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Sample records for finite difference scheme

  1. Nonstandard finite difference schemes for differential equations

    Directory of Open Access Journals (Sweden)

    Mohammad Mehdizadeh Khalsaraei

    2014-12-01

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

  2. Finite-difference schemes for anisotropic diffusion

    Energy Technology Data Exchange (ETDEWEB)

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

    2014-09-01

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

  3. PERTURBATIONAL FINITE DIFFERENCE SCHEME OF CONVECTION-DIFFUSION EQUATION

    Institute of Scientific and Technical Information of China (English)

    2002-01-01

    The Perturbational Finite Difference (PFD) method is a kind of high-order-accurate compact difference method, But its idea is different from the normal compact method and the multi-nodes method. This method can get a Perturbational Exact Numerical Solution (PENS) scheme for locally linearlized Convection-Diffusion (CD) equation. The PENS scheme is similar to the Finite Analytical (FA) scheme and Exact Difference Solution (EDS) scheme, which are all exponential schemes, but PENS scheme is simpler and uses only 3, 5 and 7 nodes for 1-, 2- and 3-dimensional problems, respectively. The various approximate schemes of PENS scheme are also called Perturbational-High-order-accurate Difference (PHD) scheme. The PHD schemes can be got by expanding the exponential terms in the PENS scheme into power series of grid Renold number, and they are all upwind schemes and remain the concise structure form of first-order upwind scheme. For 1-dimensional (1-D) CD equation and 2-D incompressible Navier-Stokes equation, their PENS and PHD schemes were constituted in this paper, they all gave highly accurate results for the numerical examples of three 1-D CD equations and an incompressible 2-D flow in a square cavity.

  4. Explicit and implicit finite difference schemes for fractional Cattaneo equation

    Science.gov (United States)

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

    2010-09-01

    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.

  5. Higher order finite difference schemes for the magnetic induction equations

    CERN Document Server

    Koley, Ujjwal; Risebro, Nils Henrik; Svärd, Magnus

    2011-01-01

    We describe high order accurate and stable finite difference schemes for the initial-boundary value problem associated with the magnetic induction equations. These equations model the evolution of a magnetic field due to a given velocity field. The finite difference schemes are based on Summation by Parts (SBP) operators for spatial derivatives and a Simultaneous Approximation Term (SAT) technique for imposing boundary conditions. We present various numerical experiments that demonstrate both the stability as well as high order of accuracy of the schemes.

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

    Science.gov (United States)

    Fisher, Travis C.; Carpenter, Mark H.

    2013-01-01

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

  7. Finite Boltzmann schemes

    NARCIS (Netherlands)

    Sman, van der R.G.M.

    2006-01-01

    In the special case of relaxation parameter = 1 lattice Boltzmann schemes for (convection) diffusion and fluid flow are equivalent to finite difference/volume (FD) schemes, and are thus coined finite Boltzmann (FB) schemes. We show that the equivalence is inherent to the homology of the

  8. A FINITE DIFFERENCE SCHEME FOR THE GENERALIZED NONLINEAR SCHRODINGER EQUATION WITH VARIABLE COEFFICIENTS

    Institute of Scientific and Technical Information of China (English)

    Wei-zhong Dai; Raja Nassar

    2000-01-01

    A finite difference scheme for the generalized nonlinear Schrodinger equation with variable coefficients is developed. The scheme is shown to satisfy two conser vation laws. Numerical results show that the scheme is accurate and efficient.

  9. On the monotonicity of multidimensional finite difference schemes

    Science.gov (United States)

    Kovyrkina, O.; Ostapenko, V.

    2016-10-01

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

  10. DIFFERENCE SCHEME AND NUMERICAL SIMULATION BASED ON MIXED FINITE ELEMENT METHOD FOR NATURAL CONVECTION PROBLEM

    Institute of Scientific and Technical Information of China (English)

    罗振东; 朱江; 谢正辉; 张桂芳

    2003-01-01

    The non-stationary natural convection problem is studied. A lowest order finite difference scheme based on mixed finite element method for non-stationary natural convection problem, by the spatial variations discreted with finite element method and time with finite difference scheme was derived, where the numerical solution of velocity, pressure, and temperature can be found together, and a numerical example to simulate the close square cavity is given, which is of practical importance.

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

    NARCIS (Netherlands)

    Erdogan, Utku; Ozis, Turgut

    2011-01-01

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

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

    NARCIS (Netherlands)

    Erdogan, Utku; Ozis, Turgut

    2011-01-01

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

  13. Overlapping Domain Decomp osition Finite Difference Algorithm for Compact Difference Scheme of the Heat Conduction Equation

    Institute of Scientific and Technical Information of China (English)

    ZHANG Hong-mei

    2015-01-01

    In this paper, a modified additive Schwarz finite difference algorithm is applied in the heat conduction equation of the compact difference scheme. The algorithm is on the basis of domain decomposition and the subspace correction. The basic train of thought is the introduction of the units function decomposition and reasonable distribution of the overlap of correction. The residual correction is conducted on each subspace while the computation is completely parallel. The theoretical analysis shows that this method is completely characterized by parallel.

  14. AN EXPLICIT MULTI-CONSERVATION FINITE-DIFFERENCE SCHEME FOR SHALLOW-WATER-WAVE EQUATION

    Institute of Scientific and Technical Information of China (English)

    Bin Wang

    2008-01-01

    An explicit multi-conservation finite-difference scheme for solving the spherical shallowwater-wave equation set of barotropic atmosphere has been proposed. The numerical scheme is based on a special semi-discrete form of the equations that conserves four basic physical integrals including the total energy, total mass, total potential vorticity and total enstrophy. Numerical tests show that the new scheme performs closely like but is much more time-saving than the implicit multi-conservation scheme.

  15. Finite-difference scheme for the numerical solution of the Schroedinger equation

    Science.gov (United States)

    Mickens, Ronald E.; Ramadhani, Issa

    1992-01-01

    A finite-difference scheme for numerical integration of the Schroedinger equation is constructed. Asymptotically (r goes to infinity), the method gives the exact solution correct to terms of order r exp -2.

  16. Solving moving interface problems using a higher order accurate finite difference scheme

    Science.gov (United States)

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

    2017-07-01

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

  17. Optimal convergence rate of the explicit finite difference scheme for American option valuation

    Science.gov (United States)

    Hu, Bei; Liang, Jin; Jiang, Lishang

    2009-08-01

    An optimal convergence rate O([Delta]x) for an explicit finite difference scheme for a variational inequality problem is obtained under the stability condition using completely PDE methods. As a corollary, a binomial tree scheme of an American put option (where ) is convergent unconditionally with the rate O(([Delta]t)1/2).

  18. A sixth order hybrid finite difference scheme based on the minimized dispersion and controllable dissipation technique

    Science.gov (United States)

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

    2014-08-01

    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.

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

    DEFF Research Database (Denmark)

    Naulin, V.; Nielsen, A.H.

    2003-01-01

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

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

    CERN Document Server

    Schreilechner, Magdalena

    2015-01-01

    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.

  1. Semi-discrete finite difference multiscale scheme for a concrete corrosion model: approximation estimates and convergence

    CERN Document Server

    Chalupecký, Vladimír

    2011-01-01

    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.

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

    Directory of Open Access Journals (Sweden)

    Henryk Leszczyński

    2014-01-01

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

  3. High Order Finite Difference Schemes for the Elastic Wave Equation in Discontinuous Media

    CERN Document Server

    Virta, Kristoffer

    2013-01-01

    Finite difference schemes for the simulation of elastic waves in materi- als with jump discontinuities are presented. The key feature is the highly accurate treatment of interfaces where media discontinuities arise. The schemes are constructed using finite difference operators satisfying a sum- mation - by - parts property together with a penalty technique to impose interface conditions at the material discontinuity. Two types of opera- tors are used, termed fully compatible or compatible. Stability is proved for the first case by bounding the numerical solution by initial data in a suitably constructed semi - norm. Numerical experiments indicate that the schemes using compatible operators are also stable. However, the nu- merical studies suggests that fully compatible operators give identical or better convergence and accuracy properties. The numerical experiments are also constructed to illustrate the usefulness of the proposed method to simulations involving typical interface phenomena in elastic materials...

  4. Lie group invariant finite difference schemes for the neutron diffusion equation

    Energy Technology Data Exchange (ETDEWEB)

    Jaegers, P.J.

    1994-06-01

    Finite difference techniques are used to solve a variety of differential equations. For the neutron diffusion equation, the typical local truncation error for standard finite difference approximation is on the order of the mesh spacing squared. To improve the accuracy of the finite difference approximation of the diffusion equation, the invariance properties of the original differential equation have been incorporated into the finite difference equations. Using the concept of an invariant difference operator, the invariant difference approximations of the multi-group neutron diffusion equation were determined in one-dimensional slab and two-dimensional Cartesian coordinates, for multiple region problems. These invariant difference equations were defined to lie upon a cell edged mesh as opposed to the standard difference equations, which lie upon a cell centered mesh. Results for a variety of source approximations showed that the invariant difference equations were able to determine the eigenvalue with greater accuracy, for a given mesh spacing, than the standard difference approximation. The local truncation errors for these invariant difference schemes were found to be highly dependent upon the source approximation used, and the type of source distribution played a greater role in determining the accuracy of the invariant difference scheme than the local truncation error.

  5. A TVD-WAF-based hybrid finite volume and finite difference scheme for nonlinearly dispersive wave equations

    Directory of Open Access Journals (Sweden)

    Jing Yin

    2015-07-01

    Full Text Available A total variation diminishing-weighted average flux (TVD-WAF-based hybrid numerical scheme for the enhanced version of nonlinearly dispersive Boussinesq-type equations was developed. The one-dimensional governing equations were rewritten in the conservative form and then discretized on a uniform grid. The finite volume method was used to discretize the flux term while the remaining terms were approximated with the finite difference method. The second-order TVD-WAF method was employed in conjunction with the Harten-Lax-van Leer (HLL Riemann solver to calculate the numerical flux, and the variables at the cell interface for the local Riemann problem were reconstructed via the fourth-order monotone upstream-centered scheme for conservation laws (MUSCL. The time marching scheme based on the third-order TVD Runge-Kutta method was used to obtain numerical solutions. The model was validated through a series of numerical tests, in which wave breaking and a moving shoreline were treated. The good agreement between the computed results, documented analytical solutions, and experimental data demonstrates the correct discretization of the governing equations and high accuracy of the proposed scheme, and also conforms the advantages of the proposed shock-capturing scheme for the enhanced version of the Boussinesq model, including the convenience in the treatment of wave breaking and moving shorelines and without the need for a numerical filter.

  6. A nonstandard finite difference scheme for a basic model of cellular immune response to viral infection

    Science.gov (United States)

    Korpusik, Adam

    2017-02-01

    We present a nonstandard finite difference scheme for a basic model of cellular immune response to viral infection. The main advantage of this approach is that it preserves the essential qualitative features of the original continuous model (non-negativity and boundedness of the solution, equilibria and their stability conditions), while being easy to implement. All of the qualitative features are preserved independently of the chosen step-size. Numerical simulations of our approach and comparison with other conventional simulation methods are presented.

  7. A new fifth order finite difference WENO scheme for solving hyperbolic conservation laws

    Science.gov (United States)

    Zhu, Jun; Qiu, Jianxian

    2016-08-01

    In this paper a new simple fifth order weighted essentially non-oscillatory (WENO) scheme is presented in the finite difference framework for solving the hyperbolic conservation laws. The new WENO scheme is a convex combination of a fourth degree polynomial with two linear polynomials in a traditional WENO fashion. This new fifth order WENO scheme uses the same five-point information as the classical fifth order WENO scheme [14,20], could get less absolute truncation errors in L1 and L∞ norms, and obtain the same accuracy order in smooth region containing complicated numerical solution structures simultaneously escaping nonphysical oscillations adjacent strong shocks or contact discontinuities. The associated linear weights are artificially set to be any random positive numbers with the only requirement that their sum equals one. New nonlinear weights are proposed for the purpose of sustaining the optimal fifth order accuracy. The new WENO scheme has advantages over the classical WENO scheme [14,20] in its simplicity and easy extension to higher dimensions. Some benchmark numerical tests are performed to illustrate the capability of this new fifth order WENO scheme.

  8. High-Order Finite Difference GLM-MHD Schemes for Cell-Centered MHD

    CERN Document Server

    Mignone, A; Bodo, G

    2010-01-01

    We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different reconstruction techniques based on recently improved versions of the weighted essentially non-oscillatory (WENO) schemes, monotonicity preserving (MP) schemes as well as slope-limited polynomial reconstruction. The proposed numerical methods are highly accurate in smooth regions of the flow, avoid loss of accuracy in proximity of smooth extrema and provide sharp non-oscillatory transitions at discontinuities. We suggest a numerical formulation based on a cell-centered approach where all of the primary flow variables are discretized at the zone center. The divergence-free condition is enforced by augmenting the MHD equations with a generalized Lagrange multiplier yielding a mixed hyperbolic/parabolic correction, as in Dedner et al. (J. Comput. Phys. 175 (2002) 645-673). The resulting...

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

    Science.gov (United States)

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

    2008-07-01

    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.

  10. Finite Difference Weighted Essentially Non-Oscillatory Schemes with Constrained Transport for Ideal Magnetohydrodynamics

    CERN Document Server

    Christlieb, Andrew J; Tang, Qi

    2013-01-01

    In this work we develop a class of high-order finite difference weighted essentially non-oscillatory (FD-WENO) schemes for solving the ideal magnetohydrodynamic (MHD) equations in 2D and 3D. The philosophy of this work is to use efficient high-order WENO spatial discretizations with high-order strong stability-preserving Runge-Kutta (SSP-RK) time-stepping schemes. Numerical results have shown that with such methods we are able to resolve solution structures that are only visible at much higher grid resolutions with lower-order schemes. The key challenge in applying such methods to ideal MHD is to control divergence errors in the magnetic field. We achieve this by augmenting the base scheme with a novel high-order constrained transport approach that updates the magnetic vector potential. The predicted magnetic field from the base scheme is replaced by a divergence-free magnetic field that is obtained from the curl of this magnetic potential. The non-conservative weakly hyperbolic system that the magnetic vecto...

  11. Stability analysis of finite difference schemes for quantum mechanical equations of motion

    Science.gov (United States)

    Chattaraj, P. K.; Deb, B. M.; Koneru, S. Rao

    1987-10-01

    For a pdf involving both space and time variables, stability criteria are presently shown to change drastically when the equation contains i, as in the quantum-mechanical equations of motion. It is further noted that the stability of finite difference schemes for quantum-mechanical equations of motion depends on both spatial and temporal zoning. It is possible to compare a free particle Green's function to the solution of a simple diffusion equation, and the quantum-mechanical motion of a free particle to Fresnel diffraction in optics.

  12. On the convergence of certain finite-difference schemes by an inverse-matrix method

    Science.gov (United States)

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

    1975-01-01

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

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

    Science.gov (United States)

    Zhang, Yijie; Gao, Jinghuai

    2014-10-01

    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.

  14. Implicit predictor-corrector central finite difference scheme for the equations of magnetohydrodynamic simulations

    Science.gov (United States)

    Tsai, T. C.; Yu, H.-S.; Hsieh, M.-S.; Lai, S. H.; Yang, Y.-H.

    2015-11-01

    Nowadays most of supercomputers are based on the frame of PC cluster; therefore, the efficiency of parallel computing is of importance especially with the increasing computing scale. This paper proposes a high-order implicit predictor-corrector central finite difference (iPCCFD) scheme and demonstrates its high efficiency in parallel computing. Of special interests are the large scale numerical studies such as the magnetohydrodynamic (MHD) simulations in the planetary magnetosphere. An iPCCFD scheme is developed based on fifth-order central finite difference method and fourth-order implicit predictor-corrector method in combination with elimination-of-the-round-off-errors (ERE) technique. We examine several numerical studies such as one-dimensional Brio-Wu shock tube problem, two-dimensional Orszag-Tang vortex system, vortex type K-H instability, kink type K-H instability, field loop advection, and blast wave. All the simulation results are consistent with many literatures. iPCCFD can minimize the numerical instabilities and noises along with the additional diffusion terms. All of our studies present relatively small numerical errors without employing any divergence-free reconstruction. In particular, we obtain fairly stable results in the two-dimensional Brio-Wu shock tube problem which well conserves ∇ ṡ B = 0 throughout the simulation. The ERE technique removes the accumulation of roundoff errors in the uniform or non-disturbed system. We have also shown that iPCCFD is characterized by the high order of accuracy and the low numerical dissipation in the circularly polarized Alfvén wave tests. The proposed iPCCFD scheme is a parallel-efficient and high precision numerical scheme for solving the MHD equations in hyperbolic conservation systems.

