice Boltzmann fluid model and a Finite Difference Navier-Stokes solver. The coupling is implemented so that the entire computational domain can be divided in two regions, with the FD solver running on one of them and the LB one on the other. We show how the various physical quantities of the two approaches should be related to ensure a smooth transition at the interface between the regions. We demonstrate the feasibility of the method on the Poiseuille flow, where the LB and FD schemes are used on adjacent sub-domains. The same idea can be also developed to couple LB models with Finite Volumes, or Finite Elements calculations. The motivation for developing such a type of coupling is that, depending on the geometry of the flow, one technique can be more efficient, less memory consuming, or physically more appr...

Latt, J; Chopard, B; Albuquerque, Paul; Chopard, Bastien; Latt, Jonas

2005-01-01

307

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

Energy Technology Data Exchange (ETDEWEB)

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

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

2012-08-30

308

Reverse Time Migration (RTM) is one of the most widely used techniques for Seismic Imaging, but it in- duces very high computational cost since it is based on many successive solutions to the full wave equation. High-Order Discontinuous Galerkin Methods (DGM), coupled with High Performance Computing techniques, can be used to solve accurately this equation in complex geophysic media without increasing the computational burden. However, to fully exploit the high-order space discretization, it ...

Barucq, He?le?ne; Calandra, Henri; Diaz, Julien; Ventimiglia, Florent

2013-01-01

309

Accurate finite difference beam propagation method for complex integrated optical structures

DEFF Research Database (Denmark)

A simple and effective finite-difference beam propagation method in a z-varying nonuniform mesh is developed. The accuracy and computation time for this method are compared with a standard finite-difference method for both the 3-D and 2-D versions

Rasmussen, Thomas; Povlsen, JØrn Hedegaard

1993-01-01

310

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

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

1992-01-01

311

International Nuclear Information System (INIS)

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

312

In this article we present a new approach to the numerical valuation of derivative securities. The method is based on our previous work where we formulated the theory of pricing in terms of tradables. The basic idea is to fit a finite difference scheme to exact solutions of the pricing PDE. This can be done in a very elegant way, due to the fact that in our tradable based formulation there appear no drift terms in the PDE. We construct a mixed scheme based on this idea and apply it to price various types of arithmetic Asian options, as well as plain vanilla options (both european and american style) on stocks paying known cash dividends. We find prices which are accurate to $\\sim 0.1%$ in about 10ms on a Pentium 233MHz computer and to $\\sim 0.001%$ in a second. The scheme can also be used for market conform pricing, by fitting it to observed option prices.

Hoogland, Jiri Kamiel; Hoogland, Jiri; Neumann, Dimitri

2000-01-01

313

Pressure transient analysis in single and two-phase water by finite difference methods

International Nuclear Information System (INIS)

An important consideration in the design of LMFBR steam generators is the possibility of leakage from a steam generator water tube. The ensuing sodium/water reaction will be largely controlled by the amount of water available at the leak site, thus analysis methods treating this event must have the capability of accurately modeling pressure transients through all states of water occurring in a steam generator, whether single or two-phase. The equation systems of the present model consist of the conservation equations together with an equation of state for one-dimensional homogeneous flow. These equations are then solved using finite difference techniques with phase considerations and non-equilibrium effects being treated through the equation of state. The basis for water property computation is Keenan's 'fundamental equation of state' which is applicable to single-phase water at pressures less than 1000 bars and temperatures less than 13000C. This provides formulations allowing computation of any water property to any desired precision. Two-phase properties are constructed from values on the saturation line. The use of formulations permits the direct calculation of any thermodynamic property (or property derivative) to great precision while requiring very little computer storage, but does involve considerable computation time. For this reason an optional calculation scheme based on the method of 'transfinite interpolation' is included to give rapid computatlation' is included to give rapid computation in selected regions with decreased precision. The conservation equations were solved using the second order Lax-Wendroff scheme which includes wall friction, allows the formation of shocks and locally supersonic flow. Computational boundary conditions were found from a method-of-characteristics solution at the reservoir and receiver ends. The local characteristics were used to interpolate data from inside the pipe to the boundary

314

Poroelastic finite-difference modeling for ultrasonic waves in digital porous cores

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

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

2014-06-01

315

Directory of Open Access Journals (Sweden)

Full Text Available The article considers data on the gross domestic product, consumer expenditures, gross investments and volume of foreign trade for the national economy. It is assumed that time is a discrete variable with one year iteration. The article uses finite-difference equations. It considers models with a high degree of the regulatory function of the state with respect to the consumer market. The econometric component is based on the hypothesis that each of the above said macro-economic indicators for this year depends on the gross domestic product for the previous time periods. Such an assumption gives a possibility to engage the least-squares method for building up linear models of the pair regression. The article obtains the time series model, which allows building point and interval forecasts for the gross domestic product for the next year based on the values of the gross domestic product for the current and previous years. The article draws a conclusion that such forecasts could be considered justified at least in the short-term prospect. From the mathematical point of view the built model is a heterogeneous finite-difference equation of the second order with constant ratios. The article describes specific features of such equations. It illustrates graphically the analytical view of solutions of the finite-difference equation. This gives grounds to differentiate national economies as sustainable growth economies, one-sided, weak or being in the stage of successful re-formation. The article conducts comparison of the listed types with specific economies of modern states.

Polshkov Yulian M.

2013-11-01

316

During cold exposure, peripheral tissues undergo vasoconstriction to minimize heat loss to preserve the maintenance of a normal core temperature. However, vasoconstricted tissues exposed to cold temperatures are susceptible to freezing and frostbite-related tissue damage. Therefore, it is imperative to establish a mathematical model for the estimation of tissue necrosis due to cold stress. To this end, an explicit formula of finite difference method has been used to obtain the solution of Pennes' bio-heat equation with appropriate boundary conditions to estimate the temperature profiles of dermal and subdermal layers when exposed to severe cold temperatures. The discrete values of nodal temperature were calculated at the interfaces of skin and subcutaneous tissues with respect to the atmospheric temperatures of 25°C, 20°C, 15°C, 5°C, -5°C and -10°C. The results obtained were used to identify the scenarios under which various degrees of frostbite occur on the surface of skin as well as the dermal and subdermal areas. The explicit formula of finite difference method proposed in this model provides more accurate predictions as compared to other numerical methods. This model of predicting tissue temperatures provides researchers with a more accurate prediction of peripheral tissue temperature and, hence, the susceptibility to frostbite during severe cold exposure. PMID:25660630

Khanday, M A; Hussain, Fida

2015-02-01

317

Discrete spectrum of the two-center problem of p bar He+ atomcule

International Nuclear Information System (INIS)

A discrete spectrum of the two-center Coulomb problem of p bar He+ system is studied. For solving this problem the finite-difference scheme of the 4th-order and the continuous analog of Newton's method are applied. The algorithm for calculation of eigenvalues and eigenfunctions with optimization of the parameter of the fractional-rational transformation of the quasiradial variable to a finite interval is developed. The specific behaviour of the solutions in a vicinity of the united and separated atoms is discussed

318

Energy Technology Data Exchange (ETDEWEB)

Finite-difference acoustic-wave modeling and reverse-time depth migration based on the full wave equation are general approaches that can take into account arbitrary variations in velocity and density and can handle turning waves as well. However, conventional finite-difference methods for solving the acoustic- or elastic-wave equation suffer from numerical dispersion when too few samples per wavelength are used. The flux-corrected transport (FCT) algorithm, adapted from hydrodynamics, reduces the numerical dispersion in finite-difference wavefield continuation. The flux-correction procedure endeavors to incorporate diffusion into the wavefield continuation process only where needed to suppress the numerical dispersion. Incorporating the flux-correction procedure in conventional finite-difference modeling or reverse-time migration can provide finite-difference solutions with no numerical dispersion even for impulsive sources. The FCT correction, which can be applied to finite-difference approximations of any order in space and time, is an efficient alternative to use for finite-difference approximations of increasing order. Through demonstrations of modeling and migration on both synthetic and field data, the authors show the benefits of the FCT algorithm, as well as its inability to fully recover resolution lost when the spatial sampling becomes too coarse.

Fei, T.; Larner, K. [Colorado School of Mines, Golden, CO (United States). Center for Wave Phenomena

1995-11-01

319

Compensating finite-difference errors in 3-D migration and modeling

Energy Technology Data Exchange (ETDEWEB)

One-pass three-dimensional (3-D) depth migration potentially offers more accurate imaging results than does conventional two-pass migration, in variable velocity media. Conventional one-pass 3-D migration, done with the method of finite-difference inline and crossline splitting, however, creates large errors in imaging complex structures due to paraxial wave-equation approximation of the one-way wave equation, inline-crossline splitting, and finite-difference grid dispersion. After analyzing the finite-difference errors in conventional 3-D poststack wave field extrapolation, the paper presents a method that compensates for the errors and yet still preserves the efficiency of the conventional finite-difference splitting method. For frequency-space 3-D finite-difference migration and modeling, the compensation operator is implemented using the phase-shift method, or phase-shift plus interpolation method, depending on the extent of lateral velocity variations. The compensation operator increases the accuracy of handling steep dips, suppresses the inline and crossline splitting error, and reduces finite-difference grid dispersions. Numerical calculations show that the quality of 3-D migration and 3-D modeling is improved significantly with the finite-difference error compensation method presented in this paper. 13 refs., 7 figs.

Li, Zhiming.

1990-09-01

320

This paper focuses on the unsteady hydromagnetic mixed convective heat and mass transfer boundary layer flow of a viscous incompressible electrically conducting fluid past an accelerated infinite vertical porous flat plate in a porous medium with suction in presence of foreign species such as H2, He, H2O vapour and NH3. The governing equations are solved both analytically and numerically using error function and finite difference scheme. The flow phenomenon has been characterized with the hel...

S S Das, M. R. Saran

2014-01-01

321

Finite-Difference Approach for a 6th-Order Nonlinear Phase Equation with Self-Excitation

A range of physical systems, particularly of chemical nature involving reactions, perform self-excited oscillations coupled by diffusion. The role of diffusion is not trivial so that initial differences in the phase of the oscillations between different points in space do not necessarily disappear as time goes; they may self-sustain. The dynamics of the phase depend on the values of the controlling parameters of the system. We consider a 6th-order nonlinear partial differential equation resulting insuch dynamics. The equation is solved using central finite-difference discretization in space. The resulting system of ordinary differential equations is integrated in time using a Matlab solver. The numerical code is tested using forced versions of the equation, which admit exact analytical solutions. The comparison of the exact and numerical solutions demonstrates satisfactory agreement.

Mohammed, Mayada; Strunin, Dmitry

322

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

Lansing, F. L.