  15. DNS of Sheared Particulate Flows with a 3D Explicit Finite-Difference Scheme

    Science.gov (United States)

    Perrin, Andrew; Hu, Howard

    2007-11-01

    A 3D explicit finite-difference code for direct simulation of the motion of solid particulates in fluids has been developed, and a periodic boundary condition implemented to study the effective viscosity of suspensions in shear. The code enforces the no-slip condition on the surface of spherical particles in a uniform Cartesian grid with a special particle boundary condition based on matching the Stokes flow solutions next to the particle surface with a numerical solution away from it. The method proceeds by approximating the flow next to the particle surface as a Stokes flow in the particle's local coordinates, which is then matched to the finite difference update in the bulk fluid on a ``cage'' of grid points near the particle surface. (The boundary condition is related to the PHYSALIS method (2003), but modified for explicit schemes and with an iterative process removed.) Advantages of the method include superior accuracy of the scheme on a relatively coarse grid for intermediate particle Reynolds numbers, ease of implementation, and the elimination of the need to track the particle surface. For the sheared suspension, the effects of fluid and solid inertia and solid volume fraction on effective viscosity at moderate particle Reynolds numbers and concentrated suspensions will be discussed.

  16. Finite difference weighted essentially non-oscillatory schemes with constrained transport for ideal magnetohydrodynamics

    Science.gov (United States)

    Christlieb, Andrew J.; Rossmanith, James A.; Tang, Qi

    2014-07-01

    In this work we develop a class of high-order finite difference weighted essentially non-oscillatory (FD-WENO) schemes for solving the ideal magnetohydrodynamic (MHD) equations in 2D and 3D. The philosophy of this work is to use efficient high-order WENO spatial discretizations with high-order strong stability-preserving Runge-Kutta (SSP-RK) time-stepping schemes. Numerical results have shown that with such methods we are able to resolve solution structures that are only visible at much higher grid resolutions with lower-order schemes. The key challenge in applying such methods to ideal MHD is to control divergence errors in the magnetic field. We achieve this by augmenting the base scheme with a novel high-order constrained transport approach that updates the magnetic vector potential. The predicted magnetic field from the base scheme is replaced by a divergence-free magnetic field that is obtained from the curl of this magnetic potential. The non-conservative weakly hyperbolic system that the magnetic vector potential satisfies is solved using a version of FD-WENO developed for Hamilton-Jacobi equations. The resulting numerical method is endowed with several important properties: (1) all quantities, including all components of the magnetic field and magnetic potential, are treated as point values on the same mesh (i.e., there is no mesh staggering); (2) both the spatial and temporal orders of accuracy are fourth-order; (3) no spatial integration or multidimensional reconstructions are needed in any step; and (4) special limiters in the magnetic vector potential update are used to control unphysical oscillations in the magnetic field. Several 2D and 3D numerical examples are presented to verify the order of accuracy on smooth test problems and to show high-resolution on test problems that involve shocks.

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

    Directory of Open Access Journals (Sweden)

    G. F. Sun

    2015-01-01

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

  18. Nonstandard finite difference scheme for SIRS epidemic model with disease-related death

    Science.gov (United States)

    Fitriah, Z.; Suryanto, A.

    2016-04-01

    It is well known that SIRS epidemic with disease-related death can be described by a system of nonlinear ordinary differential equations (NL ODEs). This model has two equilibrium points where their existence and stability properties are determined by the basic reproduction number [1]. Besides the qualitative properties, it is also often needed to solve the system of NL ODEs. Euler method and 4th order Runge-Kutta (RK4) method are often used to solve the system of NL ODEs. However, both methods may produce inconsistent qualitative properties of the NL ODEs such as converging to wrong equilibrium point, etc. In this paper we apply non-standard finite difference (NSFD) scheme (see [2,3]) to approximate the solution of SIRS epidemic model with disease-related death. It is shown that the discrete system obtained by NSFD scheme is dynamically consistent with the continuous model. By our numerical simulations, we find that the solutions of NSFD scheme are always positive, bounded and convergent to the correct equilibrium point for any step size of integration (h), while those of Euler or RK4 method have the same properties only for relatively small h.

  19. Finite Difference Approach for Estimating the Thermal Conductivity by 6-point Crank-Nicolson Scheme

    Institute of Scientific and Technical Information of China (English)

    SU Ya-xin; YANG Xiang-xiang

    2005-01-01

    Based on inverse heat conduction theory, a theoretical model using 6-point Crank-Nicolson finite difference scheme was used to calculate the thermal conductivity from temperature distribution, which can be measured experimentally. The method is a direct approach of second-order and the key advantage of the present method is that it is not required a priori knowledge of the functional form of the unknown thermal conductivity in the calculation and the thermal parameters are estimated only according to the known temperature distribution. Two cases were numerically calculated and the influence of experimental deviation on the precision of this method was discussed. The comparison of numerical and analytical results showed good agreement.

  20. SHALLOW WATER EQUATION SOLUTION IN 2D USING FINITE DIFFERENCE METHOD WITH EXPLICIT SCHEME

    Directory of Open Access Journals (Sweden)

    Nuraini Nuraini

    2017-09-01

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

  1. Partially implicit finite difference scheme for calculating dynamic pressure in a terrain-following coordinate non-hydrostatic ocean model

    Science.gov (United States)

    Liu, Zhe; Lin, Lei; Xie, Lian; Gao, Huiwang

    2016-10-01

    To improve the efficiency of the terrain-following σ-coordinate non-hydrostatic ocean model, a partially implicit finite difference (PIFD) scheme is proposed. By using explicit terms instead of implicit terms to discretize the parts of the vertical dynamic pressure gradient derived from the σ-coordinate transformation, the coefficient matrix of the discrete Poisson equation that the dynamic pressure satisfies can be simplified from 15 diagonals to 7 diagonals. The PIFD scheme is shown to run stably when it is applied to simulate five benchmark cases, namely, a standing wave in a basin, a surface solitary wave, a lock-exchange problem, a periodic wave over a bar and a tidally induced internal wave. Compared with the conventional fully implicit finite difference (FIFD) scheme, the PIFD scheme produces simulation results of equivalent accuracy at only 40-60% of the computational cost. The PIFD scheme demonstrates strong applicability and can be easily implemented in σ-coordinate ocean models.

  2. A Staggered Fourth-Order Accurate Explicit Finite Difference Scheme for the Time-Domain Maxwell's Equations

    Science.gov (United States)

    Yefet, Amir; Petropoulos, Peter G.

    2001-04-01

    We consider a model explicit fourth-order staggered finite-difference method for the hyperbolic Maxwell's equations. Appropriate fourth-order accurate extrapolation and one-sided difference operators are derived in order to complete the scheme near metal boundaries and dielectric interfaces. An eigenvalue analysis of the overall scheme provides a necessary, but not sufficient, stability condition and indicates long-time stability. Numerical results verify both the stability analysis, and the scheme's fourth-order convergence rate over complex domains that include dielectric interfaces and perfectly conducting surfaces. For a fixed error level, we find the fourth-order scheme is computationally cheaper in comparison to the Yee scheme by more than an order of magnitude. Some open problems encountered in the application of such high-order schemes are also discussed.

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

    Science.gov (United States)

    Gerritsen, Margot; Olsson, Pelle

    1996-01-01

    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.

  4. On a consistent high-order finite difference scheme with kinetic energy conservation for simulating turbulent reacting flows

    Science.gov (United States)

    Trisjono, Philipp; Kang, Seongwon; Pitsch, Heinz

    2016-12-01

    The main objective of this study is to present an accurate and consistent numerical framework for turbulent reacting flows based on a high-order finite difference (HOFD) scheme. It was shown previously by Desjardins et al. (2008) [4] that a centered finite difference scheme discretely conserving the kinetic energy and an upwind-biased scheme for the scalar transport can be combined into a useful scheme for turbulent reacting flows. With a high-order spatial accuracy, however, an inconsistency among discretization schemes for different conservation laws is identified, which can disturb a scalar field spuriously under non-uniform density distribution. Various theoretical and numerical analyses are performed on the sources of the unphysical error. From this, the derivative of the mass-conserving velocity and the local Péclet number are identified as the primary factors affecting the error. As a solution, an HOFD stencil for the mass conservation is reformulated into a flux-based form that can be used consistently with an upwind-biased scheme for the scalar transport. The effectiveness of the proposed formulation is verified using two-dimensional laminar flows such as a scalar transport problem and a laminar premixed flame, where unphysical oscillations in the scalar fields are removed. The applicability of the proposed scheme is demonstrated in an LES of a turbulent stratified premixed flame.

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

    Science.gov (United States)

    Mickens, Ronald E.

    1989-01-01

    A family of conditionally stable, forward Euler finite difference equations can be constructed for the simplest equation of Schroedinger type, namely u sub t - iu sub xx. Generalization of this result to physically realistic Schroedinger type equations is presented.

  6. A Modified Equation Approach to Selecting a Nonstandard Finite Difference Scheme Applied to the Regularized Long Wave Equation

    Directory of Open Access Journals (Sweden)

    E. Momoniat

    2014-01-01

    Full Text Available Two nonstandard finite difference schemes are derived to solve the regularized long wave equation. The criteria for choosing the “best” nonstandard approximation to the nonlinear term in the regularized long wave equation come from considering the modified equation. The two “best” nonstandard numerical schemes are shown to preserve conserved quantities when compared to an implicit scheme in which the nonlinear term is approximated in the usual way. Comparisons to the single solitary wave solution show significantly better results, measured in the L2 and L∞ norms, when compared to results obtained using a Petrov-Galerkin finite element method and a splitted quadratic B-spline collocation method. The growth in the error when simulating the single solitary wave solution using the two “best” nonstandard numerical schemes is shown to be linear implying the nonstandard finite difference schemes are conservative. The formation of an undular bore for both steep and shallow initial profiles is captured without the formation of numerical instabilities.

  7. Symmetric finite volume schemes for eigenvalue problems in arbitrary dimensions

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    Based on a linear finite element space,two symmetric finite volume schemes for eigenvalue problems in arbitrary dimensions are constructed and analyzed.Some relationships between the finite element method and the finite difference method are addressed,too.

  8. Symmetric finite volume schemes for eigenvalue problems in arbitrary dimensions

    Institute of Scientific and Technical Information of China (English)

    DAI Xiaoying; YANG Zhang; ZHOU Aihui

    2008-01-01

    Based on a linear finite element space, two symmetric finite volume schemes for eigenvalue problems in arbitrary dimensions are constructed and analyzed. Some relationships between the finite element method and the finite difference method are addressed, too.

  9. Optimal fourth-order staggered-grid finite-difference scheme for 3D frequency-domain viscoelastic wave modeling

    Science.gov (United States)

    Li, Y.; Han, B.; Métivier, L.; Brossier, R.

    2016-09-01

    We investigate an optimal fourth-order staggered-grid finite-difference scheme for 3D frequency-domain viscoelastic wave modeling. An anti-lumped mass strategy is incorporated to minimize the numerical dispersion. The optimal finite-difference coefficients and the mass weighting coefficients are obtained by minimizing the misfit between the normalized phase velocities and the unity. An iterative damped least-squares method, the Levenberg-Marquardt algorithm, is utilized for the optimization. Dispersion analysis shows that the optimal fourth-order scheme presents less grid dispersion and anisotropy than the conventional fourth-order scheme with respect to different Poisson's ratios. Moreover, only 3.7 grid-points per minimum shear wavelength are required to keep the error of the group velocities below 1%. The memory cost is then greatly reduced due to a coarser sampling. A parallel iterative method named CARP-CG is used to solve the large ill-conditioned linear system for the frequency-domain modeling. Validations are conducted with respect to both the analytic viscoacoustic and viscoelastic solutions. Compared with the conventional fourth-order scheme, the optimal scheme generates wavefields having smaller error under the same discretization setups. Profiles of the wavefields are presented to confirm better agreement between the optimal results and the analytic solutions.

  10. A Finite Difference Scheme for Solving the Undamped Timoshenko Beam Equations with Both Ends Free

    Institute of Scientific and Technical Information of China (English)

    Fu-le LI; Zong-hu XIU

    2012-01-01

    In this paper,a boundary feedback system of a class of non-uniform undamped Timoshenko beam with both ends free is considered.A linearized three-level difference scheme for the Timoshenko beam equations is derived by the method of reduction of order on uniform meshes.The unique solvability,unconditional stability and convergence of the difference scheme are proved by the discrete energy method.The convergence order in maximum norm is of order two in both space and time. The validity of this theoretical analysis is verified experimentally.

  11. Eighth-Order Compact Finite Difference Scheme for 1D Heat Conduction Equation

    Directory of Open Access Journals (Sweden)

    Asma Yosaf

    2016-01-01

    Full Text Available The purpose of this paper is to develop a high-order compact finite difference method for solving one-dimensional (1D heat conduction equation with Dirichlet and Neumann boundary conditions, respectively. A parameter is used for the direct implementation of Dirichlet and Neumann boundary conditions. The introduced parameter adjusts the position of the neighboring nodes very next to the boundary. In the case of Dirichlet boundary condition, we developed eighth-order compact finite difference method for the entire domain and fourth-order accurate proposal is presented for the Neumann boundary conditions. In the case of Dirichlet boundary conditions, the introduced parameter behaves like a free parameter and could take any value from its defined domain but for the Neumann boundary condition we obtained a particular value of the parameter. In both proposed compact finite difference methods, the order of accuracy is the same for all nodes. The time discretization is performed by using Crank-Nicholson finite difference method. The unconditional convergence of the proposed methods is presented. Finally, a set of 1D heat conduction equations is solved to show the validity and accuracy of our proposed methods.

  12. Finite difference schemes for a nonlinear black-scholes model with transaction cost and volatility risk

    DEFF Research Database (Denmark)

    Mashayekhi, Sima; Hugger, Jens

    2015-01-01

    market. In this paper, we compare several finite difference methods for the solution of this model with respect to precision and order of convergence within a computationally feasible domain allowing at most 200 space steps and 10000 time steps. We conclude that standard explicit Euler comes out...

  13. Mean square convergent three points finite difference scheme for random partial differential equations

    Directory of Open Access Journals (Sweden)

    Magdy A. El-Tawil

    2012-10-01

    Full Text Available In this paper, the random finite difference method with three points is used in solving random partial differential equations problems mainly: random parabolic, elliptic and hyperbolic partial differential equations. The conditions of the mean square convergence of the numerical solutions are studied. The numerical solutions are computed through some numerical case studies.

  14. COMPACT FOURTH-ORDER FINITE DIFFERENCE SCHEMES FOR HELMHOLTZ EQUATION WITH HIGH WAVE NUMBERS

    Institute of Scientific and Technical Information of China (English)

    Yiping Fu

    2008-01-01

    In this paper,two fourth-order accurate compact difference schemes are presented for solving the Helmholtz equation in two space dimensions when the corresponding wave numbers are large.The main idea is to derive and to study a fourth-order accurate compact difference scheme whose leading truncation term,namely,the O(h4) term,is independent of the wave number and the sohrtion of the Helmholtz equation.The convergence property of the compact schemes are analyzed and the implementation of solving the resulting linear algebraic system based on a FFT approach is considered.Numerical results are presented,which support our theoretical predictions.Mathematics subject classification:65M06,65N12.

  15. A second-order high resolution finite difference scheme for a structured erythropoiesis model subject to malaria infection.

    Science.gov (United States)

    Ackleh, Azmy S; Ma, Baoling; Thibodeaux, Jeremy J

    2013-09-01

    We develop a second-order high-resolution finite difference scheme to approximate the solution of a mathematical model describing the within-host dynamics of malaria infection. The model consists of two nonlinear partial differential equations coupled with three nonlinear ordinary differential equations. Convergence of the numerical method to the unique weak solution with bounded total variation is proved. Numerical simulations demonstrating the achievement of the designed accuracy are presented.

  16. A finite difference scheme for fractional sub-diffusion equations on an unbounded domain using artificial boundary conditions

    Science.gov (United States)

    Gao, Guang-hua; Sun, Zhi-zhong; Zhang, Ya-nan

    2012-04-01

    One-dimensional fractional anomalous sub-diffusion equations on an unbounded domain are considered in our work. Beginning with the derivation of the exact artificial boundary conditions, the original problem on an unbounded domain is converted into mainly solving an initial-boundary value problem on a finite computational domain. The main contribution of our work, as compared with the previous work, lies in the reduction of fractional differential equations on an unbounded domain by using artificial boundary conditions and construction of the corresponding finite difference scheme with the help of method of order reduction. The difficulty is the treatment of Neumann condition on the artificial boundary, which involves the time-fractional derivative operator. The stability and convergence of the scheme are proven using the discrete energy method. Two numerical examples clarify the effectiveness and accuracy of the proposed method.

  17. ONE-DIMENSIONAL GAS DYNAMICS PROBLEMS AND THEIR SOLUTION BASED ON HIGH-RESOLUTION FINITE DIFFERENCE SCHEMES

    Directory of Open Access Journals (Sweden)

    P. V. Bulat

    2015-07-01

    Full Text Available One-dimensional unsteady gas dynamics problems are revealing tests for the accuracy estimation of numerical solution with respect to simulation of supersonic flows of inviscid compressible gas. Numerical solution of Euler equations describing flows of inviscid compressible gas and conceding continuous and discontinuous solutions is considered. Discretization of Euler equations is based on finite volume method and WENO finite difference schemes. The numerical solutions computed are compared with the exact solution of Riemann problem. Monotonic correction of derivatives makes possible avoiding new extremes and ensures monotonicity of the numerical solution near the discontinuity, but it leads to the smoothness of the existing minimums and maximums and to the accuracy loss. Calculations with the use of WENO schemes give the possibility for obtaining accurate and monotonic solution with the presence of weak and strong gas dynamical discontinuities.

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

    Energy Technology Data Exchange (ETDEWEB)

    Karlsen, Kenneth Hvistendal; Risebro, Nils Henrik

    2000-09-01

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

  19. An optimized staggered variable-grid finite-difference scheme and its application in cross-well acoustic survey

    Institute of Scientific and Technical Information of China (English)

    ZHAO HaiBo; WANG XiuMing

    2008-01-01

    In this paper, an optimized staggered variable-grid finite-difference (FD) method is developed in veloc-ity-stress elastic wave equations. On the basis of the dispersion-relation-preserving (DRP), a fourth-order finite-difference operator on non-uniform grids is constructed. The proposed algorithm is a continuous variable-grid method. It does not need interpolations for the field variables between re-gions with the fine spacing and the coarse one. The accuracy of the optimized scheme has been veri-fied with an analytical solution and a regular staggered-grid FD method for the eighth order accuracy in space. The comparisons of the proposed scheme with the variable-grid FD method based on Taylor series expansion are made. It is demonstrated that this optimized scheme has less dispersion errors than that with Taylor's series expansion. Thus, the proposed scheme uses coarser grids in numerical simulations than that constructed by the Taylor's series expansion. Finally, the capability of the opti-mized FD is demonstrated for a complex cross-well acoustic simulation. The numerical experiment shows that this method greatly saves storage requirements and computational time, and is stable.

  20. A no-cost improved velocity-stress staggered-grid finite-difference scheme for modelling seismic wave propagation

    Science.gov (United States)

    Etemadsaeed, Leila; Moczo, Peter; Kristek, Jozef; Ansari, Anooshiravan; Kristekova, Miriam

    2016-10-01

    We investigate the problem of finite-difference approximations of the velocity-stress formulation of the equation of motion and constitutive law on the staggered grid (SG) and collocated grid (CG). For approximating the first spatial and temporal derivatives, we use three approaches: Taylor expansion (TE), dispersion-relation preserving (DRP), and combined TE-DRP. The TE and DRP approaches represent two fundamental extremes. We derive useful formulae for DRP and TE-DRP approximations. We compare accuracy of the numerical wavenumbers and numerical frequencies of the basic TE, DRP and TE-DRP approximations. Based on the developed approximations, we construct and numerically investigate 14 basic TE, DRP and TE-DRP finite-difference schemes on SG and CG. We find that (1) the TE second-order in time, TE fourth-order in space, 2-point in time, 4-point in space SG scheme (that is the standard (2,4) VS SG scheme, say TE-2-4-2-4-SG) is the best scheme (of the 14 investigated) for large fractions of the maximum possible time step, or, in other words, in a homogeneous medium; (2) the TE second-order in time, combined TE-DRP second-order in space, 2-point in time, 4-point in space SG scheme (say TE-DRP-2-2-2-4-SG) is the best scheme for small fractions of the maximum possible time step, or, in other words, in models with large velocity contrasts if uniform spatial grid spacing and time step are used. The practical conclusion is that in computer codes based on standard TE-2-4-2-4-SG, it is enough to redefine the values of the approximation coefficients by those of TE-DRP-2-2-2-4-SG for increasing accuracy of modelling in models with large velocity contrast between rock and sediments.

  1. Finite difference schemes for a nonlinear black-scholes model with transaction cost and volatility risk

    DEFF Research Database (Denmark)

    Mashayekhi, Sima; Hugger, Jens

    2015-01-01

    Several nonlinear Black-Scholes models have been proposed to take transaction cost, large investor performance and illiquid markets into account. One of the most comprehensive models introduced by Barles and Soner in [4] considers transaction cost in the hedging strategy and risk from an illiquid...... market. In this paper, we compare several finite difference methods for the solution of this model with respect to precision and order of convergence within a computationally feasible domain allowing at most 200 space steps and 10000 time steps. We conclude that standard explicit Euler comes out...

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

    Institute of Scientific and Technical Information of China (English)

    Wang Hua; Tao Guo; Shang Xue-Feng; Fang Xin-Ding; Daniel R. Burns

    2013-01-01

    In acoustic logging-while-drilling (ALWD) finite difference in time domain (FDTD) simulations, large drill collar occupies, most of the fluid-filled borehole and divides the borehole fluid into two thin fluid columns (radius~27 mm). Fine grids and large computational models are required to model the thin fluid region between the tool and the formation. As a result, small time step and more iterations are needed, which increases the cumulative numerical error. Furthermore, due to high impedance contrast between the drill collar and fluid in the borehole (the difference is>30 times), the stability and efficiency of the perfectly matched layer (PML) scheme is critical to simulate complicated wave modes accurately. In this paper, we compared four different PML implementations in a staggered grid finite difference in time domain (FDTD) in the ALWD simulation, including field-splitting PML (SPML), multiaxial PML(M-PML), non-splitting PML (NPML), and complex frequency-shifted PML (CFS-PML). The comparison indicated that NPML and CFS-PML can absorb the guided wave reflection from the computational boundaries more efficiently than SPML and M-PML. For large simulation time, SPML, M-PML, and NPML are numerically unstable. However, the stability of M-PML can be improved further to some extent. Based on the analysis, we proposed that the CFS-PML method is used in FDTD to eliminate the numerical instability and to improve the efficiency of absorption in the PML layers for LWD modeling. The optimal values of CFS-PML parameters in the LWD simulation were investigated based on thousands of 3D simulations. For typical LWD cases, the best maximum value of the quadratic damping profile was obtained using one d0. The optimal parameter space for the maximum value of the linear frequency-shifted factor (α0) and the scaling factor (β0) depended on the thickness of the PML layer. For typical formations, if the PML thickness is 10 grid points, the global error can be reduced to<1%using

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

    KAUST Repository

    Brinkman, Daniel

    2014-01-01

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

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

    CERN Document Server

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

    2001-01-01

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

  5. Two finite-difference schemes that preserve the dissipation of energy in a system of modified wave equations

    CERN Document Server

    Macías-Díaz, J E; 10.1016/j.cnsns.2009.04.017

    2011-01-01

    In this work, we present two numerical methods to approximate solutions of systems of dissipative sine-Gordon equations that arise in the study of one-dimensional, semi-infinite arrays of Josephson junctions coupled through superconducting wires. Also, we present schemes for the total energy of such systems in association with the finite-difference schemes used to approximate the solutions. The proposed methods are conditionally stable techniques that yield consistent approximations not only in the domains of the solution and the total energy, but also in the approximation to the rate of change of energy with respect to time. The methods are employed in the estimation of the threshold at which nonlinear supratransmission takes place, in the presence of parameters such as internal and external damping, generalized mass, and generalized Josephson current. Our results are qualitatively in agreement with the corresponding problem in mechanical chains of coupled oscillators, under the presence of the same paramete...

  6. ANALYSIS OF FINITE-DIFFERENCE SCHEMES BASED ON EXACT AND APPROXIMATE SOLUTION OF RIEMANN PROBLEM

    Directory of Open Access Journals (Sweden)

    P. V. Bulat

    2015-01-01

    Full Text Available The Riemann problem of one-dimensional arbitrary discontinuity breakdown for parameters of unsteady gas flow is considered as applied to the design of Godunov-type numerical methods. The problem is solved in exact and approximate statements (Osher-Solomon difference scheme used in shock capturing numerical methods: the intensities (the ratio of static pressures and flow velocities on the sides of the resulting breakdowns and waves are determined, and then the other parameters are calculated in all regions of the flow. Comparison of calculation results for model flows by exact and approximate solutions is performed. The concept of velocity function is introduced. The dependence of the velocity function on the breakdown intensity is investigated. A special intensity at which isentropic wave creates the same flow rate as the shock wave is discovered. In the vicinity of this singular intensity approximate methods provide the highest accuracy. The domain of applicability for the approximate Osher-Solomon solution is defined by performing test calculations. The results are presented in a form suitable for usage in the numerical methods. The results obtained can be used in the high-resolution numerical methods.

  7. 铁磁链Landau-Lifshitz方程的显式差分法%AN EXPLICIT FINITE DIFFERENCE SCHEME FOR THELANDAU-LIFSHITZ EQUATION OF THEFERROMAGNETIC SPIN CHAIN

    Institute of Scientific and Technical Information of China (English)

    万桂华

    2000-01-01

    In this paper, the Landau-Lifshitz equation with periodic initial boundary valued problem which is govnered by ()/(t)=-1 ( )+2( ) is discreted by using the Euler-forword finite difference method. The proposed scheme is explicit so that the parallel algorithm can be used to simulate numerically on computer. Moreove, the convergence and stability of the proposed scheme are proved by the finite extensive method of the nonlinear function. Finally, the numerical experiments are provided to check the theoritical results.

  8. Explicit Finite-Difference Scheme for the Numerical Solution of the Model Equation of Nonlinear Hereditary Oscillator with Variable-Order Fractional Derivatives

    Directory of Open Access Journals (Sweden)

    Parovik Roman I.

    2016-09-01

    Full Text Available The paper deals with the model of variable-order nonlinear hereditary oscillator based on a numerical finite-difference scheme. Numerical experiments have been carried out to evaluate the stability and convergence of the difference scheme. It is argued that the approximation, stability and convergence are of the first order, while the scheme is stable and converges to the exact solution.

  9. A Finite Difference Scheme on a Priori Adapted Meshes for a Singularly Perturbed Parabolic Convection-Diffusion Equation

    Institute of Scientific and Technical Information of China (English)

    Grigory I. Shishkin

    2008-01-01

    A boundary value problem is considered for a singularly perturbed parabolic convection-diffusion equation; we construct a finite difference scheme on a priori (se-quentially) adapted meshes and study its convergence. The scheme on a priori adapted meshes is constructed using a majorant function for the singular component of the discrete solution, which allows us to find a priori a subdomain where the computed solution requires a further improvement. This subdomain is defined by the perturbation parameter ε, the step-size of a uniform mesh in x, and also by the required accuracy of the discrete solution and the prescribed number of refinement iterations K for im-proving the solution. To solve the discrete problems aimed at the improvement of the solution, we use uniform meshes on the subdomains. The error of the numerical so-lution depends weakly on the parameter ε. The scheme converges almost ε-uniformly, precisely, under the condition N-1 = o(ev), where N denotes the number of nodes in the spatial mesh, and the value v=v(K) can be chosen arbitrarily small for suitable K.

  10. A stable high-order finite difference scheme for the compressible Navier Stokes equations: No-slip wall boundary conditions

    Science.gov (United States)

    Svärd, Magnus; Nordström, Jan

    2008-05-01

    A stable wall boundary procedure is derived for the discretized compressible Navier-Stokes equations. The procedure leads to an energy estimate for the linearized equations. We discretize the equations using high-order accurate finite difference summation-by-parts (SBP) operators. The boundary conditions are imposed weakly with penalty terms. We prove linear stability for the scheme including the wall boundary conditions. The penalty imposition of the boundary conditions is tested for the flow around a circular cylinder at Ma=0.1 and Re=100. We demonstrate the robustness of the SBP-SAT technique by imposing incompatible initial data and show the behavior of the boundary condition implementation. Using the errors at the wall we show that higher convergence rates are obtained for the high-order schemes. We compute the vortex shedding from a circular cylinder and obtain good agreement with previously published (computational and experimental) results for lift, drag and the Strouhal number. We use our results to compare the computational time for a given for a accuracy and show the superior efficiency of the 5th-order scheme.

  11. A global multilevel atmospheric model using a vector semi-Lagrangian finite-difference scheme. I - Adiabatic formulation

    Science.gov (United States)

    Bates, J. R.; Moorthi, S.; Higgins, R. W.

    1993-01-01

    An adiabatic global multilevel primitive equation model using a two time-level, semi-Lagrangian semi-implicit finite-difference integration scheme is presented. A Lorenz grid is used for vertical discretization and a C grid for the horizontal discretization. The momentum equation is discretized in vector form, thus avoiding problems near the poles. The 3D model equations are reduced by a linear transformation to a set of 2D elliptic equations, whose solution is found by means of an efficient direct solver. The model (with minimal physics) is integrated for 10 days starting from an initialized state derived from real data. A resolution of 16 levels in the vertical is used, with various horizontal resolutions. The model is found to be stable and efficient, and to give realistic output fields. Integrations with time steps of 10 min, 30 min, and 1 h are compared, and the differences are found to be acceptable.

  12. Computational Aero-Acoustic Using High-order Finite-Difference Schemes

    DEFF Research Database (Denmark)

    Zhu, Wei Jun; Shen, Wen Zhong; Sørensen, Jens Nørkær

    2007-01-01

    In this paper, a high-order technique to accurately predict flow-generated noise is introduced. The technique consists of solving the viscous incompressible flow equations and inviscid acoustic equations using a incompressible/compressible splitting technique. The incompressible flow equations ar...... discretizations of the acoustic equations. The classical fourth-order Runge-Kutta time scheme is applied to the acoustic equations for time discretization....

  13. A note on the leap-frog scheme in two and three dimensions. [finite difference method for partial differential equations

    Science.gov (United States)

    Abarbanel, S.; Gottlieb, D.

    1976-01-01

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

  14. Parallel adaptive mesh refinement method based on WENO finite difference scheme for the simulation of multi-dimensional detonation

    Science.gov (United States)

    Wang, Cheng; Dong, XinZhuang; Shu, Chi-Wang

    2015-10-01

    For numerical simulation of detonation, computational cost using uniform meshes is large due to the vast separation in both time and space scales. Adaptive mesh refinement (AMR) is advantageous for problems with vastly different scales. This paper aims to propose an AMR method with high order accuracy for numerical investigation of multi-dimensional detonation. A well-designed AMR method based on finite difference weighted essentially non-oscillatory (WENO) scheme, named as AMR&WENO is proposed. A new cell-based data structure is used to organize the adaptive meshes. The new data structure makes it possible for cells to communicate with each other quickly and easily. In order to develop an AMR method with high order accuracy, high order prolongations in both space and time are utilized in the data prolongation procedure. Based on the message passing interface (MPI) platform, we have developed a workload balancing parallel AMR&WENO code using the Hilbert space-filling curve algorithm. Our numerical experiments with detonation simulations indicate that the AMR&WENO is accurate and has a high resolution. Moreover, we evaluate and compare the performance of the uniform mesh WENO scheme and the parallel AMR&WENO method. The comparison results provide us further insight into the high performance of the parallel AMR&WENO method.