1980-01-01

323

International Nuclear Information System (INIS)

A method based in the pseudo-harmonics method was developed to solve the fixed source problem. The pseudo-harmonics method is based on the eigenfunctions associated with the leakage and removal matrix operator of the neutron diffusion equation, which will be treated here in three dimensions and two groups of energy. This matrix is built in this work through the nodal discretization supplied by coarse mesh finite differences method (CMFDM). CMFDM has as input data the average currents and the average fluxes in the faces of the node, and the average flux in the node, previously obtained by the nodal expansion method. The results obtained with the pseudo-harmonics procedure show good accuracy when compared to the reference results of the source problem tested. Moreover, it is a method which can be easily implemented to solve this type of problems

324

Unconditionally stable time marching scheme for Reynolds stress models

Progress toward a stable and efficient numerical treatment for the compressible Favre-Reynolds-averaged Navier-Stokes equations with a Reynolds-stress model (RSM) is presented. The mean-flow and the Reynolds stress model equations are discretized using finite differences on a curvilinear coordinates mesh. The convective flux is approximated by a third-order upwind biased MUSCL scheme. The diffusive flux is approximated using second-order central differencing, based on a full-viscous stencil. The novel time-marching approach relies on decoupled, implicit time integration, that is, the five mean-flow equations are solved separately from the seven Reynolds-stress closure equations. The key idea is the use of the unconditionally positive-convergent implicit scheme (UPC), originally developed for two-equation turbulence models. The extension of the UPC scheme for RSM guarantees the positivity of the normal Reynolds-stress components and the turbulence (specific) dissipation rate for any time step. Thanks to the UPC matrix-free structure and the decoupled approach, the resulting computational scheme is very efficient. Special care is dedicated to maintain the implicit operator compact, involving only nearest neighbor grid points, while fully supporting the larger discretized residual stencil. Results obtained from two- and three-dimensional numerical simulations demonstrate the significant progress achieved in this work toward optimally convergent solution of Reynolds stress models. Furthermore, the scheme is shown to be unconditionally stable and positive.

Mor-Yossef, Y.

2014-11-01

325

The two most important problems in 2D seismic imaging of complex structures using wave equation migration are (1) steep dips and (2) moderate to severe lateral velocity variations. To tackle this problem in wave-equation based migration schemes we have developed an optimized Fourier finite-difference (FFD) method based on a Taylor's series expansion of the square root operator in the one-way wave equation followed by a two-stage optimization process. Unlike other methods, we expand the square root operator at the reference velocity only, resulting in large errors during the truncation of the infinite series. This degrades the phase approximation severely, even when the lateral velocity variations are moderate To reduce this truncation error we do a first stage of optimization using Chebyshev polynomials. These are a special class of polynomials in which the generating function is a cosine and thus they have a maximum magnitude of 1 on the interval (-1, 1). We use these polynomials to improve the efficiency of the truncated power series (i.e. obtaining higher accuracy with fewer terms as well as a reduction of the truncation error). This requires converting our original power series to a form that can use Chebyshev polynomials. The crucial step of this conversion is a mapping of the interval in which the dependent variable in the original power series is defined onto the interval on which Chebyshev polynomials are defined i.e. (-1, 1). Once this mapping is done we use Chebyshev polynomials to rewrite the power series and then truncate it. After the truncation is done we then invert this truncated Chebyshev polynomial series to recover a truncated and optimized form of our original power series. This gives us the phase approximation after the first stage which is similar in form to Ristow and Ruhl's (1994) FFD approximation. In the second stage of optimization we optimize two coefficients in the phase approximation that we obtained after the first stage with the goal of maximizing the dip angle that is accurately migrated (defined as the dip angle where the relative phase error first exceeds one percent). This optimization is done by using a search algorithm based on simulated annealing (SA). The aim is to provide us with values of the two coefficients that maximize the dip angle under the one percent error constraint. The phase approximation that we finally obtain can migrate dip angles in the range of 65-69 degrees under extremely large velocity contrasts (ratio between the reference and actual velocity being as low as 0.33). This is comparable in accuracy to the Globally optimized Fourier finite-difference method (Huang et al.) and is far more accurate than all other existing migration schemes based on the one-way wave equation (for example 16-20 degrees more accurate than the unoptimized FFD). We demonstrate the accuracy of our method using impulse responses and synthetic examples.

Sen, S.; Anandakrishnan, S.

2003-12-01

326

Three-dimensional Finite Difference-Time Domain Solution of Dirac Equation

The Dirac equation is solved using three-dimensional Finite Difference-Time Domain (FDTD) method. $Zitterbewegung$ and the dynamics of a well-localized electron are used as examples of FDTD application to the case of free electrons.

Simicevic, Neven

2008-01-01

327

Hybrid lattice-Boltzmann and finite-difference simulation of electroosmotic flow in a microchannel

International Nuclear Information System (INIS)

A three-dimensional (3D) transient mathematical model is developed to simulate electroosmotic flows (EOFs) in a homogeneous, square cross-section microchannel, with and without considering the effects of axial pressure gradients. The general governing equations for electroosmotic transport are incompressible Navier-Stokes equations for fluid flow and the nonlinear Poisson-Boltzmann (PB) equation for electric potential distribution within the channel. In the present numerical approach, the hydrodynamic equations are solved using a lattice-Boltzmann (LB) algorithm and the PB equation is solved using a finite-difference (FD) method. The hybrid LB-FD numerical scheme is implemented on an iterative framework solving the system of coupled time-dependent partial differential equations subjected to the pertinent boundary conditions. Transient behavior of the EOF and effects due to the variations of different physicochemical parameters on the electroosmotic velocity profile are investigated. Transport characteristics for the case of combined electroosmotic- and pressure-driven microflows are also examined with the present model. For the sake of comparison, the cases of both favorable and adverse pressure gradients are considered. EOF behaviors of the non-Newtonian fluid are studied through implementation of the power-law model in the 3D LB algorithm devised for the fluid flow analysis. Numerical simulations reveal that the rheological characteristic of the fluid changes the EOcharacteristic of the fluid changes the EOF pattern to a considerable extent and can have significant consequences in the design of electroosmotically actuated bio-microfluidic systems. To improve the performance of the numerical solver, the proposed algorithm is implemented for parallel computing architectures and the overall parallel performance is found to improve with the number of processors.

328

Enhancing coronary Wave Intensity Analysis robustness by high order central finite differences

DEFF Research Database (Denmark)

BACKGROUND: Coronary Wave Intensity Analysis (cWIA) is a technique capable of separating the effects of proximal arterial haemodynamics from cardiac mechanics. Studies have identified WIA-derived indices that are closely correlated with several disease processes and predictive of functional recovery following myocardial infarction. The cWIA clinical application has, however, been limited by technical challenges including a lack of standardization across different studies and the derived indices' sensitivity to the processing parameters. Specifically, a critical step in WIA is the noise removal for evaluation of derivatives of the acquired signals, typically performed by applying a Savitzky-Golay filter, to reduce the high frequency acquisition noise. METHODS: The impact of the filter parameter selection on cWIA output, and on the derived clinical metrics (integral areas and peaks of the major waves), is first analysed. The sensitivity analysis is performed either by using the filter as a differentiator to calculate the signals' time derivative or by applying the filter to smooth the ensemble-averaged waveforms. Furthermore, the power-spectrum of the ensemble-averaged waveforms contains little high-frequency components, which motivated us to propose an alternative approach to compute the time derivatives of the acquired waveforms using a central finite difference scheme. RESULTS AND CONCLUSION: The cWIA output and consequently the derived clinical metrics are significantly affected by the filter parameters, irrespective of its use as a smoothing filter or a differentiator. The proposed approach is parameter-free and, when applied to the 10 in-vivo human datasets and the 50 in-vivo animal datasets, enhances the cWIA robustness by significantly reducing the outcome variability (by 60%).

Rivolo, Simone; Asrress, Kaleab N

2014-01-01

329

Stochastic finite difference lattice Boltzmann method for steady incompressible viscous flows

With the advent of state-of-the-art computers and their rapid availability, the time is ripe for the development of efficient uncertainty quantification (UQ) methods to reduce the complexity of numerical models used to simulate complicated systems with incomplete knowledge and data. The spectral stochastic finite element method (SSFEM) which is one of the widely used UQ methods, regards uncertainty as generating a new dimension and the solution as dependent on this dimension. A convergent expansion along the new dimension is then sought in terms of the polynomial chaos system, and the coefficients in this representation are determined through a Galerkin approach. This approach provides an accurate representation even when only a small number of terms are used in the spectral expansion; consequently, saving in computational resource can be realized compared to the Monte Carlo (MC) scheme. Recent development of a finite difference lattice Boltzmann method (FDLBM) that provides a convenient algorithm for setting the boundary condition allows the flow of Newtonian and non-Newtonian fluids, with and without external body forces to be simulated with ease. Also, the inherent compressibility effect in the conventional lattice Boltzmann method, which might produce significant errors in some incompressible flow simulations, is eliminated. As such, the FDLBM together with an efficient UQ method can be used to treat incompressible flows with built in uncertainty, such as blood flow in stenosed arteries. The objective of this paper is to develop a stochastic numerical solver for steady incompressible viscous flows by combining the FDLBM with a SSFEM. Validation against MC solutions of channel/Couette, driven cavity, and sudden expansion flows are carried out.

Fu, S. C.; So, R. M. C.; Leung, W. W. F.

2010-08-01

330

Stochastic finite difference lattice Boltzmann method for steady incompressible viscous flows

International Nuclear Information System (INIS)

With the advent of state-of-the-art computers and their rapid availability, the time is ripe for the development of efficient uncertainty quantification (UQ) methods to reduce the complexity of numerical models used to simulate complicated systems with incomplete knowledge and data. The spectral stochastic finite element method (SSFEM) which is one of the widely used UQ methods, regards uncertainty as generating a new dimension and the solution as dependent on this dimension. A convergent expansion along the new dimension is then sought in terms of the polynomial chaos system, and the coefficients in this representation are determined through a Galerkin approach. This approach provides an accurate representation even when only a small number of terms are used in the spectral expansion; consequently, saving in computational resource can be realized compared to the Monte Carlo (MC) scheme. Recent development of a finite difference lattice Boltzmann method (FDLBM) that provides a convenient algorithm for setting the boundary condition allows the flow of Newtonian and non-Newtonian fluids, with and without external body forces to be simulated with ease. Also, the inherent compressibility effect in the conventional lattice Boltzmann method, which might produce significant errors in some incompressible flow simulations, is eliminated. As such, the FDLBM together with an efficient UQ method can be used to treat incompressible flows with built in uncertainty, such as blood flith built in uncertainty, such as blood flow in stenosed arteries. The objective of this paper is to develop a stochastic numerical solver for steady incompressible viscous flows by combining the FDLBM with a SSFEM. Validation against MC solutions of channel/Couette, driven cavity, and sudden expansion flows are carried out.

331

In this paper, the wave propagation in free space and different dielectric material by using Finite Difference Time Domain (FDTD) method has been studied. Among various numerical methods Finite Difference Time Domain method is being used to study the time evolution behavior of electromagnetic field by solving the Maxwell’sequation in time domain. In this paper, FDTD method has been employed to study the wave propagation in free space and different dielectric materials. The wave equations ar...

Md. Kamal Hossain; Mohammad Ashraf Hossain Sadi; Ifat-Al-Baqee,; Md. Mokarrom Hossain,; Hossain Mahmud Shamim Farhad

2010-01-01

332

A novel 3-D higher-order finite-difference time-domain framework with complex frequency-shifted perfectly matched layer for the modeling of wave propagation in cold plasma is presented. Second- and fourth-order spatial approximations are used to discretize Maxwell's curl equations and a uniaxial perfectly matched layer with the complex frequency-shifted equations is introduced to terminate the computational domain. A numerical dispersion study of second- and higher-order techniques is elaborated and their stability criteria are extracted for each scheme. Comparisons with analytical solutions verify the accuracy of the proposed methods and the low dispersion error of the higher-order schemes.

Prokopidis, Konstantinos P

2013-01-01

333

Uniformly convergent scheme for Convection-Diffusion problem

Directory of Open Access Journals (Sweden)

Full Text Available In this paper a study of uniformly convergent method proposed by Il’in –Allen-South well scheme was made. A condition was contemplated for uniform convergence in the specified domain. This developed scheme is uniformly convergent for any choice of the diffusion parameter. The search provides a first- order uniformly convergent method with discrete maximum norm. It was observed that the error increases as step size h gets smaller for mid range values of perturbation parameter. Then an analysis carried out by [16] was employed to check the validity of solution with respect to physical aspect and it was in agreement with the analytical solution. The uniformly convergent method gives better results than the finite difference methods. The computed and plotted solutions of this method are in good – agreement with the exact solution.