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

    KAUST Repository

    Zhan, Ge

    2013-02-19

    The pure P-wave equation for modelling and migration in tilted transversely isotropic (TTI) media has attracted more and more attention in imaging seismic data with anisotropy. The desirable feature is that it is absolutely free of shear-wave artefacts and the consequent alleviation of numerical instabilities generally suffered by some systems of coupled equations. However, due to several forward-backward Fourier transforms in wavefield updating at each time step, the computational cost is significant, and thereby hampers its prevalence. We propose to use a hybrid pseudospectral (PS) and finite-difference (FD) scheme to solve the pure P-wave equation. In the hybrid solution, most of the cost-consuming wavenumber terms in the equation are replaced by inexpensive FD operators, which in turn accelerates the computation and reduces the computational cost. To demonstrate the benefit in cost saving of the new scheme, 2D and 3D reverse-time migration (RTM) examples using the hybrid solution to the pure P-wave equation are carried out, and respective runtimes are listed and compared. Numerical results show that the hybrid strategy demands less computation time and is faster than using the PS method alone. Furthermore, this new TTI RTM algorithm with the hybrid method is computationally less expensive than that with the FD solution to conventional TTI coupled equations. © 2013 Sinopec Geophysical Research Institute.

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

    KAUST Repository

    Kiessling, Jonas

    2014-05-06

    Option prices in exponential Lévy models solve certain partial integro-differential equations. This work focuses on developing novel, computable error approximations for a finite difference scheme that is suitable for solving such PIDEs. The scheme was introduced in (Cont and Voltchkova, SIAM J. Numer. Anal. 43(4):1596-1626, 2005). The main results of this work are new estimates of the dominating error terms, namely the time and space discretisation errors. In addition, the leading order terms of the error estimates are determined in a form that is more amenable to computations. The payoff is only assumed to satisfy an exponential growth condition, it is not assumed to be Lipschitz continuous as in previous works. If the underlying Lévy process has infinite jump activity, then the jumps smaller than some (Formula presented.) are approximated by diffusion. The resulting diffusion approximation error is also estimated, with leading order term in computable form, as well as the dependence of the time and space discretisation errors on this approximation. Consequently, it is possible to determine how to jointly choose the space and time grid sizes and the cut off parameter (Formula presented.). © 2014 Springer Science+Business Media Dordrecht.

  17. ASSESSMENT OF A CENTRAL DIFFERENCE FINITE VOLUME SCHEME FOR MODELING OF CAVITATING FLOWS USING PRECONDITIONED MULTIPHASE EULER EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    HEJRANFAR Kazem; FATTAH-HESARY Kasra

    2011-01-01

    A numerical treatment for the prediction of cavitating flows is presented and assessed.The algorithm uses the preconditioned multiphase Euler equations with appropriate mass transfer terms.A central difference finite volume scheme with suitable dissipation terms to account for density jumps across the cavity interface is shown to yield an effective method for solving the multiphase Euler equations.The Euler equations are utilized herein for the cavitation modeling, because some certain characteristics of cavitating flows can be obtained using the solution of this system of equations with relative low computational effort.In addition, the Euler equations are appropriate for the assessment of the numerical method used, because of the sensitivity of the solution to the numerical instabilities.For this reason, a sensitivity study is conducted to evaluate the effects of various parameters, such as numerical dissipation coefficients and grid size, on the accuracy and performance of the solution.The computations are performed for steady cavitating flows around the NACA 0012 and NACA 66 (MOD) hydrofoils and also an axisymmetric hemispherical fore-body under different conditions and the results are compared with the available numerical and experimental data.The solution procedure presented is shown to be accurate and efficient for predicting steady sheet- and super-cavitation for 2D/axisymmetric geometries.

  18. Finite difference schemes for the singularly perturbed reaction-diffusion equation in the case of spherical symmetry

    Science.gov (United States)

    Shishkin, G. I.; Shishkina, L. P.

    2009-05-01

    The boundary value problem for the singularly perturbed reaction-diffusion parabolic equation in a ball in the case of spherical symmetry is considered. The derivatives with respect to the radial variable appearing in the equation are written in divergent form. The third kind boundary condition, which admits the Dirichlet and Neumann conditions, is specified on the boundary of the domain. The Laplace operator in the differential equation involves a perturbation parameter ɛ2, where ɛ takes arbitrary values in the half-open interval (0, 1]. When ɛ → 0, the solution of such a problem has a parabolic boundary layer in a neighborhood of the boundary. Using the integro-interpolational method and the condensing grid technique, conservative finite difference schemes on flux grids are constructed that converge ɛ-uniformly at a rate of O( N -2ln2 N + N {0/-1}), where N + 1 and N 0 + 1 are the numbers of the mesh points in the radial and time variables, respectively.

  19. Improving the Stability Problem of the Finite Difference Scheme for Reaction-diffusion Equation%提高反应—扩散方程有限差分格式的稳定性问题

    Institute of Scientific and Technical Information of China (English)

    徐琛梅

    2008-01-01

    This paper deals with the special nonlinear reaction-diffusion equation.The finite difference scheme with incremental unknowns approximating to the differential equation (2.1) is set up by means of introducing incremental unknowns methods.Through the stability analyzing for the scheme,it was shown that the stability conditions of the finite difference schemes with the incremental unknowns are greatly improved when compared with the stability conditions of the corresponding classic difference scheme.

  20. Finite-volume scheme for anisotropic diffusion

    Energy Technology Data Exchange (ETDEWEB)

    Es, Bram van, E-mail: bramiozo@gmail.com [Centrum Wiskunde & Informatica, P.O. Box 94079, 1090GB Amsterdam (Netherlands); FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, The Netherlands" 1 (Netherlands); Koren, Barry [Eindhoven University of Technology (Netherlands); Blank, Hugo J. de [FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, The Netherlands" 1 (Netherlands)

    2016-02-01

    In this paper, we apply a special finite-volume scheme, limited to smooth temperature distributions and Cartesian grids, to test the importance of connectivity of the finite volumes. The area of application is nuclear fusion plasma with field line aligned temperature gradients and extreme anisotropy. We apply the scheme to the anisotropic heat-conduction equation, and compare its results with those of existing finite-volume schemes for anisotropic diffusion. Also, we introduce a general model adaptation of the steady diffusion equation for extremely anisotropic diffusion problems with closed field lines.

  1. Finite volume renormalization scheme for fermionic operators

    Energy Technology Data Exchange (ETDEWEB)

    Monahan, Christopher; Orginos, Kostas [JLAB

    2013-11-01

    We propose a new finite volume renormalization scheme. Our scheme is based on the Gradient Flow applied to both fermion and gauge fields and, much like the Schr\\"odinger functional method, allows for a nonperturbative determination of the scale dependence of operators using a step-scaling approach. We give some preliminary results for the pseudo-scalar density in the quenched approximation.

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

    Science.gov (United States)

    Yang, Lei; Yan, Hongyong; Liu, Hong

    2017-03-01

    Implicit staggered-grid finite-difference (ISFD) scheme is competitive for its great accuracy and stability, whereas its coefficients are conventionally determined by the Taylor-series expansion (TE) method, leading to a loss in numerical precision. In this paper, we modify the TE method using the minimax approximation (MA), and propose a new optimal ISFD scheme based on the modified TE (MTE) with MA method. The new ISFD scheme takes the advantage of the TE method that guarantees great accuracy at small wavenumbers, and keeps the property of the MA method that keeps the numerical errors within a limited bound at the same time. Thus, it leads to great accuracy for numerical solution of the wave equations. We derive the optimal ISFD coefficients by applying the new method to the construction of the objective function, and using a Remez algorithm to minimize its maximum. Numerical analysis is made in comparison with the conventional TE-based ISFD scheme, indicating that the MTE-based ISFD scheme with appropriate parameters can widen the wavenumber range with high accuracy, and achieve greater precision than the conventional ISFD scheme. The numerical modeling results also demonstrate that the MTE-based ISFD scheme performs well in elastic wave simulation, and is more efficient than the conventional ISFD scheme for elastic modeling.

  3. A Finite Difference Scheme for Double-Diffusive Unsteady Free Convection from a Curved Surface to a Saturated Porous Medium with a Non-Newtonian Fluid

    KAUST Repository

    El-Amin, Mohamed

    2011-05-14

    In this paper, a finite difference scheme is developed to solve the unsteady problem of combined heat and mass transfer from an isothermal curved surface to a porous medium saturated by a non-Newtonian fluid. The curved surface is kept at constant temperature and the power-law model is used to model the non-Newtonian fluid. The explicit finite difference method is used to solve simultaneously the equations of momentum, energy and concentration. The consistency of the explicit scheme is examined and the stability conditions are determined for each equation. Boundary layer and Boussinesq approximations have been incorporated. Numerical calculations are carried out for the various parameters entering into the problem. Velocity, temperature and concentration profiles are shown graphically. It is found that as time approaches infinity, the values of wall shear, heat transfer coefficient and concentration gradient at the wall, which are entered in tables, approach the steady state values.

  4. The Stability Research for the Finite Difference Scheme of a Nonlinear Reaction-diffusion Equation%一类非线性反应-扩散方程有限差分格式的稳定性研究

    Institute of Scientific and Technical Information of China (English)

    徐琛梅

    2008-01-01

    In the article,the fully discrete finite difference scheme for a type of nonlinear reaction-diffusion equation is established.Then the new function space is introduced and the stability problem for the finite difference scheme is discussed by means of variational approximation method in this function space.The approach used is of a simple characteristic in gaining the stability condition of the scheme.

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

    KAUST Repository

    Settle, Sean O.

    2013-01-01

    The primary aim of this paper is to answer the question, What are the highest-order five- or nine-point compact finite difference schemes? To answer this question, we present several simple derivations of finite difference schemes for the one- and two-dimensional Poisson equation on uniform, quasi-uniform, and nonuniform face-to-face hyperrectangular grids and directly prove the existence or nonexistence of their highest-order local accuracies. Our derivations are unique in that we do not make any initial assumptions on stencil symmetries or weights. For the one-dimensional problem, the derivation using the three-point stencil on both uniform and nonuniform grids yields a scheme with arbitrarily high-order local accuracy. However, for the two-dimensional problem, the derivation using the corresponding five-point stencil on uniform and quasi-uniform grids yields a scheme with at most second-order local accuracy, and on nonuniform grids yields at most first-order local accuracy. When expanding the five-point stencil to the nine-point stencil, the derivation using the nine-point stencil on uniform grids yields at most sixth-order local accuracy, but on quasi- and nonuniform grids yields at most fourth- and third-order local accuracy, respectively. © 2013 Society for Industrial and Applied Mathematics.

  6. Finite volume schemes for Boussinesq type equations

    OpenAIRE

    2011-01-01

    6 pages, 2 figures, 18 references. Published in proceedings of Colloque EDP-Normandie held at Caen (France), on 28 & 29 October 2010. Other author papers can be dowloaded at http://www.lama.univ-savoie.fr/~dutykh/; Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive water wave models, in particular to Boussinesq type systems. We focus mainly on the application of the m...

  7. Finite volume schemes for Boussinesq type equations

    CERN Document Server

    Dutykh, Denys; Mitsotakis, Dimitrios

    2011-01-01

    Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive water wave models, in particular to Boussinesq type systems. We focus mainly on the application of the method to bidirectional nonlinear, dispersive wave propagation in one space dimension. Special emphasis is given to important nonlinear phenomena such as solitary waves interactions.

  8. Optimal staggered-grid finite-difference schemes by combining Taylor-series expansion and sampling approximation for wave equation modeling

    Science.gov (United States)

    Yan, Hongyong; Yang, Lei; Li, Xiang-Yang

    2016-12-01

    High-order staggered-grid finite-difference (SFD) schemes have been universally used to improve the accuracy of wave equation modeling. However, the high-order SFD coefficients on spatial derivatives are usually determined by the Taylor-series expansion (TE) method, which just leads to great accuracy at small wavenumbers for wave equation modeling. Some conventional optimization methods can achieve high accuracy at large wavenumbers, but they hardly guarantee the small numerical dispersion error at small wavenumbers. In this paper, we develop new optimal explicit SFD (ESFD) and implicit SFD (ISFD) schemes for wave equation modeling. We first derive the optimal ESFD and ISFD coefficients for the first-order spatial derivatives by applying the combination of the TE and the sampling approximation to the dispersion relation, and then analyze their numerical accuracy. Finally, we perform elastic wave modeling with the ESFD and ISFD schemes based on the TE method and the optimal method, respectively. When the appropriate number and interval for the sampling points are chosen, these optimal schemes have extremely high accuracy at small wavenumbers, and can also guarantee small numerical dispersion error at large wavenumbers. Numerical accuracy analyses and modeling results demonstrate the optimal ESFD and ISFD schemes can efficiently suppress the numerical dispersion and significantly improve the modeling accuracy compared to the TE-based ESFD and ISFD schemes.

  9. A fourth order accuracy summation-by-parts finite difference scheme for acoustic reverse time migration in boundary-conforming grids

    Science.gov (United States)

    Wang, Ying; Zhou, Hui; Yuan, Sanyi; Ye, Yameng

    2017-01-01

    The fourth order accuracy finite difference scheme is known advantageous in reducing memory and improving efficiency. Summation-by-parts finite difference operator is a natural way for wavefield simulation in complicated domains containing surface topography and irregular interfaces. The application of summation-by-parts method guarantees the stability of numerical approximation for heterogeneous media on curvilinear grids. This paper extends the second order summation-by-parts finite difference method to the fourth order case for the discretization of acoustic wave equation and perfect matched layer in boundary-conforming grids. In particular, the implementation of the fourth order method for wavefield simulation and reverse time migration in complicated domains can significantly improve the efficiency and decrease the storage. The elliptic method is applied for boundary-conforming grid generation in complicated domains. Under such grids, the two-dimensional acoustic wave equation in second order displacement formulation is compactly reformulated for forward modeling and reverse time migration, and the symmetric and compact form of perfectly matched layers expressed in a curvilinear coordinate system are applied to suppress artificial reflections. The discretizations of the acoustic wave equation and perfectly matched layer formula are fourth and second order accuracy in space and time respectively, where the spatial discretization satisfies the principle of summation-by-parts and is stable. Numerical experiments are presented to compare the accuracy of the second with fourth order summation-by-parts finite difference methods and to evaluate the efficiency of reverse time migration by using these two methods. As well, comparisons are performed between the fourth order accuracy summation-by-parts finite difference method and central finite difference method to illustrate the stability superiority of summation-by-parts operators.

  10. A dispersion and norm preserving finite difference scheme with transparent boundary conditions for the Dirac equation in (1+1)D

    CERN Document Server

    Hammer, René; Arnold, Anton

    2013-01-01

    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...

  11. Direct Numerical Simulation of Transitional and Turbulent Flow Over a Heated Flat Plate Using Finite-Difference Schemes

    Science.gov (United States)

    Madavan, Nateri K.

    1995-01-01

    The work in this report was conducted at NASA Ames Research Center during the period from August 1993 to January 1995 deals with the direct numerical simulation of transitional and turbulent flow at low Mach numbers using high-order-accurate finite-difference techniques. A computation of transition to turbulence of the spatially-evolving boundary layer on a heated flat plate in the presence of relatively high freestream turbulence was performed. The geometry and flow conditions were chosen to match earlier experiments. The development of the momentum and thermal boundary layers was documented. Velocity and temperature profiles, as well as distributions of skin friction, surface heat transfer rate, Reynolds shear stress, and turbulent heat flux were shown to compare well with experiment. The numerical method used here can be applied to complex geometries in a straightforward manner.

  12. Generalized support varieties for finite group schemes

    CERN Document Server

    Friedlander, Eric M

    2011-01-01

    We construct two families of refinements of the (projectivized) support variety of a finite dimensional module $M$ for a finite group scheme $G$. For an arbitrary finite group scheme, we associate a family of {\\it non maximal rank varieties} $\\Gamma^j(G)_M$, $1\\leq j \\leq p-1$, to a $kG$-module $M$. For $G$ infinitesimal, we construct a finer family of locally closed subvarieties $V^{\\ul a}(G)_M$ of the variety of one parameter subgroups of $G$ for any partition $\\ul a$ of $\\dim M$. For an arbitrary finite group scheme $G$, a $kG$-module $M$ of constant rank, and a cohomology class $\\zeta$ in $\\HHH^1(G,M)$ we introduce the {\\it zero locus} $Z(\\zeta) \\subset \\Pi(G)$. We show that $Z(\\zeta)$ is a closed subvariety, and relate it to the non-maximal rank varieties. We also extend the construction of $Z(\\zeta)$ to an arbitrary extension class $\\zeta \\in \\Ext^n_G(M,N)$ whenever $M$ and $N$ are $kG$-modules of constant Jordan type.

  13. Assessment of some high-order finite difference schemes on the scalar conservation law with periodical conditions

    Directory of Open Access Journals (Sweden)

    Alina BOGOI

    2016-12-01

    Full Text Available Supersonic/hypersonic flows with strong shocks need special treatment in Computational Fluid Dynamics (CFD in order to accurately capture the discontinuity location and his magnitude. To avoid numerical instabilities in the presence of discontinuities, the numerical schemes must generate low dissipation and low dispersion error. Consequently, the algorithms used to calculate the time and space-derivatives, should exhibit a low amplitude and phase error. This paper focuses on the comparison of the numerical results obtained by simulations with some high resolution numerical schemes applied on linear and non-linear one-dimensional conservation low. The analytical solutions are provided for all benchmark tests considering smooth periodical conditions. All the schemes converge to the proper weak solution for linear flux and smooth initial conditions. However, when the flux is non-linear, the discontinuities may develop from smooth initial conditions and the shock must be correctly captured. All the schemes accurately identify the shock position, with the price of the numerical oscillation in the vicinity of the sudden variation. We believe that the identification of this pure numerical behavior, without physical relevance, in 1D case is extremely useful to avoid problems related to the stability and convergence of the solution in the general 3D case.

  14. Comparative study on triangular and quadrilateral meshes by a finite-volume method with a central difference scheme

    KAUST Repository

    Yu, Guojun

    2012-10-01

    In this article, comparative studies on computational accuracies and convergence rates of triangular and quadrilateral meshes are carried out in the frame work of the finite-volume method. By theoretical analysis, we conclude that the number of triangular cells needs to be 4/3 times that of quadrilateral cells to obtain similar accuracy. The conclusion is verified by a number of numerical examples. In addition, the convergence rates of the triangular meshes are found to be slower than those of the quadrilateral meshes when the same accuracy is obtained with these two mesh types. © 2012 Taylor and Francis Group, LLC.

  15. Verification of a Higher-Order Finite Difference Scheme for the One-Dimensional Two-Fluid Model

    Directory of Open Access Journals (Sweden)

    William D. Fullmer

    2013-06-01

    Full Text Available The one-dimensional two-fluid model is widely acknowledged as the most detailed and accurate macroscopic formulation model of the thermo-fluid dynamics in nuclear reactor safety analysis. Currently the prevailing one-dimensional thermal hydraulics codes are only first-order accurate. The benefit of first-order schemes is numerical viscosity, which serves as a regularization mechanism for many otherwise ill-posed two-fluid models. However, excessive diffusion in regions of large gradients leads to poor resolution of phenomena related to void wave propagation. In this work, a higher-order shock capturing method is applied to the basic equations for incompressible and isothermal flow of the one-dimensional two-fluid model. The higher-order accuracy is gained by a strong stability preserving multi-step scheme for the time discretization and a minmod flux limiter scheme for the convection terms. Additionally the use of a staggered grid allows for several second-order centered terms, when available. The continuity equations are first tested by manipulating the two-fluid model into a pair of linear wave equations and tested for smooth and discontinuous initial data. The two-fluid model is benchmarked with the water faucet problem. With the higher-order method, the ill-posed nature of the governing equations presents severe challenges due to a growing void fraction jump in the solution. Therefore the initial and boundary conditions of the problem are modified in order to eliminate a large counter-current flow pattern that develops. With the modified water faucet problem the numerical models behave well and allow a convergence study. Using the L1 norm of the liquid fraction, it is verified that the first and higher-order numerical schemes converge to the quasi-analytical solution at a rate of O(1/2 and O(2/3, respectively. It is also shown that the growing void jump is a contact discontinuity, i.e. it is a linearly degenerate wave. The sub

  16. Finite elements and finite differences for transonic flow calculations

    Science.gov (United States)

    Hafez, M. M.; Murman, E. M.; Wellford, L. C.

    1978-01-01

    The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.

  17. Difference Schemes and Applications

    Science.gov (United States)

    2015-02-06

    of the shallow water equations that is well suited for complex geometries and moving boundaries. Another (similar) regularization of...the solid wall extrapolation followed by the interpolation in the phase space (by solving the Riemann problem between the internal cell averages and...scheme. This Godunov-type scheme enjoys all major advantages of Riemann -problem-solver-free, non-oscillatory central schemes and, at the same time, have

  18. Two Conservative Difference Schemes for Rosenau-Kawahara Equation

    Directory of Open Access Journals (Sweden)

    Jinsong Hu

    2014-01-01

    Full Text Available Two conservative finite difference schemes for the numerical solution of the initialboundary value problem of Rosenau-Kawahara equation are proposed. The difference schemes simulate two conservative quantities of the problem well. The existence and uniqueness of the difference solution are proved. It is shown that the finite difference schemes are of second-order convergence and unconditionally stable. Numerical experiments verify the theoretical results.

  19. Conservative Linear Difference Scheme for Rosenau-KdV Equation

    Directory of Open Access Journals (Sweden)

    Jinsong Hu

    2013-01-01

    Full Text Available A conservative three-level linear finite difference scheme for the numerical solution of the initial-boundary value problem of Rosenau-KdV equation is proposed. The difference scheme simulates two conservative quantities of the problem well. The existence and uniqueness of the difference solution are proved. It is shown that the finite difference scheme is of second-order convergence and unconditionally stable. Numerical experiments verify the theoretical results.

  20. High resolution finite volume scheme for the quantum hydrodynamic equations

    Science.gov (United States)

    Lin, Chin-Tien; Yeh, Jia-Yi; Chen, Jiun-Yeu

    2009-03-01

    The theory of quantum fluid dynamics (QFD) helps nanotechnology engineers to understand the physical effect of quantum forces. Although the governing equations of quantum fluid dynamics and classical fluid mechanics have the same form, there are two numerical simulation problems must be solved in QFD. The first is that the quantum potential term becomes singular and causes a divergence in the numerical simulation when the probability density is very small and close to zero. The second is that the unitarity in the time evolution of the quantum wave packet is significant. Accurate numerical evaluations are critical to the simulations of the flow fields that are generated by various quantum fluid systems. A finite volume scheme is developed herein to solve the quantum hydrodynamic equations of motion, which significantly improve the accuracy and stability of this method. The QFD equation is numerically implemented within the Eulerian method. A third-order modified Osher-Chakravarthy (MOC) upwind-centered finite volume scheme was constructed for conservation law to evaluate the convective terms, and a second-order central finite volume scheme was used to map the quantum potential field. An explicit Runge-Kutta method is used to perform the time integration to achieve fast convergence of the proposed scheme. In order to meet the numerical result can conform to the physical phenomenon and avoid numerical divergence happening due to extremely low probability density, the minimum value setting of probability density must exceed zero and smaller than certain value. The optimal value was found in the proposed numerical approach to maintain a converging numerical simulation when the minimum probability density is 10 -5 to 10 -12. The normalization of the wave packet remains close to unity through a long numerical simulation and the deviations from 1.0 is about 10 -4. To check the QFD finite difference numerical computations, one- and two-dimensional particle motions were

  1. A Finite Volume Scheme on the Cubed Sphere Grid

    Science.gov (United States)

    Putman, William M.; Lin, S. J.

    2008-01-01

    The performance of a multidimensional finite-volume scheme for global atmospheric dynamics is evaluated on the cubed-sphere geometry. We will explore the properties of the finite volume scheme through traditional advection and shallow water test cases. Baroclinic evaluations performed via a recently developed deterministic initial value baroclinic test case from Jablonowski and Williamson that assesses the evolution of an idealized baroclinic wave in the Northern Hemisphere for a global 3-dimensional atmospheric dynamical core. Comparisons will be made when available to the traditional latitude longitude discretization of the finite-volume dynamical core, as well as other traditional gridpoint and spectral formulations for atmospheric dynamical cores.

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

    Energy Technology Data Exchange (ETDEWEB)

    Kim, S. [Purdue Univ., West Lafayette, IN (United States)

    1994-12-31

    Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.

  3. Adaptive finite difference for seismic wavefield modelling in acoustic media.

    Science.gov (United States)

    Yao, Gang; Wu, Di; Debens, Henry Alexander

    2016-08-05

    Efficient numerical seismic wavefield modelling is a key component of modern seismic imaging techniques, such as reverse-time migration and full-waveform inversion. Finite difference methods are perhaps the most widely used numerical approach for forward modelling, and here we introduce a novel scheme for implementing finite difference by introducing a time-to-space wavelet mapping. Finite difference coefficients are then computed by minimising the difference between the spatial derivatives of the mapped wavelet and the finite difference operator over all propagation angles. Since the coefficients vary adaptively with different velocities and source wavelet bandwidths, the method is capable to maximise the accuracy of the finite difference operator. Numerical examples demonstrate that this method is superior to standard finite difference methods, while comparable to Zhang's optimised finite difference scheme.

  4. Finite volume schemes for dispersive wave propagation and runup

    Science.gov (United States)

    Dutykh, Denys; Katsaounis, Theodoros; Mitsotakis, Dimitrios

    2011-04-01

    Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive water wave models, in particular to Boussinesq type systems. We focus mainly on the application of the method to bidirectional nonlinear, dispersive wave propagation in one space dimension. Special emphasis is given to important nonlinear phenomena such as solitary waves interactions, dispersive shock wave formation and the runup of breaking and non-breaking long waves.

  5. Finite volume schemes for dispersive wave propagation and runup

    CERN Document Server

    Dutykh, Denys; Mitsotakis, Dimitrios

    2010-01-01

    Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive water wave models, in particular to Boussinesq type systems. We focus mainly on the application of the method to bidirectional nonlinear, dispersive wave propagation in one space dimension. Special emphasis is given to important nonlinear phenomena such as solitary waves interactions, dispersive shock wave formation and the runup of breaking and non-breaking long waves.

  6. The Relation of Finite Element and Finite Difference Methods

    Science.gov (United States)

    Vinokur, M.

    1976-01-01

    Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.

  7. Development and application of a third order scheme of finite differences centered in mesh; Desarrollo y aplicacion de un esquema de tercer orden de diferencias finitas centradas en malla

    Energy Technology Data Exchange (ETDEWEB)

    Delfin L, A.; Alonso V, G. [ININ, 52045 Ocoyoacac, Estado de Mexico (Mexico); Valle G, E. del [IPN-ESFM, 07738 Mexico D.F. (Mexico)]. e-mail: adl@nuclear.inin.mx

    2003-07-01

    In this work the development of a third order scheme of finite differences centered in mesh is presented and it is applied in the numerical solution of those diffusion equations in multi groups in stationary state and X Y geometry. Originally this scheme was developed by Hennart and del Valle for the monoenergetic diffusion equation with a well-known source and they show that the one scheme is of third order when comparing the numerical solution with the analytical solution of a model problem using several mesh refinements and boundary conditions. The scheme by them developed it also introduces the application of numeric quadratures to evaluate the rigidity matrices and of mass that its appear when making use of the finite elements method of Galerkin. One of the used quadratures is the open quadrature of 4 points, no-standard, of Newton-Cotes to evaluate in approximate form the elements of the rigidity matrices. The other quadrature is that of 3 points of Radau that it is used to evaluate the elements of all the mass matrices. One of the objectives of these quadratures are to eliminate the couplings among the Legendre moments 0 and 1 associated to the left and right faces as those associated to the inferior and superior faces of each cell of the discretization. The other objective is to satisfy the particles balance in weighed form in each cell. In this work it expands such development to multiplicative means considering several energy groups. There are described diverse details inherent to the technique, particularly those that refer to the simplification of the algebraic systems that appear due to the space discretization. Numerical results for several test problems are presented and are compared with those obtained with other nodal techniques. (Author)

  8. NEW ALTERNATING DIRECTION FINITE ELEMENT SCHEME FOR NONLINEAR PARABOLIC EQUATION

    Institute of Scientific and Technical Information of China (English)

    崔霞

    2002-01-01

    A new alternating direction (AD) finite element (FE) scheme for 3-dimensional nonlinear parabolic equation and parabolic integro-differential equation is studied. By using AD,the 3-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using FE, high accuracy is kept; by using various techniques for priori estimate for differential equations such as inductive hypothesis reasoning, the difficulty arising from the nonlinearity is treated. For both FE and ADFE schemes, the convergence properties are rigorously demonstrated, the optimal H1- and L2-norm space estimates and the O((△t)2) estimate for time variable are obtained.

  9. Massive renormalization scheme and perturbation theory at finite temperature

    Energy Technology Data Exchange (ETDEWEB)

    Blaizot, Jean-Paul, E-mail: jean-paul.blaizot@cea.fr [Institut de Physique Théorique, CNRS/URA2306, CEA-Saclay, 91191 Gif-sur-Yvette (France); Wschebor, Nicolás [Instituto de Fìsica, Faculdad de Ingeniería, Universidade de la República, 11000 Montevideo (Uruguay)

    2015-02-04

    We argue that the choice of an appropriate, massive, renormalization scheme can greatly improve the apparent convergence of perturbation theory at finite temperature. This is illustrated by the calculation of the pressure of a scalar field theory with quartic interactions, at 2-loop order. The result, almost identical to that obtained with more sophisticated resummation techniques, shows a remarkable stability as the coupling constant grows, in sharp contrast with standard perturbation theory.

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

    NARCIS (Netherlands)

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

    2012-01-01

    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 geo

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

    NARCIS (Netherlands)

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

    2012-01-01

    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

  12. Convergence Rates of Finite Difference Stochastic Approximation Algorithms

    Science.gov (United States)

    2016-06-01

    examine the rates of convergence for the Kiefer-Wolfowitz algorithm and the mirror descent algorithm , under various updating schemes using finite...dfferences as gradient approximations. It is shown that the convergence of these algorithms can be accelerated by controlling the implementation of the...Kiefer-Wolfowitz algorithm , mirror descent algorithm , finite-difference approximation, Monte Carlo methods REPORT DOCUMENTATION PAGE 11. SPONSOR

  13. A finite volume scheme for the transport of radionucleides in porous media

    OpenAIRE

    Chénier, Eric; Eymard,, Robert; Nicolas, Xavier

    2004-01-01

    International audience; The COUPLEX1 Test case (Bourgeat et al., 2003) is devoted to the comparison of numerical schemes on a convection-diffusion-reaction problem. We first show that the results of the simulation can be mainly predicted by a simple analysis of the data. A finite volume scheme, with three different treatments of the convective term, is then shown to deliver accurate and stable results under a low computational cost.

  14. Convergence of a finite difference method for combustion model problems

    Institute of Scientific and Technical Information of China (English)

    YING; Long'an

    2004-01-01

    We study a finite difference scheme for a combustion model problem. A projection scheme near the combustion wave, and the standard upwind finite difference scheme away from the combustion wave are applied. Convergence to weak solutions with a combustion wave is proved under the normal Courant-Friedrichs-Lewy condition. Some conditions on the ignition temperature are given to guarantee the solution containing a strong detonation wave or a weak detonation wave. Convergence to strong detonation wave solutions for the random projection method is also proved.