K. Sharath Babu

2012-02-01

334

Directory of Open Access Journals (Sweden)

Full Text Available Digital watermarking is the process to hide digital pattern directly into a digital content. Digital watermarking techniques are used to address digital rights management, protect information and conceal secrets. An invisible non-blind watermarking approach for gray scale images is proposed in this paper. The host image is decomposed into 3-levels using Discrete Wavelet Transform. Based on the parent-child relationship between the wavelet coefficients the Set Partitioning in Hierarchical Trees (SPIHT compression algorithm is performed on the LH3, LH2, HL3 and HL2 subbands to find out the significant coefficients. The most significant coefficients of LH2 and HL2 bands are selected to embed a binary watermark image. The selected significant coefficients are modulated using Noise Visibility Function, which is considered as the best strength to ensure better imperceptibility. The approach is tested against various image processing attacks such as addition of noise, filtering, cropping, JPEG compression, histogram equalization and contrast adjustment. The experimental results reveal the high effectiveness of the method.

Abdur Shahid

2012-09-01

335

An analysis is performed to study the transient laminar natural convection flows along an inclined semi-infinite flat plate in which the wall temperature T {/w '} and species concentration on the wall C {/w '} vary as the power of the axial co-ordinate in the form T {/w '} (x)= T {?/'}+ ax n and C {/w '}= C {?/'}+ bx m respectively. The dimensionless governing equations considered here are unsteady, two-dimensional, coupled and non-linear integro-differential equations. A finite difference scheme of Crank-Nicolson type is employed to solve the problem. The velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number are studied in detail for various sets of values of parameters. Correlation equations are also established for Nusselt number and Sherwood number in terms of parameters.

Ekambavanan, K.; Ganesan, P.

1995-12-01

336

International Nuclear Information System (INIS)

An orifice flow system is developed and could be used for calibration of high vacuum gauges ranging from 10.3 mbar to 10.6 mbar with argon gas. A standard transfer gauge (SRG) confirms the applicability of the experimental set-up and obtained results. It is shown that this standard system could be used for calibration of high vacuum gauges with in the experimental error reported. The experimental results obtained .in two pressure zones are numerically modeled. A three dimensional system of Navier-Stokes equations is reduced to one dimension governing equations using symmetric technique. A finite difference method is applied to this reduced system together with prescribed boundary conditions. An SaR iterative scheme is employed to solve the system up to a fair accuracy. Numerical solutions of ID system are compared and reported to close accuracy with the experimental data. (author)

337

We propose an efficient procedure to obtain Green's functions by combining the shifted conjugate orthogonal conjugate gradient (shifted COCG) method with the nonequilibrium Green's function (NEGF) method based on a real-space finite-difference (RSFD) approach. The bottleneck of the computation in the NEGF scheme is matrix inversion of the Hamiltonian including the self-energy terms of electrodes to obtain perturbed Green's function in the transition region. This procedure first computes unperturbed Green's functions and calculates perturbed Green's functions from the unperturbed ones using a mathematically strict relation. Since the matrices to be inverted to obtain the unperturbed Green's functions are sparse, complex-symmetric and shifted for a given set of sampling energy points, we can use the shifted COCG method, in which once the Green's function for a reference energy point has been calculated, the Green's functions for the other energy points can be obtained with a moderate computational cost. We calc...

Iwase, Shigeru; Ono, Tomoya

2015-01-01

338

In the urban environment, surface temperatures and conductive heat fluxes through solid media (roofs, walls, roads and vegetated surfaces) are of paramount importance for the comfort of residents (indoors) and for microclimatic conditions (outdoors). Fully discrete numerical methods are currently used to model heat transfer in these solid media in parametrisations of built surfaces commonly used in weather prediction models. These discrete methods usually use finite difference schemes in both space and time. We propose a spatially-analytical scheme where the temperature field and conductive heat fluxes are solved analytically in space. Spurious numerical oscillations due to temperature discontinuities at the sublayer interfaces can be avoided since the method does not involve spatial discretisation. The proposed method is compared to the fully discrete method for a test case of one-dimensional heat conduction with sinusoidal forcing. Subsequently, the analytical scheme is incorporated into the offline version of the current urban canopy model (UCM) used in the Weather Research and Forecasting model and the new UCM is validated against field measurements using a wireless sensor network and other supporting measurements over a suburban area under real-world conditions. Results of the comparison clearly show the advantage of the proposed scheme over the fully discrete model, particularly for more complicated cases.

Wang, Zhi-Hua; Bou-Zeid, Elie; Smith, James A.

2011-02-01

339

We solve the elastic wave equation in spherical coordinates {?,?,?} by a high-order finite-difference (FD) scheme. The Earth model and the required fields are defined on a staggered grid, independent in ?, and thus rotationally symmetric with respect to the axis ? = 0,?. This scheme allows us to model P-SV wave propagation in a heterogeneous two-dimensional Earth model. Since a uniform grid spacing in ? and ? is used, the maximum depth and epicentral distance that can be modeled is limited. Comparison with seismograms obtained by the Reflectivity Method (RM), and the Direct Solution Method (DSM), demonstrates the accuracy of the FD scheme. We use this algorithm to study the effects of heterogeneities in the core-mantle transition zone, the D? layer, on long-period P-waves. Long-wavelength topography of a reflector in D? produces significant focusing and defocusing. Random fluctuations (maximum perturbation ±10%) in a D? layer of 300 km thickness produce a wave-field similar to that of a sharp discontinuity only 200 km above the coremantle boundary (CMB) at the dominant period considered (15 seconds). Maps of global variations of D? thickness determined with long-period data may therefore be severely biased.

Igel, Heiner; Weber, Michael

340

A finite difference solution to 2-dimensional radiative transfer equation for small-animal imaging

Diffuse optical tomography (DOT) has been increasingly studied in the past decades. In DOT, the radiative transfer equation (RTE) and its P1 approximation, i.e. the diffuse equation (DE), have been used as the forward models. Since the DE-based DOT fails where biological tissue has a void-like region and when the source-detector separation is less than 5 mean free pathlengths, as in the situations of small animal imaging, the RTE-based DOT methodology has become a focus of investigation. Therefore, the complete formalism of the RTE is attracting more and more interest. It is clear that the quality of the reconstructed image depends strongly on the accuracy of the forward model. In this paper, A FDM was developed for solving two-dimensional RTE in a 2cm×2cm square homogeneous tissue with two groups of the optical properties and different schemes of the spatial and solid angle discretization. The results of the FDM are compared with the MC simulations. It is shown that when the step size of the spatial mesh becomes small, more discretized angle number is needed.

Jin, Meng; Jiao, Yuting; Gao, Feng; Zhao, Huijuan

2010-02-01

341

Energy Technology Data Exchange (ETDEWEB)

Finite-difference acoustic-wave modeling and reverse-time depth migration based on the full wave equation are general approaches that can take into account arbitary variations in velocity and density, and can handle turning waves well. However, conventional finite-difference methods for solving the acousticwave equation suffer from numerical dispersion when too few samples per wavelength are used. Here, we present two flux-corrected transport (FCT) algorithms, one based the second-order equation and the other based on first-order wave equations derived from the second-order one. Combining the FCT technique with conventional finite-difference modeling or reverse-time wave extrapolation can ensure finite-difference solutions without numerical dispersion even for shock waves and impulsive sources. Computed two-dimensional migration images show accurate positioning of reflectors with greater than 90-degree dip. Moreover, application to real data shows no indication of numerical dispersion. The FCT correction, which can be applied to finite-difference approximations of any order in space and time, is an efficient alternative to use of approximations of increasing order.

Fei, Tong; Larner, K.

1993-11-01

342

We present a numerical comparison of some time-stepping schemes for the discretization and solution of the non-stationary incompressible Navier- Stokes equations. The spatial discretization is by non-conforming quadrilateral finite elements which satisfy the LBB condition. The major focus is on the differences in accuracy and efficiency between the backward Euler, Crank-Nicolson and fractional-step schemes used in discretizing the momentum equations. Further, the differences between fully coupled solvers and operator-splitting techniques (projection methods) and the influence of the treatment of the nonlinear advection term are considered. The combination of both discrete projection schemes and non-conforming finite elements allows the comparison of schemes which are representative for many methods used in practice. On Cartesian grids this approach encompasses some well-known staggered grid finite difference discretizations too. The results which are obtained for several typical flow problems are thought to be representative and should be helpful for a fair rating of solution schemes, particularly in long-time simulations

Turek, Stefan

1996-05-01

343

This paper presents an implementation of a 2.5-D finite-difference (FD) code to model acoustic full waveform monopole logging in cylindrical coordinates accelerated by using the new parallel computing devices (PCDs). For that purpose we use the industry open standard Open Computing Language (OpenCL) and an open-source toolkit called PyOpenCL. The advantage of OpenCL over similar languages is that it allows one to program a CPU (central processing unit) a GPU (graphics processing unit), or multiple GPUs and their interaction among them and with the CPU, or host device. We describe the code and give a performance test in terms of speed using six different computing devices under different operating systems. A maximum speedup factor over 34.2, using the GPU is attained when compared with the execution of the same program in parallel using a CPU quad-core. Furthermore, the results obtained with the finite differences are validated using the discrete wavenumber method (DWN) achieving a good agreement. To provide the Geoscience and the Petroleum Science communities with an open tool for numerical simulation of full waveform sonic logs that runs on the PCDs, the full implementation of the 2.5-D finite difference with PyOpenCL is included.

Iturrarán-Viveros, Ursula; Molero, Miguel

2013-07-01

344

Numerical modeling of geodynamic processes typically requires the solution of the Stokes equations for creeping, highly viscous flows. Since material properties such as effective viscosity of rocks can vary many orders of magnitudes over small spatial scales, the Stokes solver needs to be robust even in the case of highly variable viscosity. Currently, a number of different techniques (e.g. finite element, finite difference and spectral methods) are in use by different authors. Benchmark studies indicate that the accuracy of the velocity solution is satisfying for most methods. The accuracy of deviatoric stresses and pressures, however, is typically less than that of velocities. In the case of highly varying viscosity, some methods even result in oscillating pressures. Over recent years there has been an increased demand for accurate pressures. E.g. melt migration through compacting, two- phase flow materials requires solving equations for the fluid and the solid matrix. Shear-localization in partially molten rocks couples moving fluid within a deforming solid. Therefore it is necessary to have accurate knowledge of pressures, which feed back to the solution. It becomes increasingly important to understand the accuracy of numerical methods for Stokes flow in the presence of large variations in material properties. The objective of this study is therefore to evaluate the accuracy of the pressure solution for a number of numerical techniques. Thereby, we make use of a 2-D analytical solution for the stress distribution inside and around a viscous inclusion in a matrix of different viscosity subjected to pure-shear boundary conditions. Furthermore, numerical simulations have been compared with the analytical solution for density-driven flow (Rayleigh-Taylor instabilities). Results are presented for a staggered grid velocity- pressure finite difference method, a stream function finite difference method and a rotated staggered grid velocity- pressure finite difference method. The staggered grid and stream function formulations require viscosities to be defined both at center and at corner points of control volumes, while the rotated staggered grid finite difference method only requires viscosity defined at center points. We demonstrate that the manner in which viscosities are defined at these locations is of extreme importance for the accuracy of the overall solution. The problem is investigated by studying a simple physical quasi 1-D model with a contact of two media representing the contact between an inclusion embedded in a matrix (2-D case). Analytically and numerically, it is demonstrated that viscosity interpolation using harmonic averaging yields the best results. 2-D numerical results for the above mentioned setups show that for different interpolation methods the errors can vary one order of magnitude. Accuracy of velocity solutions are more than half an order of magnitude better than pressure solutions. The Rayleigh-Taylor instability test, on the other hand, has a weaker sensitivity to viscosity interpolation methods. Results are mainly dependent on the manner in which density is interpolated, which is the driving force in this system. Differences between the three numerical schemes for both setups are secondary compared to the effect of the viscosity interpolation. The best averaging method, for the setups studied here, is a geometric- harmonic averaging of viscosity and an arithmetic averaging of density.