  15. General difference schemes with intrinsic parallelism for nonlinear parabolic systems

    Institute of Scientific and Technical Information of China (English)

    周毓麟; 袁光伟

    1997-01-01

    The boundary value problem for nonlinear parabolic system is solved by the finite difference method with intrinsic parallelism. The existence of the discrete vector solution for the general finite difference schemes with intrinsic parallelism is proved by the fixed-point technique in finite-dimensional Euclidean space. The convergence and stability theorems of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. The limitation vector function is just the unique generalized solution of the original problem for the parabolic system.

  16. Galerkin finite element scheme for magnetostrictive structures and composites

    Science.gov (United States)

    Kannan, Kidambi Srinivasan

    The ever increasing-role of magnetostrictives in actuation and sensing applications is an indication of their importance in the emerging field of smart structures technology. As newer, and more complex, applications are developed, there is a growing need for a reliable computational tool that can effectively address the magneto-mechanical interactions and other nonlinearities in these materials and in structures incorporating them. This thesis presents a continuum level quasi-static, three-dimensional finite element computational scheme for modeling the nonlinear behavior of bulk magnetostrictive materials and particulate magnetostrictive composites. Models for magnetostriction must deal with two sources of nonlinearities-nonlinear body forces/moments in equilibrium equations governing magneto-mechanical interactions in deformable and magnetized bodies; and nonlinear coupled magneto-mechanical constitutive models for the material of interest. In the present work, classical differential formulations for nonlinear magneto-mechanical interactions are recast in integral form using the weighted-residual method. A discretized finite element form is obtained by applying the Galerkin technique. The finite element formulation is based upon three dimensional eight-noded (isoparametric) brick element interpolation functions and magnetostatic infinite elements at the boundary. Two alternative possibilities are explored for establishing the nonlinear incremental constitutive model-characterization in terms of magnetic field or in terms of magnetization. The former methodology is the one most commonly used in the literature. In this work, a detailed comparative study of both methodologies is carried out. The computational scheme is validated, qualitatively and quantitatively, against experimental measurements published in the literature on structures incorporating the magnetostrictive material Terfenol-D. The influence of nonlinear body forces and body moments of magnetic origin

  17. An assessment of unstructured grid finite volume schemes for cold gas hypersonic flow calculations

    Directory of Open Access Journals (Sweden)

    João Luiz F. Azevedo

    2009-06-01

    Full Text Available A comparison of five different spatial discretization schemes is performed considering a typical high speed flow application. Flowfields are simulated using the 2-D Euler equations, discretized in a cell-centered finite volume procedure on unstructured triangular meshes. The algorithms studied include a central difference-type scheme, and 1st- and 2nd-order van Leer and Liou flux-vector splitting schemes. These methods are implemented in an efficient, edge-based, unstructured grid procedure which allows for adaptive mesh refinement based on flow property gradients. Details of the unstructured grid implementation of the methods are presented together with a discussion of the data structure and of the adaptive refinement strategy. The application of interest is the cold gas flow through a typical hypersonic inlet. Results for different entrance Mach numbers and mesh topologies are discussed in order to assess the comparative performance of the various spatial discretization schemes.

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

    Directory of Open Access Journals (Sweden)

    Oluwaseun Egbelowo

    2017-05-01

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

  19. A finite-volume scheme for a kidney nephron model

    Directory of Open Access Journals (Sweden)

    Seguin Nicolas

    2012-04-01

    Full Text Available We present a finite volume type scheme to solve a transport nephron model. The model consists in a system of transport equations with specific boundary conditions. The transport velocity is driven by another equation that can undergo sign changes during the transient regime. This is the main difficulty for the numerical resolution. The scheme we propose is based on an explicit resolution and is stable under a CFL condition which does not depend on the stiffness of source terms. Nous présentons un schéma numérique de type volume fini que l’on applique à un modèle de transport dans le néphron. Ce modèle consiste en un système d’équations de transport, avec des conditions aux bords spécifiques. La vitesse du transport est la solution d’un autre système d’équation et peut changer de signe au cours du régime transitoire. Ceci constitue la principale difficulté pour la résolution numérique. Le schéma proposé, basé sur une résolution explicite, est stable sous une condition CFL non restrictive.

  20. A numerical scheme based on radial basis function finite difference (RBF-FD) technique for solving the high-dimensional nonlinear Schrödinger equations using an explicit time discretization: Runge-Kutta method

    Science.gov (United States)

    Dehghan, Mehdi; Mohammadi, Vahid

    2017-08-01

    In this research, we investigate the numerical solution of nonlinear Schrödinger equations in two and three dimensions. The numerical meshless method which will be used here is RBF-FD technique. The main advantage of this method is the approximation of the required derivatives based on finite difference technique at each local-support domain as Ωi. At each Ωi, we require to solve a small linear system of algebraic equations with a conditionally positive definite matrix of order 1 (interpolation matrix). This scheme is efficient and its computational cost is same as the moving least squares (MLS) approximation. A challengeable issue is choosing suitable shape parameter for interpolation matrix in this way. In order to overcome this matter, an algorithm which was established by Sarra (2012), will be applied. This algorithm computes the condition number of the local interpolation matrix using the singular value decomposition (SVD) for obtaining the smallest and largest singular values of that matrix. Moreover, an explicit method based on Runge-Kutta formula of fourth-order accuracy will be applied for approximating the time variable. It also decreases the computational costs at each time step since we will not solve a nonlinear system. On the other hand, to compare RBF-FD method with another meshless technique, the moving kriging least squares (MKLS) approximation is considered for the studied model. Our results demonstrate the ability of the present approach for solving the applicable model which is investigated in the current research work.

  1. Interpolation scheme for fictitious domain techniques and topology optimization of finite strain elastic problems

    DEFF Research Database (Denmark)

    Wang, Fengwen; Lazarov, Boyan Stefanov; Sigmund, Ole

    2014-01-01

    The focus of this paper is on interpolation schemes for fictitious domain and topology optimization approaches with structures undergoing large displacements. Numerical instability in the finite element simulations can often be observed, due to excessive distortion in low stiffness regions. A new...... for a challenging test geometry as well as for topology optimization of minimum compliance and compliant mechanisms. The effect of combining the proposed interpolation scheme with different hyperelastic material models is investigated as well. Numerical results show that the proposed approach alleviates...... the problems in the low stiffness regions and for the simulated cases, results in stable topology optimization of structures undergoing large displacements. © 2014 Elsevier B.V....

  2. Finite element and finite difference methods in electromagnetic scattering

    CERN Document Server

    Morgan, MA

    2013-01-01

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

  3. LONG-TIME BEHAVIOR OF FINITE DIFFERENCE SOLUTIONS OF A NONLINEAR SCHRODINGER EQUATION WITH WEAKLY DAMPED

    Institute of Scientific and Technical Information of China (English)

    Fa-yong Zhang; Shu-juan Lu

    2001-01-01

    A weakly demped Schrodinger equation possessing a global attractor are considered.The dynamical properties of a class of finite difference scheme are analysed. The exsitence of global attractor is proved for the discrete system. The stability of the difference scheme and the error estimate of the difference solution are obtained in the autonomous system case. Finally, long-time stability and convergence of the class of finite difference scheme also are analysed in the nonautonomous system case.

  4. Finite-volume WENO scheme for viscous compressible multicomponent flows

    Science.gov (United States)

    Coralic, Vedran; Colonius, Tim

    2014-01-01

    We develop a shock- and interface-capturing numerical method that is suitable for the simulation of multicomponent flows governed by the compressible Navier-Stokes equations. The numerical method is high-order accurate in smooth regions of the flow, discretely conserves the mass of each component, as well as the total momentum and energy, and is oscillation-free, i.e. it does not introduce spurious oscillations at the locations of shockwaves and/or material interfaces. The method is of Godunov-type and utilizes a fifth-order, finite-volume, weighted essentially non-oscillatory (WENO) scheme for the spatial reconstruction and a Harten-Lax-van Leer contact (HLLC) approximate Riemann solver to upwind the fluxes. A third-order total variation diminishing (TVD) Runge-Kutta (RK) algorithm is employed to march the solution in time. The derivation is generalized to three dimensions and nonuniform Cartesian grids. A two-point, fourth-order, Gaussian quadrature rule is utilized to build the spatial averages of the reconstructed variables inside the cells, as well as at cell boundaries. The algorithm is therefore fourth-order accurate in space and third-order accurate in time in smooth regions of the flow. We corroborate the properties of our numerical method by considering several challenging one-, two- and three-dimensional test cases, the most complex of which is the asymmetric collapse of an air bubble submerged in a cylindrical water cavity that is embedded in 10% gelatin. PMID:25110358

  5. Efficient interface conditions for the finite difference beam propagation method

    NARCIS (Netherlands)

    Hoekstra, Hugo; Krijnen, Gijsbertus J.M.; Lambeck, Paul

    1992-01-01

    It is shown that by adapting the refractive indexes in the vicinity of interfaces, the 2-D beam propagation method based on the finite-difference (FDBPM) scheme can be made much more effective. This holds especially for TM modes propagating in structures with high-index contrasts, such as surface

  6. EXTERNAL BODY FORCE IN FINITE DIFFERENCE LATTICE BOLTZMANN METHOD

    Institute of Scientific and Technical Information of China (English)

    CHEN Sheng; LIU Zhao-hui; SHI Bao-chang; ZHENG Chu-guang

    2005-01-01

    A new finite difference lattice Boltzmann scheme is developed. Because of analyzing the influence of external body force roundly, the correct Navier-Stokes equations with the external body force are recovered, without any additional unphysical terms. And some numerical results are presented. The result which close agreement with analytical data shows the good performance of the model.

  7. Finite volume schemes for multi-dimensional hyperbolic systems based on the use of bicharacteristics

    OpenAIRE

    Lukácová-Medvid'ová, Maria; Saibertova, Jitka

    2004-01-01

    In this paper we present recent results for the bicharacteristic based finite volume schemes, the so-called finite volume evolution Galerkin (FVEG) schemes. These methods were proposed to solve multi-dimensional hyperbolic conservation laws. They combine the usually conflicting design objectives of using the conservation form and following the characteristics, or bicharacteristics. This is realized by combining the finite volume formulation with approximate evolution operators, which use bich...

  8. Finite volume schemes for multidimensional hyperbolic systems based on the use of bicharacteristics

    OpenAIRE

    Lukácová-Medvid'ová, Maria

    2003-01-01

    In this survey paper we present an overview on recent results for the bicharacteristics based finite volume schemes, the so-called finite volume evolution Galerkin (FVEG) schemes. These methods were proposed to solve multidimensional hyperbolic conservation laws. They combine the usually conflicting design objectives of using the conservation form and following the characteritics, or bicharacteritics. This is realized by combining the finite volume formulation with approximate evolution opera...

  9. Three-dimensional Finite Element Optimization Analysis of Different Seepage Control Schemes of Lizhou RCC Arch Dam%立洲RCC拱坝渗控方案的三维有限元优化分析

    Institute of Scientific and Technical Information of China (English)

    行亚楠; 胡升伟; 王滔; 吴震宇; 陈建康

    2013-01-01

    The seepage control measures were investigated for the dam area of Lizhou hydroelectric project in Muli River of Si‐chuan Province .A three‐dimensional finite element seepage model was developed using ANSYS12 .1 to analyze the seepage char‐acteristics and variations of seepage pressure under different seepage control schemes .The seepage gradient and seepage amount of key positions and the seepage pressure and groundwater level of typical profiles of seepage field for different seepage control schemes were compared .The results showed that (1) the impervious curtain and drainage hole in the design scheme of seepage control measures of Lizhou arch dam can decrease the seepage saturation line effectively ,lower the uplift pressure on dam foun‐dation and dam abutment ,and improve the stress conditions of dam foundation and dam abutment ;(2) the deepening curtain , drainage hole ,and thickening curtain have insignificant effects on decreasing the seepage pressure ;and (3) increasing the depth of impervious curtain near the f 5 fault can prevent the formation of leakage passage in the f 5 fault .In addition ,removing the drainage hole in the first layer and decreasing the extending length of the impervious curtain of dam abutment can save the cost of seepage control measures without breaking seepage safety .%  以四川木里河立洲水电枢纽工程为研究对象,对坝区的渗控措施展开研究.利用ANSYS12.1建立三维有限元渗流模型,计算分析得到了各渗控方案的渗流特征和渗透压力变化规律.对各方案中关键部位的渗透比降、渗漏量和典型剖面渗流场的渗压、地下水位等特征量进行比较分析后,得知:(1)立洲拱坝渗控措施设计方案的防渗帷幕和排水孔幕能有效降低坝后渗流浸润线,对于减小坝基、坝肩扬压力、改善坝基和坝肩受力条件起到了良好的作用;(2)加深帷幕和排水孔幕、增厚帷幕对降低坝

  10. Generalized Rayleigh quotient and finite element two-grid discretization schemes

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    This study discusses generalized Rayleigh quotient and high efficiency finite element discretization schemes. Some results are as follows: 1) Rayleigh quotient accelerate technique is extended to nonselfadjoint problems. Generalized Rayleigh quotients of operator form and weak form are defined and the basic relationship between approximate eigenfunction and its generalized Rayleigh quotient is established. 2) New error estimates are obtained by replacing the ascent of exact eigenvalue with the ascent of finite element approximate eigenvalue. 3) Based on the work of Xu Jinchao and Zhou Aihui, finite element two-grid discretization schemes are established to solve nonselfadjoint elliptic differential operator eigenvalue problems and these schemes are used in both conforming finite element and non-conforming finite element. Besides, the efficiency of the schemes is proved by both theoretical analysis and numerical experiments. 4) Iterated Galerkin method, interpolated correction method and gradient recovery for selfadjoint elliptic differential operator eigenvalue problems are extended to nonselfadjoint elliptic differential operator eigenvalue problems.

  11. Generalized Rayleigh quotient and finite element two-grid discretization schemes

    Institute of Scientific and Technical Information of China (English)

    YANG YiDu; FAN XinYue

    2009-01-01

    This study discusses generalized Rayleigh quotient and high efficiency finite element dis-cretization schemes. Some results are as follows: 1) Rayleigh quotient accelerate technique is extended to nonselfadjoint problems. Generalized Rayleigh quotients of operator form and weak form are defined and the basic relationship between approximate eigenfunction and its generalized Rayleigh quotient is established. 2) New error estimates are obtained by replacing the ascent of exact eigenvalue with the ascent of finite element approximate eigenvalue. 3) Based on the work of Xu Jinchao and Zhou Aihui, finite element two-grid discretization schemes are established to solve nonselfadjoint elliptic differential operator eigenvalue problems and these schemes are used in both conforming finite element and non-conforming finite element. Besides, the efficiency of the schemes is proved by both theoretical analysis and numerical experiments. 4) Iterated Galerkin method, interpolated correction method and gradient recovery for selfadjoint elliptic differential operator eigenvalue problems are extended to nonselfadjoint elliptic differential operator eigenvalue problems.

  12. Accuracy property of certain hyperbolic difference schemes

    Energy Technology Data Exchange (ETDEWEB)

    Hicks, D.L.; Madsen, M.M.

    1976-12-01

    An accuracy property called the CFL1 property is shared by several successful difference schemes. It appears to be a property at least as important as the property of higher-order accuracy for hyperbolic difference schemes when weak solutions (e.g., shocks) are sought. Investigation of this property leads to suggestions of ways to improve the accuracy in such wavecodes as WONDY, CHARTD, and THREEDY. 10 figures.

  13. ON LOCKING-FREE FINITE ELEMENT SCHEMES FOR THREE-DIMENSIONAL ELASTICITY

    Institute of Scientific and Technical Information of China (English)

    He Qi; Lie-heng Wang; Wei-ying Zheng

    2005-01-01

    In the present paper, the authors discuss the locking phenomenon of the finite element method for three-dimensional elasticity as the Lame constant λ→∞. Three kinds of finite elements are proposed and analyzed to approximate the three-dimensional elasticity with pure displacement boundary condition. Optimal order error estimates which are uniform with respect to λ∈ (0, +∞) are obtained for three schemes. Furthermore, numerical results are presented to show that, our schemes are locking-free and and the trilinear conforming finite element scheme is locking.