Deubelbeiss, Y.; Kaus, B. J.

2007-12-01

345

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

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

Gedney, Stephen

2011-01-01

346

International Nuclear Information System (INIS)

A useful computer simulation method based on the explicit finite-difference technique can be used to address transient dynamic situations associated with nuclear reactor design and analysis. An introduction to explicit finite-difference technology, the theoretical background (physical and numerical) a review of some explicit codes, a discussion of nuclear reactor applications, and a brief description of EPRI's STEALTH codes are presented. STEALTH computer code manuals are available which describe the numerical equations, programming architecture, input conventions, sample and verification problems, and plotting system. The STEALTH codes are based entirely on the published technology of the Lawrence Livermore Laboratory (LLL), Livermore, California, and Sandia Laboratories, Albuquerque, New Mexico

347

International Nuclear Information System (INIS)

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

348

A Second Order Finite Difference Approximation for the Fractional Diffusion Equation

Directory of Open Access Journals (Sweden)

Full Text Available We consider an approximation of one-dimensional fractional diffusion equation. We claim and show that the finite difference approximation obtained from the Grünwald-Letnikov formulation, often claimed to be of first order accuracy, is in fact a second order approximation of the fractional derivative at a point away from the grid points. We use this fact to device a second order accurate finite difference approximation for the fractional diffusion equation. The proposed method is also shown to be unconditionally stable. By this approach, we treat three cases of difference approximations in a unified setting. The results obtained are justified by numerical examples.

H. M. Nasir

2013-07-01

349

The reliability of a finite-difference method for the solution of the inverse scattering problem

International Nuclear Information System (INIS)

The properties and the applicability of the finite-difference method of Hooshyar and Razavy for the solution of the inverse scattering problem are studied. Testing the method for the reconstruction of potentials under realistic conditions leads to significant systematic differences between the reconstructed and the input potentials. The inversion procedure does not converge and exhibits a characteristic instability for small variations of the scattering input. Therefore, this finite-difference method appears to be unsuitable for the extraction of reliable potentials from experimental scattering data. (orig.)

350

Directory of Open Access Journals (Sweden)

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

Vineet K. Srivastava

2013-12-01

351

Energy Technology Data Exchange (ETDEWEB)

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

Srivastava, Vineet K., E-mail: vineetsriiitm@gmail.com [ISRO Telemetry, Tracking and Command Network (ISTRAC), Bangalore-560058 (India); Awasthi, Mukesh K. [Department of Mathematics, University of Petroleum and Energy Studies, Dehradun-248007 (India); Singh, Sarita [Department of Mathematics, WIT- Uttarakhand Technical University, Dehradun-248007 (India)

2013-12-15

352

Flood routing using finite differences and the fourth order Runge-Kutta method

International Nuclear Information System (INIS)

The Saint-Venant continuity and momentum equations are solved numerically by discretising the time variable using finite differences and then the Runge-Kutta method is employed to solve the resulting ODE. A model of the Rufiji river downstream on the proposed Stiegler Gourge Dam is used to provide numerical results for comparison. The present approach is found to be superior to an earlier analysis using finite differences in both space and time. Moreover, the steady and unsteady flow analyses give almost identical predictions for the stage downstream provided that the variations of the discharge and stage upstream are small. (author)

353

Locally conformal finite-difference time-domain techniques for particle-in-cell plasma simulation

The Dey-Mittra [S. Dey, R. Mitra, A locally conformal finite-difference time-domain (FDTD) algorithm for modeling three-dimensional perfectly conducting objects, IEEE Microwave Guided Wave Lett. 7 (273) 1997] finite-difference time-domain partial cell method enables the modeling of irregularly shaped conducting surfaces while retaining second-order accuracy. We present an algorithm to extend this method to include charged particle emission and absorption in particle-in-cell codes. Several examples are presented that illustrate the possible improvements that can be realized using the new algorithm for problems relevant to plasma simulation.

Clark, R. E.; Welch, D. R.; Zimmerman, W. R.; Miller, C. L.; Genoni, T. C.; Rose, D. V.; Price, D. W.; Martin, P. N.; Short, D. J.; Jones, A. W. P.; Threadgold, J. R.

2011-02-01

354

Directory of Open Access Journals (Sweden)

Full Text Available Este trabalho tem por objetivo apresentar os resultados da modelagem sísmica em meios com fortes descontinuidades de propriedades físicas, com ênfase na existência de difrações e múltiplas reflexões, tendo a Bacia do Amazonas como referência à modelagem. As condições de estabilidade e de fronteiras utilizadas no cálculo do campo de ondas sísmicas foram analisadas numericamente pelo método das diferenças finitas, visando melhor compreensão e controle da interpretação de dados sísmicos. A geologia da Bacia do Amazonas é constituída por rochas sedimentares depositadas desde o Ordoviciano até o Recente que atingem espessuras da ordem de 5 km. Os corpos de diabásio, presentes entre os sedimentos paleozóicos, estão dispostos na forma de soleiras, alcançam espessuras de centenas de metros e perfazem um volume total de aproximadamente 90000 Km³. A ocorrência de tais estruturas é responsável pela existência de reflexões múltiplas durante a propagação da onda sísmica o que impossibilita melhor interpretação dos horizontes refletores que se encontram abaixo destas soleiras. Para representar situações geológicas desse tipo foram usados um modelo (sintético acústico de velocidades e um código computacional elaborado via método das diferenças finitas com aproximação de quarta ordem no espaço e no tempo da equação da onda. A aplicação dos métodos de diferenças finitas para o estudo de propagação de ondas sísmicas melhorou a compreensão sobre a propagação em meios onde existem heterogeneidades significativas, tendo como resultado boa resolução na interpretação dos eventos de reflexão sísmica em áreas de interesse. Como resultado dos experimentos numéricos realizados em meio de geologia complexa, foi observada a influência significativa das reflexões múltiplas devido à camada de alta velocidade, isto provocou maior perda de energia e dificultou a interpretação dos alvos. Por esta razão recomenda-se a integração de dados de superfície com os de poço, com o objetivo de obter melhor imagem dos alvos abaixo das soleiras de diabásio.This paper discusses the seismic modeling in medium with strong discontinuities in its physical properties. The approach takes in consideration the existences diffractions and multiple reflections in the analyzed medium, which, at that case, is the Amazon Basin. The stability and boundary conditions of modeling were analyzed by the method of the finite differences. Sedimentary rocks deposited since the Ordovician to the present, reaching depth up to 5 Km. The bodies of diabasic between the paleozoic sediments are layers reaching thickness of hundred meters, which add to 90.000 km3, form the geology of the Amazon Basin. The occurrence of these structures is responsible for multiple reflections during the propagation of the seismic waves, which become impossible a better imaging of horizons located bellow the layers. The representation this geological situation was performed an (synthetic acoustic velocity model. The numerical discretization scheme is based in a fourth order approximation of the acoustic wave equation in space and time The understanding of the wave propagation heterogeneous medium has improved for the application of the finite difference method. The method achieves a good resolution in the interpretation of seismic reflection events. The numerical results discusses in this paper have allowed to observed the influence of the multiple reflection in a high velocity layer. It increase a loss of energy and difficult the interpretation of the target. For this reason the integration of surface data with the well data is recommended, with the objective to get one better image of the targets below of the diabasic layer.

Lindemberg Lima Fernandes

2009-03-01

355

Scientific Electronic Library Online (English)

Full Text Available Este trabalho tem por objetivo apresentar os resultados da modelagem sísmica em meios com fortes descontinuidades de propriedades físicas, com ênfase na existência de difrações e múltiplas reflexões, tendo a Bacia do Amazonas como referência à modelagem. As condições de estabilidade e de fronteiras [...] utilizadas no cálculo do campo de ondas sísmicas foram analisadas numericamente pelo método das diferenças finitas, visando melhor compreensão e controle da interpretação de dados sísmicos. A geologia da Bacia do Amazonas é constituída por rochas sedimentares depositadas desde o Ordoviciano até o Recente que atingem espessuras da ordem de 5 km. Os corpos de diabásio, presentes entre os sedimentos paleozóicos, estão dispostos na forma de soleiras, alcançam espessuras de centenas de metros e perfazem um volume total de aproximadamente 90000 Km³. A ocorrência de tais estruturas é responsável pela existência de reflexões múltiplas durante a propagação da onda sísmica o que impossibilita melhor interpretação dos horizontes refletores que se encontram abaixo destas soleiras. Para representar situações geológicas desse tipo foram usados um modelo (sintético) acústico de velocidades e um código computacional elaborado via método das diferenças finitas com aproximação de quarta ordem no espaço e no tempo da equação da onda. A aplicação dos métodos de diferenças finitas para o estudo de propagação de ondas sísmicas melhorou a compreensão sobre a propagação em meios onde existem heterogeneidades significativas, tendo como resultado boa resolução na interpretação dos eventos de reflexão sísmica em áreas de interesse. Como resultado dos experimentos numéricos realizados em meio de geologia complexa, foi observada a influência significativa das reflexões múltiplas devido à camada de alta velocidade, isto provocou maior perda de energia e dificultou a interpretação dos alvos. Por esta razão recomenda-se a integração de dados de superfície com os de poço, com o objetivo de obter melhor imagem dos alvos abaixo das soleiras de diabásio. Abstract in english This paper discusses the seismic modeling in medium with strong discontinuities in its physical properties. The approach takes in consideration the existences diffractions and multiple reflections in the analyzed medium, which, at that case, is the Amazon Basin. The stability and boundary conditions [...] of modeling were analyzed by the method of the finite differences. Sedimentary rocks deposited since the Ordovician to the present, reaching depth up to 5 Km. The bodies of diabasic between the paleozoic sediments are layers reaching thickness of hundred meters, which add to 90.000 km3, form the geology of the Amazon Basin. The occurrence of these structures is responsible for multiple reflections during the propagation of the seismic waves, which become impossible a better imaging of horizons located bellow the layers. The representation this geological situation was performed an (synthetic) acoustic velocity model. The numerical discretization scheme is based in a fourth order approximation of the acoustic wave equation in space and time The understanding of the wave propagation heterogeneous medium has improved for the application of the finite difference method. The method achieves a good resolution in the interpretation of seismic reflection events. The numerical results discusses in this paper have allowed to observed the influence of the multiple reflection in a high velocity layer. It increase a loss of energy and difficult the interpretation of the target. For this reason the integration of surface data with the well data is recommended, with the objective to get one better image of the targets below of the diabasic layer.

Lindemberg Lima, Fernandes; João Carlos Ribeiro, Cruz; Claudio José Cavalcante, Blanco; Ana Rosa Baganha, Barp.

2009-03-01

356

Interpolating discrete advection-diffusion propagators at Leja sequences

We propose and analyze the ReLPM (Real Leja Points Method) for evaluating the propagator ?(?tB)v via matrix interpolation polynomials at spectral Leja sequences. Here B is the large, sparse, nonsymmetric matrix arising from stable 2D or 3D finite-difference discretization of linear advection-diffusion equations, and ?(z) is the entire function ?(z)=(ez-1)/z. The corresponding stiff differential system , is solved by the exact time marching scheme yi+1Dyi+?ti?(?tiB)(Byi+g), i=0,1,..., where the time-step is controlled simply via the variation percentage of the solution, and can be large. Numerical tests show substantial speed-ups (up to one order of magnitude) with respect to a classical variable step-size Crank-Nicolson solver.

Caliari, M.; Vianello, M.; Bergamaschi, L.

2004-11-01

357

Finite-difference equation and quasi-diagonal form in quantum statistical mechanics

International Nuclear Information System (INIS)

A finite-difference Liouville-von Neumann equation is considered for the density operator rho which shows some peculiar new features of the evolution of a quantum system. In particular this equation automatically leads to the quasi-diagonal form in the energy representation. Furthermore, the new formulation proposed seems to be of interest for a consistent quantum theory of measurement

358

Detailed balance principle and finite-difference stochastic equation in a field theory

International Nuclear Information System (INIS)

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

359

Principle of detailed balance and the finite-difference stochastic equation in field theory

International Nuclear Information System (INIS)

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

360

Finite-difference field calculations for one-dimensionally confined X-ray waveguides

International Nuclear Information System (INIS)

The propagation of X-rays in one-dimensionally confined waveguides is analyzed by means of finite-difference calculations based on the parabolic wave equation. We compare the numerical results to an analytical approach and investigate the transmission and coherence properties of a waveguide depending on its length and the number of guided modes corresponding to the guiding layer thickness

361

The Wigner function of the relativistic finite-difference oscillator in an external field

Energy Technology Data Exchange (ETDEWEB)

The phase-space representation for a relativistic linear oscillator in a homogeneous external field expressed through the finite-difference equation is constructed. Explicit expressions of the relativistic oscillator Wigner quasi-distribution function for the stationary states as well as for the states of thermodynamical equilibrium are obtained and their correct limits are shown.

Nagiyev, S M; Guliyeva, G H; Jafarov, E I [Institute of Physics, Azerbaijan National Academy of Sciences, Javid av. 33, AZ1143 Baku (Azerbaijan)], E-mail: ejafarov@physics.ab.az

2009-10-30

362

International Nuclear Information System (INIS)

The reactor code PUMA, developed in CNEA, simulates nuclear reactors discretizing space in finite difference elements. Core representation is performed by means a cylindrical mesh, but the reactor channels are arranged in an hexagonal lattice. That is why a mapping using volume intersections must be used. This spatial treatment is the reason of an overestimation of the control rod reactivity values, which must be adjusted modifying the incremental cross sections. Also, a not very good treatment of the continuity conditions between core and reflector leads to an overestimation of channel power of the peripherical fuel elements between 5 to 8 per cent. Another code, DELFIN, developed also in CNEA, treats the spatial discretization using heterogeneous finite elements, allowing a correct treatment of the continuity of fluxes and current among elements and a more realistic representation of the hexagonal lattice of the reactor. A comparison between results obtained using both methods in done in this paper. (author). 4 refs., 3 figs

363

Astrointerferometry with discrete optics

We propose an innovative scheme exploiting discrete diffraction in a two dimensional array of coupled waveguides to determine the phase and amplitude of the mutual correlation function between any pair of three telescopes of an astrointerferometer.

Minardi, Stefano; Pertsch, Thomas

2010-01-01

364

Energy Technology Data Exchange (ETDEWEB)

The finite-difference based integration method for evolution-line equations is discussed in detail and framed within the general context of the evolution operator picture. Exact analytical methods are described to solve evolution-like equations in a quite general physical context. The numerical technique based on the factorization formulae of exponential operator is then illustrated and applied to the evolution-operator in both classical and quantum framework. Finally, the general view to the finite differencing schemes is provided, displaying the wide range of applications from the classical Newton equation of motion to the quantum field theory.

Dattoli, Giuseppe; Torre, Amalia [ENEA, Centro Ricerche Frascati, Rome (Italy). Dipt. Innovazione; Ottaviani, Pier Luigi [ENEA, Centro Ricerche Bologna (Italy); Vasquez, Luis [Madris, Univ. Complutense (Spain). Dept. de Matemateca Aplicado

1997-10-01

365

Two Conservative Difference Schemes for the Generalized Rosenau Equation

Directory of Open Access Journals (Sweden)

Full Text Available Numerical solutions for generalized Rosenau equation are considered and two energy conservative finite difference schemes are proposed. Existence of the solutions for the difference scheme has been shown. Stability, convergence, and priori error estimate of the scheme are proved using energy method. Numerical results demonstrate that two schemes are efficient and reliable.

Zheng Kelong

2010-01-01

366

The main goal of the new staggered-grid finite difference version of the LaMEM code is a stable and efficient solution of the highly heterogeneous and nonlinear geodynamic models on the massively parallel computers. The key components of the new branch of the code are: i) complete MPI-based parallelization ii) stable and computationally cheap spatial discretization iii) diffusion-resistive treatment of material advection with marker-in-cell technique iv) accurate treatment of the free surface by properly removing air cells v) consistent implementation of the viso-(elasto)-plastic rock rheologies vi) scalable linear and non-linear solvers via PETSc infrastructure In this work we show details of the algorithms and implementation together with a few common benchmarks and example models. Acknowledgements. Funding was provided by the European Research Council under the European Community's Seventh Framework Program (FP7/2007-2013) / ERC Grant agreement #258830. Numerical computations have been performed on JUQUEEN of the Jülich high-performance computing center.

Popov, Anton; Kaus, Boris

2013-04-01

367

Global seismic wave propagation through laterally heterogeneous realistic Earth models can efficiently be simulated by the 2.5-D finite-difference modeling in spherical coordinates. The 2.5-D approach assumes the global structures to be axisymmetric with respect to the axis through a seismic source followed by modeling of 3-D wavefields only on a 2-D cross-section of the whole sphere, so that, at the beginning, this approach was restricted within axisymmetric structures and sources about the source axis. We have been working to construct a method which removes the restriction but maintains the efficiency of the axisymmetric approach. First we proposed ``quasi-spherical FDM'' which solves the elastodynamic equation by the velocity-stress staggered-grid finite-difference method (FDM) not in usual spherical domain but instead in ``quasi-spherical domain''. It can treat asymmetric structures about the source axis with the same computation time and storage as the axisymmetric modeling (Toyokuni et al., 2005, GRL). Arbitrary moment-tensor point sources are then introduced into the axisymmetric modeling through Fourier expansion of wavefield variables in transverse (? ) direction (Toyokuni & Takenaka, 2006, EPS). Coincidently we adopted the so-called effective parameters into our FDM scheme to improve the accuracy, and proposed an analytical way to compute these parameters for major four standard Earth models (Toyokuni & Takenaka, 2009, CAGEO). Furthermore, anelastic attenuation had been taken into account (Toyokuni & Takenaka, 2008, AGU Fall Meeting), the so-called multidomain consisted of several domains with different lateral grid spacings connected in radial (r) direction was adopted for stability of FD computation around the center of the Earth (Toyokuni & Takenaka, 2008, WPGM), and introduced the Earth's center using linear interpolation (Toyokuni & Takenaka, 2009, AGU Fall Meeting). Now we incorporate self-gravitation of the Earth, i.e., an essential phenomenon for both seismic and gravimetric observations with periods larger than 100 s. Equations of motion for the self-gravitating Earth contain terms with gravitational potential and the Eulerian perturbation of this potential due to seismic wavefields. This time we adopt the effects of gravity within the Cowling approximation (Cowling, 1941, Mon. Not. R. astr. Soc.) neglecting the term for the gravity perturbation, which is equivalent to eliminate the mass redistribution caused by seismic waves. The resulting equations are known as the displacement-velocity-stress equations since it include the displacement, the particle velocity, and the stress, but we propose a special scheme to exchange these equations to the simple velocity-stress equations that are easily solved by the FDM.

Toyokuni, G.; Takenaka, H.

2010-12-01

368

Energy Technology Data Exchange (ETDEWEB)

In this paper, a data-parallel computer is used to provide the memory and reduction in computer time for solving large finite-difference bidomain problems. The finite-difference grid is mapped effectively to the processors of the parallel computer, simply by mapping one node to one (virtual) processor. Implemented on the connection machines (CM`s) CM-200 and CM-5, the data-parallel finite-difference algorithm has allowed the solution of finite-difference bidomain problems with over 2 million nodes. Details on the algorithm are presented together with computational performance results. 19 refs., 5 figs.

Saleheen, H.I. [Concurrent Technologies Corporation, Johnstown, PA (United States); Claessen, P.D. [Arizona State Univ., Tempe, AZ (United States); Ng, K.T. [New Mexico State Univ., Las Cruces, NM (United States)

1997-02-01

369

The scattering of seismic waves from small spatial variations of material properties (e.g., density and seismic wave velocity) affects all seismic observables including amplitudes and travel-times and also gives rise to seismic coda waves. Analysis of seismic scattering has provided a means to quantify small-scale seismic properties that cannot be determined through travel-time analysis or ray theoretical approaches. Numerical wave propagation techniques, such as Finite Difference (FD) techniques, have been utilized in analyzing the full waveform effects of the scattered wave field, although application of these techniques has been focused on studies in regional distance ranges. In order to simulate scattering in numerical schemes, random heterogeneity is added to a models seismic structure using a method based on the 2- or 3-D Fourier Transform (FT). The FT method is well-suited for introducing random perturbations into models on the regional scale in Cartesian geometries.Yet, numerical techniques for larger scale seismic simulation, e.g., global wave propagation, require computationally parallelized solutions and are generally not parameterized on a Cartesian grid. Both of these factors make use of the FT method problematic. The FT method is also restrictive in that constructing models with variable scale-length heterogeneity introduces a first-order discontinuity into the model space. We develop a new technique of generating models of random heterogeneity for numerical wave propagation by application of the Karhunen-Loève Transform (KLT). In contrast to the FT method, which computes the 2- or 3-D convolution of a correlation function with a set of random numbers to produce a realization of random media, the KLT method determines an orthogonal basis of a theoretical covariance matrix by calculating its eigenvectors and eigenvalues. This orthogonal basis is then used to construct a transform matrix by which the random media can be generated. The KLT is ideal as it allows one to construct the transform matrix with a minimum set of basis vectors. We demonstrate the following advantages of the KLT based method: (1) the technique works for both isotropic and anisotropic correlation structures on Cartesian and non-Cartesian grids, (2) the technique is readily parallelizable, and (3) the technique can be used to generate models with non-stationary correlation structures without introducing first-order discontinuities. Initial set-up of the KLT technique is in general slower than the FT technique; however multiple realizations of the random media may be rapidly generated and kriging interpolation can also be used to further accelerate the set-up. We compute 2-D FD synthetic seismograms for models with random heterogeneity and compare waveforms for models constructed with both the FT and KLT based techniques. We generate models with a change of correlation structure with depth, comparing predictions with first-order discontinuous and smoothly varying correlation structure. We also demonstrate the effects of scattering on the SH-wave field in global simulations using the axi-symmetric FD method, showing how the inclusion of random heterogeneity broadens the pulse width of teleseismic body wave arrivals and delays their peak arrival times. Coda wave energy is also generated which is observed as additional energy after prominent body wave arrivals.

Thorne, M. S.; Myers, S. C.; Harris, D. B.; Rodgers, A. J.