  14. Finite difference computing with PDEs a modern software approach

    CERN Document Server

    Langtangen, Hans Petter

    2017-01-01

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

  15. Finite-Difference Algorithms For Computing Sound Waves

    Science.gov (United States)

    Davis, Sanford

    1993-01-01

    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.

  16. Stability-Controllable Second-Order Difference Scheme for Convection Term

    Institute of Scientific and Technical Information of China (English)

    1998-01-01

    A new finite difference scheme-SCSD scheme has been propsed based on CD( Central Difference) scheme and SUD(Second-order Upwind Difference)scheme.Its basic feature is controllable convective stability and always second-order accuracy(Stability-Controllable Second-order Difference),It has been proven that this Scheme is convective-Stable if the grid Peclet number|PΔ|≤2/β(0≤β≤1).The advantage of this new scheme has been discussed based on the modified wavenumber analysis by using Fourier transform.This scheme has been applied to the 2-D incompressible convective-diffusive equation and 2-D compressible Euler equation,and corresponding finite difference equations have been derived.Numerical examples of 1-D Burgers equation and 2-D transport equation have been presented to show its good accuracy and controllable convective stability.

  17. Explicit finite difference methods for the delay pseudoparabolic equations.

    Science.gov (United States)

    Amirali, I; Amiraliyev, G M; Cakir, M; Cimen, E

    2014-01-01

    Finite difference technique is applied to numerical solution of the initial-boundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities two-level difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stable and convergent of order two in space and of order one in time. The error estimates are obtained in the discrete norm. Some numerical results confirming the expected behavior of the method are shown.

  18. An Average Linear Difference Scheme for the Generalized Rosenau-KdV Equation

    Directory of Open Access Journals (Sweden)

    Maobo Zheng

    2014-01-01

    Full Text Available An average linear finite difference scheme for the numerical solution of the initial-boundary value problem of Generalized Rosenau-KdV equation is proposed. The existence, uniqueness, and conservation for energy of the difference solution are proved by the discrete energy norm method. It is shown that the finite difference scheme is 2nd-order convergent and unconditionally stable. Numerical experiments verify that the theoretical results are right and the numerical method is efficient and reliable.

  19. Finite difference solutions to shocked acoustic waves

    Science.gov (United States)

    Walkington, N. J.; Eversman, W.

    1983-01-01

    The MacCormack, Lambda and split flux finite differencing schemes are used to solve a one dimensional acoustics problem. Two duct configurations were considered, a uniform duct and a converging-diverging nozzle. Asymptotic solutions for these two ducts are compared with the numerical solutions. When the acoustic amplitude and frequency are sufficiently high the acoustic signal shocks. This condition leads to a deterioration of the numerical solutions since viscous terms may be required if the shock is to be resolved. A continuous uniform duct solution is considered to demonstrate how the viscous terms modify the solution. These results are then compared with a shocked solution with and without viscous terms. Generally it is found that the most accurate solutions are those obtained using the minimum possible viscosity coefficients. All of the schemes considered give results accurate enough for acoustic power calculations with no one scheme performing significantly better than the others.

  20. Scale-selective dissipation in energy-conserving finite element schemes for two-dimensional turbulence

    CERN Document Server

    Natale, Andrea

    2016-01-01

    We analyse the multiscale properties of energy-conserving upwind-stabilised finite element discretisations of the two-dimensional incompressible Euler equations. We focus our attention on two particular methods: the Lie derivative discretisation introduced in Natale and Cotter (2016a) and the SUPG discretisation of the vorticity advection equation. Such discretisations provide control on enstrophy by modelling different types of scale interactions. We quantify the performance of the schemes in reproducing the non-local energy backscatter that characterises two-dimensional turbulent flows.

  1. Explicit finite-difference lattice Boltzmann method for curvilinear coordinates.

    Science.gov (United States)

    Guo, Zhaoli; Zhao, T S

    2003-06-01

    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.

  2. Generalized rectangular finite difference beam propagation method.

    Science.gov (United States)

    Sujecki, Slawomir

    2008-08-10

    A method is proposed that allows for significant improvement of the numerical efficiency of the standard finite difference beam propagation algorithm. The advantages of the proposed method derive from the fact that it allows for an arbitrary selection of the preferred direction of propagation. It is demonstrated that such flexibility is particularly useful when studying the properties of obliquely propagating optical beams. The results obtained show that the proposed method achieves the same level of accuracy as the standard finite difference beam propagation method but with lower order Padé approximations and a coarser finite difference mesh.

  3. Design and Verification Methodology of Boundary Conditions for Finite Volume Schemes

    Science.gov (United States)

    2012-07-01

    Finite Volume Schemes 5a. CONTRACT NUMBER In-House 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Folkner, D., Katz , A and Sankaran...July 9-13, 2012 ICCFD7-2012-1001 Design and Verification Methodology of Boundary Conditions for Finite Volume Schemes D. Folkner∗, A. Katz ∗ and V...Office (ARO), under the supervision of Dr. Frederick Ferguson. The authors would like to thank Dr. Ferguson for his continuing support of this research

  4. A class of the fourth order finite volume Hermite weighted essentially non-oscillatory schemes

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    In this paper,we developed a class of the fourth order accurate finite volume Hermite weighted essentially non-oscillatory(HWENO)schemes based on the work(Computers&Fluids,34:642-663(2005))by Qiu and Shu,with Total Variation Diminishing Runge-Kutta time discretization method for the two-dimensional hyperbolic conservation laws.The key idea of HWENO is to evolve both with the solution and its derivative,which allows for using Hermite interpolation in the reconstruction phase,resulting in a more compact stencil at the expense of the additional work.The main difference between this work and the formal one is the procedure to reconstruct the derivative terms.Comparing with the original HWENO schemes of Qiu and Shu,one major advantage of new HWENOschemes is its robust in computation of problem with strong shocks.Extensive numerical experiments are performed to illustrate the capability of the method.

  5. High Order Finite Difference Methods for Multiscale Complex Compressible Flows

    Science.gov (United States)

    Sjoegreen, Bjoern; Yee, H. C.

    2002-01-01

    The classical way of analyzing finite difference schemes for hyperbolic problems is to investigate as many as possible of the following points: (1) Linear stability for constant coefficients; (2) Linear stability for variable coefficients; (3) Non-linear stability; and (4) Stability at discontinuities. We will build a new numerical method, which satisfies all types of stability, by dealing with each of the points above step by step.

  6. Finite difference methods for the solution of unsteady potential flows

    Science.gov (United States)

    Caradonna, F. X.

    1985-01-01

    A brief review is presented of various problems which are confronted in the development of an unsteady finite difference potential code. This review is conducted mainly in the context of what is done for a typical small disturbance and full potential methods. The issues discussed include choice of equation, linearization and conservation, differencing schemes, and algorithm development. A number of applications including unsteady three-dimensional rotor calculation, are demonstrated.

  7. A finite difference method for free boundary problems

    KAUST Repository

    Fornberg, Bengt

    2010-04-01

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

  8. Calculation of compressible boundary layer flow about airfoils by a finite element/finite difference method

    Science.gov (United States)

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

    1992-01-01

    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.

  9. A discontinous Galerkin finite element method with an efficient time integration scheme for accurate simulations

    KAUST Repository

    Liu, Meilin

    2011-07-01

    A discontinuous Galerkin finite element method (DG-FEM) with a highly-accurate time integration scheme is presented. The scheme achieves its high accuracy using numerically constructed predictor-corrector integration coefficients. Numerical results show that this new time integration scheme uses considerably larger time steps than the fourth-order Runge-Kutta method when combined with a DG-FEM using higher-order spatial discretization/basis functions for high accuracy. © 2011 IEEE.

  10. 带吸收边界条件的声波方程显式差分格式的稳定性分析%STABILITY ANALYSIS OF EXPLICIT FINITE DIFFERENCE SCHEMES FOR THE ACOUSTIC WAVE EQUATION WITH ABSORBING BOUNDARY CONDITIONS

    Institute of Scientific and Technical Information of China (English)

    邵秀民; 刘臻

    2001-01-01

    It is well known that in numerical computations of wave equationsby utiliz ing explicit schemes the stability is an extremely important problem when artifi cial boundaries are introduced and absorbing boundary conditions are imposed on them. In this paper, the stability of finite difference schemes for the acoustic wave equation with the first-and the second-order Clayton-Engquist-Majda absorbing boundary conditions is discussed by using energy techniques. The corresponding stability conditions (i.e., the stability bounds of the CFL number) are given, which is sharper than those stability conditions for interior schemes or other kinds of boundary conditions. Numerical results are presented to confirm the correctness of the theoretical analysis.

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

    KAUST Repository

    Chu, Chunlei

    2012-07-01

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

  12. 一类反常次扩散方程Neumann问题的有限差分格式及收敛性分析%A Finite Difference Scheme and a Convergence Analysis of a Kind of Anomalous Diffusion Equation with Neumann Conditions

    Institute of Scientific and Technical Information of China (English)

    马亮亮; 刘冬兵

    2014-01-01

    A finite difference method and a convergence problem for a kind of anomalous diffusion equation with Neumann conditions are discussed. A finite difference scheme is obtained by adopting the method of the first-order forward difference quotient and second-order space center difference quotient and the formula of higher-order linear multistep method to discrete the fractional derivatives. The stability of the difference scheme is analyzed by means of Fourier analysis and the errors and convergence of the schemes are also discussed.%利用一阶向前差商和空间二阶中心差商以及高阶线性多步法公式构造了反常次扩散方程Neumann问题的有限差分格式,借助 Fourier分析方法对差分格式的稳定性进行了分析,并讨论了差分格式的误差和收敛性问题。

  13. Numerical computation of transonic flows by finite-element and finite-difference methods

    Science.gov (United States)

    Hafez, M. M.; Wellford, L. C.; Merkle, C. L.; Murman, E. M.

    1978-01-01

    Studies on applications of the finite element approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. Finite element analogs of Murman's mixed type finite difference operators for small disturbance formulations were constructed and the time dependent approach (using finite differences in time and finite elements in space) was examined.

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2014-09-30

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

  15. A High-Accuracy Linear Conservative Difference Scheme for Rosenau-RLW Equation

    Directory of Open Access Journals (Sweden)

    Jinsong Hu

    2013-01-01

    Full Text Available We study the initial-boundary value problem for Rosenau-RLW equation. We propose a three-level linear finite difference scheme, which has the theoretical accuracy of Oτ2+h4. The scheme simulates two conservative properties of original problem well. The existence, uniqueness of difference solution, and a priori estimates in infinite norm are obtained. Furthermore, we analyze the convergence and stability of the scheme by energy method. At last, numerical experiments demonstrate the theoretical results.

  16. On the accuracy and efficiency of finite difference solutions for nonlinear waves

    DEFF Research Database (Denmark)

    Bingham, Harry B.

    2006-01-01

    We consider the relative accuracy and efficiency of low- and high-order finite difference discretizations of the exact potential flow problem for nonlinear water waves. The continuous differential operators are replaced by arbitrary order finite difference schemes on a structured but non...

  17. Implementation of Generalized Modes in a 3D Finite Difference Based Seakeeping Model

    DEFF Research Database (Denmark)

    Andersen, Matilde H.; Amini Afshar, Mostafa; Bingham, Harry B.

    This work is an extension of the finite difference potential flow solver OceanWave3D-Seakeepingdeveloped by Afshar (2014) to include generalized modes. The continuity equation is solvedusing a fourth-order centered finite difference scheme which requires that the entire fluid domainis discretized...

  18. Feedback optimal control of distributed parameter systems by using finite-dimensional approximation schemes.

    Science.gov (United States)

    Alessandri, Angelo; Gaggero, Mauro; Zoppoli, Riccardo

    2012-06-01

    Optimal control for systems described by partial differential equations is investigated by proposing a methodology to design feedback controllers in approximate form. The approximation stems from constraining the control law to take on a fixed structure, where a finite number of free parameters can be suitably chosen. The original infinite-dimensional optimization problem is then reduced to a mathematical programming one of finite dimension that consists in optimizing the parameters. The solution of such a problem is performed by using sequential quadratic programming. Linear combinations of fixed and parameterized basis functions are used as the structure for the control law, thus giving rise to two different finite-dimensional approximation schemes. The proposed paradigm is general since it allows one to treat problems with distributed and boundary controls within the same approximation framework. It can be applied to systems described by either linear or nonlinear elliptic, parabolic, and hyperbolic equations in arbitrary multidimensional domains. Simulation results obtained in two case studies show the potentials of the proposed approach as compared with dynamic programming.

  19. WEIGHT FINITE DIFFERENCE SCHEME FOR TWO-SIDED SPACE FRACTIONALLévy-Feller DIFFUSION EQUATION WITH RIESZ-FELLER POTENTIAL%含有Riesz-Feller位势的双边空间分数阶Lévy-Feller扩散方程的加权有限差分格式

    Institute of Scientific and Technical Information of China (English)

    马亮亮; 刘冬兵

    2014-01-01

    A finite difference problem for two-sided space fractional Lévy-Feller diffusion equation with Riesz-Feller potential is considered. By using the equivalent of fractional order differential operators, a weighted finite difference scheme for scattering the above diffusion equation is proposed. The stability and convergence of the scheme were analyzed. Finally, a numerical example was provided to demonstrate the validity and applicability of the difference scheme.%考虑了一类含有Riesz-Feller位势的两边空间分数阶Lévy-Feller扩散方程的差分问题。利用分数阶微分算子的等价性,提出了一种加权有限差分解法,并证明了所提出的差分格式是稳定和收敛的。最后通过一个数值例子说明了所提出的差分格式是有效和可靠的。

  20. Non-conforming curved finite element schemes for time-dependent elastic-acoustic coupled problems

    Science.gov (United States)

    Rodríguez-Rozas, Ángel; Diaz, Julien

    2016-01-01

    High-order numerical methods for solving time-dependent acoustic-elastic coupled problems are introduced. These methods, based on Finite Element techniques, allow for a flexible coupling between the fluid and the solid domain by using non-conforming meshes and curved elements. Since characteristic waves travel at different speeds through different media, specific levels of granularity for the mesh discretization are required on each domain, making impractical a possible conforming coupling in between. Advantageously, physical domains may be independently discretized in our framework due to the non-conforming feature. Consequently, an important increase in computational efficiency may be achieved compared to other implementations based on conforming techniques, namely by reducing the total number of degrees of freedom. Differently from other non-conforming approaches proposed so far, our technique is relatively simpler and requires only a geometrical adjustment at the coupling interface at a preprocessing stage, so that no extra computations are necessary during the time evolution of the simulation. On the other hand, as an advantage of using curvilinear elements, the geometry of the coupling interface between the two media of interest is faithfully represented up to the order of the scheme used. In other words, higher order schemes are in consonance with higher order approximations of the geometry. Concerning the time discretization, we analyze both explicit and implicit schemes. These schemes are energy conserving and, for the explicit case, the stability is guaranteed by a CFL condition. In order to illustrate the accuracy and convergence of these methods, a set of representative numerical tests are presented.

  1. Five-point Element Scheme of Finite Analytic Method for Unsteady Groundwater Flow

    Institute of Scientific and Technical Information of China (English)

    Xiang Bo; Mi Xiao; Ji Changming; Luo Qingsong

    2007-01-01

    In order to improve the finite analytic method's adaptability for irregular unit, by using coordinates rotation technique this paper establishes a five-point element scheme of finite analytic method. It not only solves unsteady groundwater flow equation but also gives the boundary condition. This method can be used to calculate the three typical questions of groundwater. By compared with predecessor's computed result, the result of this method is more satisfactory.