2006-12-01

370

Theoretical description of photothermal processes require analytical solution to the thermal diffusion equation. This solution takes great efforts, and in many cases an analytical expression is not accessible. In this article, additional solution methods for the thermal diffusion equation, especially for photothermal problems, are presented. These methods are the finite-element method and the finite-difference method; the latter is described in detail. They enable a closed theory for all photothermal processes using a modulated light source and measurements in the equilibrium state. The numerics are verified by comparison with some analytically solved problems. The main discussion topic is surface hardened steel samples. Here, some well-known models for hardness profiles and a new approach, calculated by the finite-difference method, are discussed.

Goch, G.; Reigl, M.

1996-06-01

371

We propose a hybrid lattice-Boltzmann finite-difference method to simulate axisymmetric multiphase flows. The hydrodynamics is simulated by the lattice-Boltzmann equations with the multiple-relaxation-time (MRT) collision model and suitable forcing terms that account for the interfacial tension and axisymmetric effects. The interface dynamics is captured by the finite-difference solution of the convective Cahn-Hilliard equation. This method is applied to simulate a quiescent drop, an oscillating drop, a drop spreading on a dry surface and a drop accelerated by a constant body force. It is validated through comparisons of the computed results for these problems with analytical solutions or numerical solutions by other different methods. It is shown that the MRT-based method is able to handle more challenging cases than that with the single-relaxation-time collision model for axisymmetric multiphase flows due to its improved stability.

Huang, Jun-Jie; Huang, Haibo; Shu, Chang; Tian Chew, Yong; Wang, Shi-Long

2013-02-01

372

International Nuclear Information System (INIS)

We propose a hybrid lattice-Boltzmann finite-difference method to simulate axisymmetric multiphase flows. The hydrodynamics is simulated by the lattice-Boltzmann equations with the multiple-relaxation-time (MRT) collision model and suitable forcing terms that account for the interfacial tension and axisymmetric effects. The interface dynamics is captured by the finite-difference solution of the convective Cahn–Hilliard equation. This method is applied to simulate a quiescent drop, an oscillating drop, a drop spreading on a dry surface and a drop accelerated by a constant body force. It is validated through comparisons of the computed results for these problems with analytical solutions or numerical solutions by other different methods. It is shown that the MRT-based method is able to handle more challenging cases than that with the single-relaxation-time collision model for axisymmetric multiphase flows due to its improved stability. (paper)

373

We demonstrate how meshfree finite difference methods can be applied to solve vector Poisson problems with electric boundary conditions. In these, the tangential velocity and the incompressibility of the vector field are prescribed at the boundary. Even on irregular domains with only convex corners, canonical nodal-based finite elements may converge to the wrong solution due to a version of the Babuska paradox. In turn, straightforward meshfree finite differences converge to the true solution, and even high-order accuracy can be achieved in a simple fashion. The methodology is then extended to a specific pressure Poisson equation reformulation of the Navier-Stokes equations that possesses the same type of boundary conditions. The resulting numerical approach is second order accurate and allows for a simple switching between an explicit and implicit treatment of the viscosity terms.

Zhou, Dong; Shirokoff, David; Chidyagwai, Prince; Rosales, Rodolfo Ruben

2013-01-01

374

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

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

2014-01-01

375

Discrete wave mechanics: An introduction

Discrete wave mechanics is formulated for particles in one-dimensional systems by use of a simple finite difference equation. The solutions involve wave vectors (instead of wave functions) as well as a newly defined “wave vector energy.” In the limit, as c ? ?, the treatment reduces to that of Schrödinger's wave mechanics. Specific calculations are made for completely free particles as well as for particles confined to a one-dimensional box. The results exhibit a striking compatibili...

Wall, Frederick T.

1986-01-01

376

We develop a stable and high-order accurate finite difference method for problems in earthquake rupture dynamics in complex geometries with multiple faults. The bulk material is an isotropic elastic solid cut by pre-existing fault interfaces that accommodate relative motion of the material on the two sides. The fields across the interfaces are related through friction laws which depend on the sliding velocity, tractions acting on the interface, and state variables which evolve according to or...

Kozdon, Jeremy E.; Dunham, Eric M.; Nordstro?m, Jan

2013-01-01

377

We present a code for solving the coupled Einstein-hydrodynamics equations to evolve relativistic, self-gravitating fluids. The Einstein field equations are solved in generalized harmonic coordinates on one grid using pseudospectral methods, while the fluids are evolved on another grid using shock-capturing finite difference or finite volume techniques. We show that the code accurately evolves equilibrium stars and accretion flows. Then we simulate an equal-mass nonspinning ...

Duez, Matthew D.; Foucart, Francois; Kidder, Lawrence E.; Pfeiffer, Harald P.; Scheel, Mark A.; Teukolsky, Saul A.

2008-01-01

378

TRUMP3-JR: a finite difference computer program for nonlinear heat conduction problems

International Nuclear Information System (INIS)

Computer program TRUMP3-JR is a revised version of TRUMP3 which is a finite difference computer program used for the solution of multi-dimensional nonlinear heat conduction problems. Pre- and post-processings for input data generation and graphical representations of calculation results of TRUMP3 are avaiable in TRUMP3-JR. The calculation equations, program descriptions and user's instruction are presented. A sample problem is described to demonstrate the use of the program. (author)

379

RODCON: a finite difference heat conduction computer code in cylindrical coordinates

International Nuclear Information System (INIS)

RODCON, a finite difference computer code, was developed to calculate the internal temperature distribution of the fuel rod simulator (FRS) for the Core Flow Test Loop (CFTL). RODCON solves the implicit, time-dependent forward-differencing heat transfer equation in 2-dimensional (Rtheta) cylindrical coordinates at an axial plane with user specified radial material zones and surface conditions at the FRS periphery. Symmetry of the boundary conditions of coolant bulk temperatures and film coefficients at the FRS periphery is not necessary

380

RODCON: a finite difference heat conduction computer code in cylindrical coordinates

Energy Technology Data Exchange (ETDEWEB)

RODCON, a finite difference computer code, was developed to calculate the internal temperature distribution of the fuel rod simulator (FRS) for the Core Flow Test Loop (CFTL). RODCON solves the implicit, time-dependent forward-differencing heat transfer equation in 2-dimensional (Rtheta) cylindrical coordinates at an axial plane with user specified radial material zones and surface conditions at the FRS periphery. Symmetry of the boundary conditions of coolant bulk temperatures and film coefficients at the FRS periphery is not necessary.

Conklin, J.C.

1980-09-16

381

A practical implicit finite-difference method: examples from seismic modelling

International Nuclear Information System (INIS)

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 whemethod 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

382

COMPARISON OF NUMERICAL SCHEMES FOR SOLVING A SPHERICAL PARTICLE DIFFUSION EQUATION

A new robust iterative numerical scheme was developed for a nonlinear diffusive model that described sorption dynamics in spherical particle suspensions. he numerical scheme had been applied to finite difference and finite element models that showed rapid convergence and stabilit...

383

An Improvement for the Locally One-Dimensional Finite-Difference Time-Domain Method

Directory of Open Access Journals (Sweden)

Full Text Available To reduce the memory usage of computing, the locally one-dimensional reduced finite-difference time-domain method is proposed. It is proven that the divergence relationship of electric-field and magnetic-field is non-zero even in charge-free regions, when the electric-field and magnetic-field are calculated with locally one-dimensional finite-difference time-domain (LOD-FDTD method, and the concrete expression of the divergence relationship is derived. Based on the non-zero divergence relationship, the LOD-FDTD method is combined with the reduced finite-difference time-domain (R-FDTD method. In the proposed method, the memory requirement of LOD-R-FDTD is reduced by1/6 (3D case of the memory requirement of LOD-FDTD averagely. The formulation is presented and the accuracy and efficiency of the proposed method is verified by comparing the results with the conventional results.

Xiuhai Jin

2011-09-01

384

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

Directory of Open Access Journals (Sweden)

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

J. Sargolzaei

2011-01-01

385

International Nuclear Information System (INIS)

Electrical modeling of piezoelectric structronic systems by analog circuits has the disadvantages of huge circuit structure and low precision. However, studies of electrical simulation of segmented distributed piezoelectric structronic plate systems (PSPSs) by using output voltage signals of high-speed digital circuits to evaluate the real-time dynamic displacements are scarce in the literature. Therefore, an equivalent dynamic model based on the finite difference method (FDM) is presented to simulate the actual physical model of the segmented distributed PSPS with simply supported boundary conditions. By means of the FDM, the four-ordered dynamic partial differential equations (PDEs) of the main structure/segmented distributed sensor signals/control moments of the segmented distributed actuator of the PSPS are transformed to finite difference equations. A dynamics matrix model based on the Newmark-? integration method is established. The output voltage signal characteristics of the lower modes (m ? 3, n ? 3) with different finite difference mesh dimensions and different integration time steps are analyzed by digital signal processing (DSP) circuit simulation software. The control effects of segmented distributed actuators with different effective areas are consistent with the results of the analytical model in relevant references. Therefore, the method of digital simulation for vibration analysis of segmented distributed PSPSs presented in this paper can provides presented in this paper can provide a reference for further research into the electrical simulation of PSPSs

386

Discretization error of Stochastic Integrals

Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional mean-squared error attains a lower bound are constructed. Two applications are given; efficient delta hedging strategies with transaction costs and effective discretization schemes for the Euler-Maruyama approximation are constructed.

Fukasawa, Masaaki

2010-01-01

387

International Nuclear Information System (INIS)

Discrete levels and their decay characteristics are required as input for nuclear reaction calculations, which replace the statistical level densities and strength functions below a certain energy Emax. Most of the data were extracted from the ENSDF library. However, many missing data such as unique spins and parities were inferred using statistical methods, while missing internal conversion coefficients (ICC) and electromagnetic decay probabilities were calculated. For each element the data have been stored in a file containing all isotopes in increasing mass order. In addition, cutoff energies Emax for completeness of level schemes and spin cutoff parameters have been determined for a large number of nuclei. The latter data have been collected in a separate data file, together with the results obtained from a constant temperature fit to the nuclear level schemes. (author)

388

We present a 3-D P wave velocity model of the crust and shallowest mantle under the Italian region, that includes a revised Moho depth map, obtained by regional seismic travel time tomography. We invert 191,850 Pn and Pg wave arrival times from 6850 earthquakes that occurred within the region from 1988 to 2007, recorded by 264 permanent seismic stations. We adopt a high-resolution linear B-spline model representation, with 0.1° horizontal and 2 km vertical grid spacing, and an accurate finite-difference forward calculation scheme. Our nonlinear iterative inversion process uses the recent European reference 3-D crustal model EPcrust as a priori information. Our resulting model shows two arcs of relatively low velocity in the crust running along both the Alps and the Apennines, underlying the collision belts between plates. Beneath the Western Alps we detect the presence of the Ivrea body, denoted by a strong high P wave velocity anomaly. We also map the Moho discontinuity resulting from the inversion, imaged as the relatively sharp transition between crust and mantle, where P wave velocity steps up to values larger than 8 km/s. This simple condition yields an image quite in agreement with previous studies that use explicit representations for the discontinuity. We find a complex lithospheric structure characterized by shallower Moho close by the Tyrrhenian Sea, intermediate depth along the Adriatic coast, and deepest Moho under the two mountain belts.

Gualtieri, L.; Serretti, P.; Morelli, A.

2014-01-01

389

International Nuclear Information System (INIS)

We present a novel numerical signal injection technique allowing unidirectional injection of a wave in a wave-guiding structure, applicable to 2D finite-difference time-domain electromagnetic codes, both Maxwell and wave-equation. It is particularly suited to continuous wave radar-like simulations. The scheme gives an unidirectional injection of a signal while being transparent to waves propagating in the opposite direction (directional coupling). The reflected or backscattered waves (returned) are separated from the probing waves allowing direct access to the information on amplitude and phase of the returned wave. It also facilitates the signal processing used to extract the phase derivative (or group delay) when simulating radar systems. Although general, the technique is particularly suited to swept frequency sources (frequency modulated) in the context of reflectometry, a fusion plasma diagnostic. The UTS applications presented here are restricted to fusion plasma reflectometry simulations for different physical situations. This method can, nevertheless, also be used in other dispersive media such as dielectrics, being useful, for example, in the simulation of plasma filled waveguides or directional couplers

390

Directory of Open Access Journals (Sweden)

Full Text Available This paper considers the magnetohydrodynamic flow and heat transfer in a viscous incompressible fluid between two parallel porous plates experiencing a discontinuous change in wall temperature. An explicit finite difference scheme has been employed to solve the coupled non-linear equations governing the flow. The flow phenomenon has been characterized by Hartmann number, suction Reynolds number, channel Reynolds number and Prandtl number. The effects of these parameters on the velocity and temperature distribution have been analyzed and the results are presented with the aid of figures. It is observed that a growing suction parameter R retards the velocity of the flow field both in MHD as well as non-MHD flow. The effect of increasing Hartmann number is to decrease the transverse component of velocity for both suction and injection and in absence of suction and injection, while it decreases the axial component of velocity up to the middle of the channel and beyond this the effect reverses. There is a sharp fluctuation in temperature near the walls and at the middle of the channel which may be attributed to the discontinuous change in wall temperature. For fluids having low Prandtl number such as air, the temperature assumes negative values.

S. S. Das, M. Mohanty, R. K. Padhy, M. Sahu

2012-01-01

391

Discrete Control Systems establishes a basis for the analysis and design of discretized/quantized control systemsfor continuous physical systems. Beginning with the necessary mathematical foundations and system-model descriptions, the text moves on to derive a robust stability condition. To keep a practical perspective on the uncertain physical systems considered, most of the methods treated are carried out in the frequency domain. As part of the design procedure, modified Nyquist–Hall and Nichols diagrams are presented and discretized proportional–integral–derivative control schemes are reconsidered. Schemes for model-reference feedback and discrete-type observers are proposed. Although single-loop feedback systems form the core of the text, some consideration is given to multiple loops and nonlinearities. The robust control performance and stability of interval systems (with multiple uncertainties) are outlined. Finally, the monograph describes the relationship between feedback-control and discrete ev...

Okuyama, Yoshifumi

2014-01-01

392

This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.

Hunt, R.J.; Anderson, M.P.; Kelson, V.A.

1998-01-01

393

Discrete Aleksandrov solutions of the Monge-Ampere equation

We give a discrete analogue of the Aleksandrov theory of the Monge-Ampere equation for nonlinear difference equations. As a consequence we obtain the convergence to the Aleksandrov solution of a monotone finite difference method and a new result on the equivalence between Aleksandrov and viscosity solutions. Our result provides a theoretical link between the geometric and the finite difference approaches to the numerical resolution of the Monge-Ampere equation.

Awanou, Gerard

2014-01-01

394

Atherosclerotic plaque rupture and progression have been the focus of intensive investigations in recent years. Plaque rupture is closely related to most severe cardiovascular syndromes such as heart attack and stroke. A computational procedure based on meshless generalized finite difference (MGFD) method and serial magnetic resonance imaging (MRI) data was introduced to quantify patient-specific carotid atherosclerotic plaque growth functions and simulate plaque progression. Participating patients were scanned three times (T(1), T(2), and T(3), at intervals of about 18 months) to obtain plaque progression data. Vessel wall thickness (WT) changes were used as the measure for plaque progression. Since there was insufficient data with the current technology to quantify individual plaque component growth, the whole plaque was assumed to be uniform, homogeneous, hyperelastic, isotropic and nearly incompressible. The linear elastic model was used. The 2D plaque model was discretized and solved using a meshless generalized finite difference (GFD) method. Starting from the T(2) plaque geometry, plaque progression was simulated by solving the solid model and adjusting wall thickness using plaque growth functions iteratively until T(3) is reached. Numerically simulated plaque progression agreed very well with actual plaque geometry at T(3) given by MRI data. We believe this is the first time plaque progression simulation based on multi-year patient-tracking data was reported. Serial MRI-based progression simulation adds time dimension to plaque vulnerability assessment and will improve prediction accuracy for potential plaque rupture risk. PMID:19774222

Yang, Chun; Tang, Dalin; Yuan, Chun; Kerwin, William; Liu, Fei; Canton, Gador; Hatsukami, Thomas S; Atluri, Satya

2008-01-01

395

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

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 (?zz, ?zzz, ?zzzz, 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. The lowest energy eigenstates of a given irreducible representation and spin can be obtained. The program can be used to perform one-particle calculations with (smooth) Coulomb and Krammers-Henneberger potentials and also DFT-type calculations using LDA or B88 exchange functionals and LYP or VWN correlations ones or the self-consistent multiplicative constant method. Solution method: Single-particle two-dimensional numerical functions (orbitals) are used to construct an antisymmetric many-electron wave function of the restricted open-shell Hartree-Fock model. The orbitals are obtained by solving the Hartree-Fock equations as coupled two-dimensional second-order (elliptic) partial differential equations (PDEs). The Coulomb and exchange potentials are obtained as solutions of the corresponding Poisson equations. The PDEs are discretized by the eighth-order central difference stencil on a two-dimensional single grid, and the resulting large and sparse system of linear equations is solved by the (multicolour) successive overrelaxation ((MC)SOR) method. The self-consistent-field iterations are interwoven with the (MC)SOR ones and orbital energies and normalization factors are used to monitor the convergence. The accuracy of solutions depends mainly on the grid and the system under consideration, which means that within double precision arithmetic one can obtain orbitals and energies having up to 12 significant figures. If more accurate results are needed, quadruple-precision floating-point arithmetic can be used. Reasons for new version: Additional features, many modifications and corrections, improved convergence rate, overhauled code and documentation. Summary of revisions: see ChangeLog found in tar.gz archive Restrictions: The present version of the program is restricted to 60 orbitals. The maximum grid size is determined at compilation time. Unusual features: The program uses two C routines for allocating and deallocating memory. Several BLAS (Basic Linear Algebra System) routines are emulated by the program. When possible they should be replaced by their libra

Kobus, Jacek

2013-03-01

396

Comparison of B?spline Method and Finite Difference Method to Solve BVP of Linear ODEs

Directory of Open Access Journals (Sweden)

Full Text Available B-spline functions play important roles in both mathematics and engineering. To describe a numerical method for solving the boundary value problem of linear ODE with second-order by using B-spline. First, the cubic B-spline basis functions are introduced, then we use the linear combination of cubic B-spline basis to approximate the solution. Finally, we obtain the numerical solution by solving tri-diagonal equations. The results are compared with finite difference method through two examples which shows that the B-spline method is feasible and efficient.

Jincai Chang

2011-10-01

397

International Nuclear Information System (INIS)

We present a code for solving the coupled Einstein-hydrodynamics equations to evolve relativistic, self-gravitating fluids. The Einstein field equations are solved in generalized harmonic coordinates on one grid using pseudospectral methods, while the fluids are evolved on another grid using shock-capturing finite difference or finite volume techniques. We show that the code accurately evolves equilibrium stars and accretion flows. Then we simulate an equal-mass nonspinning black hole-neutron star binary, evolving through the final four orbits of inspiral, through the merger, to the final stationary black hole. The gravitational waveform can be reliably extracted from the simulation.

398

Directory of Open Access Journals (Sweden)

Full Text Available Numerical simulation and theoretical analysis of seawater intrusion is the mathematical basis for modern environmental science. Its mathematical model is the nonlinear coupled system of partial differential equations with initial-boundary problems. For a generic case of a three-dimensional bounded region, two kinds of finite difference fractional steps pro- cedures are put forward. Optimal order estimates in norm are derived for the error in the approximation solution. The present method has been successfully used in predicting the consequences of seawater intrusion and protection projects.

Yirang Yuan

2012-10-01

399

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

Directory of Open Access Journals (Sweden)

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

Attique Dawood

2013-07-01

400

International Nuclear Information System (INIS)

The reflection of light from a semiconductor structure on a silicon wafer is analyzed with the finite-difference time-domain technique, with the structure gradually modified for typical defect categories. The effect of these changes on the near and far fields of the reflected light is determined, including the behavior over a continuous range. These results can be useful in designing advanced inspection instruments capable of high accuracy. More complex changes to the original structure are also studied to the same end. (paper)

401

We present a code for solving the coupled Einstein-hydrodynamics equations to evolve relativistic, self-gravitating fluids. The Einstein field equations are solved in generalized harmonic coordinates on one grid using pseudospectral methods, while the fluids are evolved on another grid using shock-capturing finite difference or finite volume techniques. We show that the code accurately evolves equilibrium stars and accretion flows. Then we simulate an equal-mass nonspinning black hole-neutron star binary, evolving through the final four orbits of inspiral, through the merger, to the final stationary black hole. The gravitational waveform can be reliably extracted from the simulation.

Duez, Matthew D; Kidder, Lawrence E; Pfeiffer, Harald P; Scheel, Mark A; Teukolsky, Saul A

2008-01-01

402

DEFF Research Database (Denmark)

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

Tanev, Stoyan; Sun, Wenbo

2012-01-01

403

A rigorous full-wave solution, via the Finite-Difference-Time-Domain (FDTD) method, is performed in an attempt to obtain realistic communication channel models for on-body wireless transmission in Body-Area-Networks (BANs), which are local data networks using the human body as a propagation medium. The problem of modeling the coupling between body mounted antennas is often not amenable to attack by hybrid techniques owing to the complex nature of the human body. For instance, the time-domain ...

Raj Mittra; Bringuier, Jonathan N.

2012-01-01

404

Simulation model of a gel shallow solar pond using finite difference method

International Nuclear Information System (INIS)

A solar pond consists of carboxy methyl cellulose as a gel layer and it floats on the convective zone. A simulation model for the gel shallow solar pond is developed by using energy balance equation. The energy balance equation for the convection zone (salt water) is written in the form of partial differential equation. The parameters involved in the energy balance equation are heat loss, heat capacity and solar energy gain though the surface insolation and is solved by finite difference method. The thermal performance of the GSSP model is analyzed by making use of monthly mean hourly radiation for Coimbatore, India (11 degree N latitude). (Author)

405

Numerical simulation of shock propatation by the finite difference lattice boltzmann method

International Nuclear Information System (INIS)

The shock process represents an abrupt change in fluid properties, in which finite variations in pressure, temperature, and density occur over a shock thickness which is comparable to the mean free path of the gas molecules involved. The fluid phenomenon is simulated by using Finite Difference Lattice Boltzmann Method(FDLBM). In this research, the new model is proposed using the lattice BGK compressible fluid model in FDLBM for the purpose of shortening in calculation time and stabilizing in simulation operation. The numerical results agree also with the theoretical predictions

406

An Exploration of the Approximation of Derivative Functions via Finite Differences

Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent approximations to various derivative functions, including those used in modeling important physical processes on uniform grids. However, our research reveals that difference approximations on uniform grids cannot be applied blindly on nonuniform grids, nor can difference formulas to form consistent approximations to second derivatives. At best, they may lose accuracy; at worst they are inconsistent. Detailed consistency and error analysis, together with simulated examples, will be given.

Jain, Brian

2010-01-01

407

A computational study of vortex-airfoil interaction using high-order finite difference methods

Simulations of the interaction between a vortex and a NACA0012 airfoil are performed with a stable, high-order accurate (in space and time), multi-block finite difference solver for the compressible Navier–Stokes equations. We begin by computing a benchmark test case to validate the code. Next, the flow with steady inflow conditions are computed on several different grids. The resolution of the boundary layer as well as the amount of the artificial dissipation is studied to establish the ne...

Sva?rd, Magnus; Lundberg, Johan; Nordstro?m, Jan

2010-01-01

408

International Nuclear Information System (INIS)

An improved solution scheme is developed for the three-dimensional radiative transfer equation (RTE) in inhomogeneous cloudy atmospheres. This solution scheme is deterministic (explicit) and utilizes spherical harmonics series expansion and the finite-volume method for discretization of the RTE. The first-order upwind finite difference is modified to take into account bidirectional flow of radiance in spherical harmonics space, and an iterative solution method is applied. The multigrid method, which is generally employed to achieve rapid convergence in iterative calculation, is incorporated into the solution scheme. The present study suggests that the restriction and prolongation procedure for the multigrid method must be also modified to account for bidirectional flow, and proposes an efficient bidirectional restriction/prolongation procedure that does not increase the computational effort for coarser grids, resulting in a type of wavelet low-pass filter. Several calculation examples for various atmosphere models indicate that the proposed solution scheme is effective for rapid convergence and suitable for obtaining adequate radiation fields in inhomogeneous cloudy atmospheres, although a comparison with the Monte Carlo method suggests that the radiances obtained by this solution scheme at certain angles tends to be smoother. -- Highlights: • We develop a deterministic solution scheme for the 3-D radiative transfer. • The multigrid method is incorporated into an iterative solution scheme. • The multigrid method needs to be modified for the incorporation. • An ingenious procedure for the restriction and prolongation is proposed. • The scheme results in rapid convergence and obtains adequate radiation fields

409

International Nuclear Information System (INIS)

The nonlinear dynamic response of doubly curved shallow shells resting on Winkler-Pasternak elastic foundation has been studied for step and sinusoidal loadings. Dynamic analogues of Von Karman-Donnel type shell equations are used. Clamped immovable and simply supported immovable boundary conditions are considered. The governing nonlinear partial differential equations of the shell are discretized in space and time domains using the harmonic differential quadrature (HDQ) and finite differences (FD) methods, respectively. The accuracy of the proposed HDQ-FD coupled methodology is demonstrated by numerical examples. The shear parameter G of the Pasternak foundation and the stiffness parameter K of the Winkler foundation have been found to have a significant influence on the dynamic response of the shell. It is concluded from the present study that the HDQ-FD methodolgy is a simple, efficient, and accurate method for the nonlinear analysis of doubly curved shallow shells resting on two-parameter elastic foundation

410

Computational modelling of geophysical data is an important step in the process of hydrocarbon exploration. It consists in simulating the exploratory procedure and realistic geological environments. It allows a preliminary evaluation of the exploration feasibility of a particular terrain or geological model, indicating the best conditions for geophysical surveys. In this paper, we assess the Finite Difference frequency domain method for modelling the electromagnetic response of a horizontal electric dipole in 1D and 2.5D geometries. The non-uniform grid is refined in regions where the electromagnetic fields vary rapidly, namely the regions where we have variation in conductivity distribution and near the source dipole. We chose the horizontal electromagnetic dipole because it is the source normally used in the marine controlled-source electromagnetic surveys (mCSEM), which is the next step in our research. The mCSEM, also known as Sea Bed Logging, is a method for detection and characterization of thin resistive structures, like hydrocarbon reservoirs, often located in regions of deep water. It consists of a mobile electric dipole or a magnetic loop as a source, positioned near the sea floor where an array of electric and magnetic receivers are deployed. The source transmitter uses a low frequency signal on the order of 1Hz, that diffuses both in the ocean and in the sediments beneath it and is captured by the receivers . Amplitude and phase of this signal depend on the electrical conductivity of the seabed environment. The complexity of the environments and the large dimensions of the geological domains that we want to investigate make the modelling procedure extremely demanding, since the Finite Difference method requires a total discretization of the studied domain, resulting in large systems of linear equations, which can make the procedure long and expensive. Non-uniform grids and exploitation of the sparse property of the Finite Difference matrices are example options to circumvent this problem. Further, the use of gradient methods to solve the system of equation is tested here. We started using the conjugate gradient method (CG) that takes advantage of the complex symmetry of the Finite Difference matrices of this problem to make the calculations faster. But when handling anisotropy for instance, which is also included in our next steps, this complex symmetry is lost, requiring the biconjugate gradient method (BiCG), that does not require this symmetry but is slower than CG. Matrix preconditioning is important for convergence of the solution, but it can also destroy the complex symmetry of the matrices and this is another reason for the use of BiCG. Results include layered media and a finite cross section target, validated by their analytical solutions.

Miranda, D. D.; Howard, A. Q.

2012-12-01

411

MasQU: Finite Differences on Masked Irregular Stokes Q,U Grids

The future detection of B-mode polarization in the CMB is one of the most important outstanding tests of inflationary cosmology. One of the necessary steps for extracting polarization information in the CMB is reducing contamination from so-called 'ambiguous modes' on a masked sky. This can be achieved by utilising derivative operators on the real-space Stokes Q and U parameters. The main result of this paper is the presentation of an algorithm and a software package to perform this procedure on the full sky, i.e. with projects such as the Planck Surveyor and future satellites in mind; in particular, the package can perform finite differences on masked, irregular grids and is applied to a semi-regular spherical pixelisation, the HEALPix grid. The formalism reduces to the known finite difference solutions in the case of a regular grid. We quantify full-sky improvements on the possible bounds of the CMB B-mode signal. We find that in the specific case of E and B-mode separation, there exists a 'pole problem' in...

Bowyer, Jude; Novikov, Dmitri I

2011-01-01

412

International Nuclear Information System (INIS)

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)

413

Modeling of tension-modulated strings using finite difference and digital waveguide techniques

Tension modulation is a nonlinear phenomenon where large-amplitude string vibrations cause the tension of the string to vary. This results in an initial pitch glide and energy coupling between modes, causing for example the generation of missing harmonics. The presentation discusses two methods for numerical simulation of the tension modulation nonlinearity from the sound synthesis point of view. The tension modulation is assumed to propagate instantaneously along the string. In the digital waveguide approach, spatially distributed fractional delay filters are used in modulating the string length during run time. Energy-preserving techniques can be used in implementing the fractional delays. In the finite difference approach, time-domain interpolation is used to artificially modulate the wave propagation velocity. The generation of missing harmonics is implemented in the finite difference model by creating an additional excitation point at the string termination. In the waveguide model, the same effect can be obtained by using suitable approximations in the string elongation calculation. Synthesis results for both techniques are presented. Also, a brief comparison of the models with a discussion on stability issues is provided. [This research has been funded by the Academy of Finland (Project No. 104934), S3TK graduate school, and Tekniikan edistamissaatio.

Pakarinen, Jyri

2005-09-01

414

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

Ibral, Asmaa; Zouitine, Asmaa; Assaid, El Mahdi; El Achouby, Hicham; Feddi, El Mustapha; Dujardin, Francis

2015-02-01

415

Perfectly matched layer stability in 3-D finitedifference time-domain simulations is demonstrated for two piezoelectric crystals: barium sodium niobate and bismuth germanate. Stability is achieved by adapting the discretization grid to meet a central-difference scheme. Stability is demonstrated by showing that the total energy of the piezoelectric system remains constant in the steady state. PMID:25768826

Nova, Omar; Peña, Néstor; Ney, Michel

2015-03-01

416

International Nuclear Information System (INIS)

Highlights: ? The hybrid SD–SGF–CN spectral nodal method. ? Accurate coarse-mesh solution to SN eigenvalue problems in X,Y geometry. ? Analytical spatial reconstruction scheme within each discretization node. ? Accurate flux profile generated from the spatial reconstruction scheme. - Abstract: Nodal methods are widely regarded as forming an accurate class of coarse-mesh methods for neutron transport problems in the discrete ordinates (SN) formulation. They are also viewed as efficient methods, as the number of floating point operations generally decrease, as a result of the reduced number of mesh points; therefore they generate accurate results in shorter running time. However, the coarse-mesh numerical solutions do not yield detailed information on the solution profile, as the grid points can be located considerably apart from each other. In this paper, we describe an analytical spatial reconstruction of coarse-mesh solutions of the SN transverse integrated nodal equations with constant approximations for the transverse leakage terms, as generated by the hybrid spectral diamond–spectral Green’s function–constant nodal (SD–SGF–CN) method for monoenergetic SN eigenvalue problems in X,Y geometry for neutron multiplying systems. Numerical results for typical model problems are given and we close with general concluding remarks and suggestions for future work

417

Simple Numerical Schemes for the Korteweg-deVries Equation

International Nuclear Information System (INIS)

Two numerical schemes, which simulate the propagation of dispersive non-linear waves, are described. The first is a split-step Fourier scheme for the Korteweg-de Vries (KdV) equation. The second is a finite-difference scheme for the modified KdV equation. The stability and accuracy of both schemes are discussed. These simple schemes can be used to study a wide variety of physical processes that involve dispersive nonlinear waves

418

Simple Numerical Schemes for the Korteweg-deVries Equation

Energy Technology Data Exchange (ETDEWEB)

Two numerical schemes, which simulate the propagation of dispersive non-linear waves, are described. The first is a split-step Fourier scheme for the Korteweg-de Vries (KdV) equation. The second is a finite-difference scheme for the modified KdV equation. The stability and accuracy of both schemes are discussed. These simple schemes can be used to study a wide variety of physical processes that involve dispersive nonlinear waves.

C. J. McKinstrie; M. V. Kozlov

2000-12-01

419

Scientific Electronic Library Online (English)

Full Text Available La ecuación de Derrida-Lebowitz-Speer-Spohn (DLSS) es una ecuación de evolución no lineal de cuarto orden. Esta aparece en el estudio de las fluctuaciones de interface de sistemas de espín y en la modelación de semicoductores cuánticos. En este artículo, se presenta una discretización por elementos [...] finitos para una formulación exponencial de la ecuación DLSS abordada como un sistema acoplado de ecuaciones. Usando la información disponible acerca del fenómeno físico, se establecen las condiciones de contorno para el sistema acoplado. Se demuestra la existencia de la solución discreta global en el tiempo via un argumento de punto fijo. Los resultados numéricos ilustran el carácter cuántico de la ecuación. Finalmente se presenta un test del orden de convergencia de la discretización porpuesta. Abstract in english The Derrida-Lebowitz-Speer-Spohn (DLSS) equation is a fourth order in space non-linear evolution equation. This equation arises in the study of interface fluctuations in spin systems and quantum semiconductor modelling. In this paper, we present a finite element discretization for a exponential form [...] ulation of a coupled-equation approach to the DLSS equation. Using the available information about the physical phenomena, we are able to set the corresponding boundary conditions for the coupled system. We prove existence of the discrete solution by fixed point argument. Numerical results illustrate the quantum character of the equation. Finally a test of order of convergence of the proposed discretization scheme is presented.

Jorge Mauricio, Ruiz Vera; Ignacio, Mantilla Prada.

2013-06-01

420

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.

Luo, Y.; Xia, J.; Xu, Y.; Zeng, C.; Liu, J.

2010-01-01