  2. Traditional and Truncation schemes for Different Multiplier

    Directory of Open Access Journals (Sweden)

    Yogesh M. Motey

    2013-03-01

    Full Text Available A rapid and proficient in power requirement multiplier is always vital in electronics industry like DSP, image processing and ALU in microprocessors. Multiplier is such an imperative block w ith respect to power consumption and area occupied in the system. In order to meet the demand for high speed, various parallel array multiplication algorithms have been proposed by a number of authors. The array multipliers use a large amount of hardware, consequently consuming a large amount of power. One of the methods for multiplication is based on Indian Vedic mathematics. The total Vedic mathematics is based on sixteen sutras (word formulae and manifests a merged structure of mathematics. The parallel multipliers for example radix 2 and radix 4 booth multiplier does the computations using less number of adders and less number of iterative steps that results in, they occupy less space to that of serial multiplier. Truncated multipliers offer noteworthy enhancements in area, delay, and power. Truncated multiplication provides different method for reducing the power dissipation and area of rounded parallel multipliers in DSP systems. Since in a truncated multiplier the x less significant bits of the full-width product are discarded thus partial products are removed and replaced by a suit- able compensation equations, match the accuracy with hardware cost. A pseudo-carry compensation truncation (PCT scheme, it is for the multiplexer based array multiplier, which yields less average error among existing truncation methods.After studying many research papers it’s found that some of the schemes for multiplier are suitable because their own uniqueness of multiplication. Such schemes are listed in this paper for example the different truncation schemes like constant-correction truncation (CCT, variable -correction truncation (VCT, pseudo-carry compensation truncation (PCT are most suitable for truncated multiplier.

  3. Finite difference order doubling in two dimensions

    Energy Technology Data Exchange (ETDEWEB)

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

    2008-03-28

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

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

    CERN Document Server

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

    2010-01-01

    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.

  5. Triviality of $\\varphi^4$ theory in a finite volume scheme adapted to the broken phase

    CERN Document Server

    Siefert, Johannes

    2014-01-01

    We study the standard one-component $\\varphi^4$-theory in four dimensions. A renormalized coupling is defined in a finite size renormalization scheme which becomes the standard scheme of the broken phase for large volumes. Numerical simulations are reported using the worm algorithm in the limit of infinite bare coupling. The cutoff dependence of the renormalized coupling closely follows the perturbative Callan Symanzik equation and the triviality scenario is hence further supported.

  6. DIFFERENCE SCHEMES BASING ON COEFFICIENT APPROXIMATION

    Institute of Scientific and Technical Information of China (English)

    MOU Zong-ze; LONG Yong-xing; QU Wen-xiao

    2005-01-01

    In respect of variable coefficient differential equations, the equations of coefficient function approximation were more accurate than the coefficient to be frozen as a constant in every discrete subinterval. Usually, the difference schemes constructed based on Taylor expansion approximation of the solution do not suit the solution with sharp function.Introducing into local bases to be combined with coefficient function approximation, the difference can well depict more complex physical phenomena, for example, boundary layer as well as high oscillatory, with sharp behavior. The numerical test shows the method is more effective than the traditional one.

  7. A combined finite volume-nonconforming finite element scheme for compressible two phase flow in porous media

    KAUST Repository

    Saad, Bilal Mohammed

    2014-06-28

    We propose and analyze a combined finite volume-nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. The diffusion term, which can be anisotropic and heterogeneous, is discretized by piecewise linear nonconforming triangular finite elements. The other terms are discretized by means of a cell-centered finite volume scheme on a dual mesh, where the dual volumes are constructed around the sides of the original mesh. The relative permeability of each phase is decentred according the sign of the velocity at the dual interface. This technique also ensures the validity of the discrete maximum principle for the saturation under a non restrictive shape regularity of the space mesh and the positiveness of all transmissibilities. Next, a priori estimates on the pressures and a function of the saturation that denote capillary terms are established. These stabilities results lead to some compactness arguments based on the use of the Kolmogorov compactness theorem, and allow us to derive the convergence of a subsequence of the sequence of approximate solutions to a weak solution of the continuous equations, provided the mesh size tends to zero. The proof is given for the complete system when the density of the each phase depends on its own pressure. © 2014 Springer-Verlag Berlin Heidelberg.

  8. High-order conservative reconstruction schemes for finite volume methods in cylindrical and spherical coordinates

    CERN Document Server

    Mignone, A

    2014-01-01

    High-order reconstruction schemes for the solution of hyperbolic conservation laws in orthogonal curvilinear coordinates are revised in the finite volume approach. The formulation employs a piecewise polynomial approximation to the zone-average values to reconstruct left and right interface states from within a computational zone to arbitrary order of accuracy by inverting a Vandermonde-like linear system of equations with spatially varying coefficients. The approach is general and can be used on uniform and non-uniform meshes although explicit expressions are derived for polynomials from second to fifth degree in cylindrical and spherical geometries with uniform grid spacing. It is shown that, in regions of large curvature, the resulting expressions differ considerably from their Cartesian counterparts and that the lack of such corrections can severely degrade the accuracy of the solution close to the coordinate origin. Limiting techniques and monotonicity constraints are revised for conventional reconstruct...

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

    DEFF Research Database (Denmark)

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

    2012-01-01

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

  10. Some Numerical Quadrature Schemes of a Non-conforming Quadrilateral Finite Element

    Institute of Scientific and Technical Information of China (English)

    Xiao-fei GUAN; Ming-xia LI; Shao-chun CHEN

    2012-01-01

    Numerical quadrature schemes of a non-conforming finite element method for general second order elliptic problems in two dimensional (2-D) and three dimensional (3-D) space are discussed in this paper.We present and analyze some optimal numerical quadrature schemes. One of the schemes contains only three sampling points,which greatly improves the efficiency of numerical computations.The optimal error estimates are derived by using some traditional approaches and techniques.Lastly,some numerical results are provided to verify our theoretical analysis.

  11. Optimal 25-Point Finite-Difference Subgridding Techniques for the 2D Helmholtz Equation

    Directory of Open Access Journals (Sweden)

    Tingting Wu

    2016-01-01

    Full Text Available We present an optimal 25-point finite-difference subgridding scheme for solving the 2D Helmholtz equation with perfectly matched layer (PML. This scheme is second order in accuracy and pointwise consistent with the equation. Subgrids are used to discretize the computational domain, including the interior domain and the PML. For the transitional node in the interior domain, the finite difference equation is formulated with ghost nodes, and its weight parameters are chosen by a refined choice strategy based on minimizing the numerical dispersion. Numerical experiments are given to illustrate that the newly proposed schemes can produce highly accurate seismic modeling results with enhanced efficiency.

  12. On the wavelet optimized finite difference method

    Science.gov (United States)

    Jameson, Leland

    1994-01-01

    When one considers the effect in the physical space, Daubechies-based wavelet methods are equivalent to finite difference methods with grid refinement in regions of the domain where small scale structure exists. Adding a wavelet basis function at a given scale and location where one has a correspondingly large wavelet coefficient is, essentially, equivalent to adding a grid point, or two, at the same location and at a grid density which corresponds to the wavelet scale. This paper introduces a wavelet optimized finite difference method which is equivalent to a wavelet method in its multiresolution approach but which does not suffer from difficulties with nonlinear terms and boundary conditions, since all calculations are done in the physical space. With this method one can obtain an arbitrarily good approximation to a conservative difference method for solving nonlinear conservation laws.

  13. A new semi-Lagrangian difference scheme

    Institute of Scientific and Technical Information of China (English)

    季仲贞; 陈嘉滨

    2001-01-01

    A new completely energy-conserving semi-Lagrangian scheme is constructed. The numerical solution of shallow water equation shows that this conservative scheme preserves the total energy in twelve significant digits, while the traditional scheme does only in five significant digits.

  14. Implicit finite difference methods on composite grids

    Science.gov (United States)

    Mastin, C. Wayne

    1987-01-01

    Techniques for eliminating time lags in the implicit finite-difference solution of partial differential equations are investigated analytically, with a focus on transient fluid dynamics problems on overlapping multicomponent grids. The fundamental principles of the approach are explained, and the method is shown to be applicable to both rectangular and curvilinear grids. Numerical results for sample problems are compared with exact solutions in graphs, and good agreement is demonstrated.

  15. A parallel finite-difference method for computational aerodynamics

    Science.gov (United States)

    Swisshelm, Julie M.

    1989-01-01

    A finite-difference scheme for solving complex three-dimensional aerodynamic flow on parallel-processing supercomputers is presented. The method consists of a basic flow solver with multigrid convergence acceleration, embedded grid refinements, and a zonal equation scheme. Multitasking and vectorization have been incorporated into the algorithm. Results obtained include multiprocessed flow simulations from the Cray X-MP and Cray-2. Speedups as high as 3.3 for the two-dimensional case and 3.5 for segments of the three-dimensional case have been achieved on the Cray-2. The entire solver attained a factor of 2.7 improvement over its unitasked version on the Cray-2. The performance of the parallel algorithm on each machine is analyzed.

  16. Interference Phenomenon for Different Chiral Bosonization Schemes

    CERN Document Server

    Abreu, Everton M C; Abreu, Everton M C; Wotzasek, Clovis

    1998-01-01

    We study the relationship between different chiral bosonization schemes (CBS) in the context of the soldering formalism\\cite{MS}, that considers the phenomenon of interference in the quantum field theory\\cite{ABW}. This analysis is done in the framework put forward by Siegel\\cite{WS} and by Floreanini and Jackiw\\cite{FJ} (FJ). We propose a field redefinition that discloses the presence of a noton, a non dynamical field, in Siegel's formulation for chiral bosons. The presence of a noton in the Siegel CBS is a new and surprising result, that separates dynamics from symmetry by diagonalising the Siegel action into the FJ and the noton action. While the first describes the chiral dynamics, the noton carries the symmetry contents, acquiring dynamics upon quantization and is fully responsible for the Siegel anomaly. The diagonal representation proposed here is used to study the effect of quantum interference between gauged rightons and leftons.

  17. SIGNCRYPTION BASED ON DIFFERENT DIGITAL SIGNATURE SCHEMES

    OpenAIRE

    Adrian Atanasiu; Laura Savu

    2012-01-01

    This article presents two new signcryption schemes. The first one is based on Schnorr digital signature algorithm and the second one is using Proxy Signature scheme introduced by Mambo. Schnorr Signcryption has been implemented in a program and here are provided the steps of the algorithm, the results and some examples. The Mambo’s Proxy Signature is adapted for Shortened Digital Signature Standard, being part of a new Proxy Signcryption scheme.

  18. Different options for noble gas categorization schemes

    Science.gov (United States)

    Kalinowski, Martin

    2010-05-01

    For noble gas monitoring it is crucial to support the decision makers who need to decide whether a decection may indicate a potential nuclear test. Several parameters are available that may help to distinguish a legitimate civilian source from a nuclear explosion. The most promising parameters are: (a) Anomaly observations with respect to the history of concentrations found at that site. (b) Isotopic activity ratios can be used to separate a nuclear reactor domain from the parameter space that is specific for nuclear explosions. (c) Correlation with source-receptor-sensitivities related to known civilian sources as determined by atmospheric transport simulations. A combination of these can be used to categorize an observation. So far, several initial ideas have been presented but the issue of noble gas categorisation has been postponed with the argument that further scientific studies and additional experience have to be awaited. This paper presents the principles of different options for noble gas categorisation and considers how they would meet the interests of different classes of member states. It discusses under different points of view what might be the best approach for the noble gas categorisation scheme.

  19. An Elgamal Encryption Scheme of Fibonacci Q-Matrix and Finite State Machine

    Directory of Open Access Journals (Sweden)

    B. Ravi Kumar

    2015-12-01

    Full Text Available Cryptography is the science of writing messages in unknown form using mathematical models. In Cryptography, several ciphers were introduced for the encryption schemes. Recent research focusing on designing various mathematical models in such a way that tracing the inverse of the designed mathematical models is infeasible for the eve droppers. In the present work, the ELGamal encryption scheme is executed using the generator of a cyclic group formed by the points on choosing elliptic curve, finite state machines and key matrices obtained from the Fibonacci sequences.

  20. Aerodynamic Noise Propagation Simulation using Immersed Boundary Method and Finite Volume Optimized Prefactored Compact Scheme

    Institute of Scientific and Technical Information of China (English)

    Min LIU; Keqi WU

    2008-01-01

    Based on the immersed boundary method (IBM) and the finite volume optimized pre-factored compact (FVOPC) scheme, a numerical simulation of noise propagation inside and outside the casing of a cross flow fan is estab-lished. The unsteady linearized Euler equations are solved to directly simulate the aero-acoustic field. In order to validate the FVOPC scheme, a simulation case: one dimensional linear wave propagation problem is carried out using FVOPC scheme, DRP scheme and HOC scheme. The result of FVOPC is in good agreement with the ana-lytic solution and it is better than the results of DRP and HOC schemes, the FVOPC is less dispersion and dissi-pation than DRP and HOC schemes. Then, numerical simulation of noise propagation problems is performed. The noise field of 36 compact rotating noise sources is obtained with the rotating velocity of 1000r/min. The PML absorbing boundary condition is applied to the sound far field boundary condition for depressing the numerical reflection. Wall boundary condition is applied to the casing. The results show that there are reflections on the casing wall and sound wave interference in the field. The FVOPC with the IBM is suitable for noise propagation problems under the complex geometries for depressing the dispersion and dissipation, and also keeping the high order precision.

  1. Integral and finite difference inequalities and applications

    CERN Document Server

    Pachpatte, B G

    2006-01-01

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

  2. The Complex-Step-Finite-Difference method

    Science.gov (United States)

    Abreu, Rafael; Stich, Daniel; Morales, Jose

    2015-07-01

    We introduce the Complex-Step-Finite-Difference method (CSFDM) as a generalization of the well-known Finite-Difference method (FDM) for solving the acoustic and elastic wave equations. We have found a direct relationship between modelling the second-order wave equation by the FDM and the first-order wave equation by the CSFDM in 1-D, 2-D and 3-D acoustic media. We present the numerical methodology in order to apply the introduced CSFDM and show an example for wave propagation in simple homogeneous and heterogeneous models. The CSFDM may be implemented as an extension into pre-existing numerical techniques in order to obtain fourth- or sixth-order accurate results with compact three time-level stencils. We compare advantages of imposing various types of initial motion conditions of the CSFDM and demonstrate its higher-order accuracy under the same computational cost and dispersion-dissipation properties. The introduced method can be naturally extended to solve different partial differential equations arising in other fields of science and engineering.

  3. Efficient discretization in finite difference method

    Science.gov (United States)

    Rozos, Evangelos; Koussis, Antonis; Koutsoyiannis, Demetris

    2015-04-01

    Finite difference method (FDM) is a plausible and simple method for solving partial differential equations. The standard practice is to use an orthogonal discretization to form algebraic approximate formulations of the derivatives of the unknown function and a grid, much like raster maps, to represent the properties of the function domain. For example, for the solution of the groundwater flow equation, a raster map is required for the characterization of the discretization cells (flow cell, no-flow cell, boundary cell, etc.), and two raster maps are required for the hydraulic conductivity and the storage coefficient. Unfortunately, this simple approach to describe the topology comes along with the known disadvantages of the FDM (rough representation of the geometry of the boundaries, wasted computational resources in the unavoidable expansion of the grid refinement in all cells of the same column and row, etc.). To overcome these disadvantages, Hunt has suggested an alternative approach to describe the topology, the use of an array of neighbours. This limits the need for discretization nodes only for the representation of the boundary conditions and the flow domain. Furthermore, the geometry of the boundaries is described more accurately using a vector representation. Most importantly, graded meshes can be employed, which are capable of restricting grid refinement only in the areas of interest (e.g. regions where hydraulic head varies rapidly, locations of pumping wells, etc.). In this study, we test the Hunt approach against MODFLOW, a well established finite difference model, and the Finite Volume Method with Simplified Integration (FVMSI). The results of this comparison are examined and critically discussed.

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

    KAUST Repository

    Osman, Hossam Omar

    2012-06-17

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

  5. Stability of Semi-implicit Finite Volume Scheme for Level Set Like Equation

    Institute of Scientific and Technical Information of China (English)

    Kim Kwang-il; Son Yong-chol

    2015-01-01

    We study numerical methods for level set like equations arising in im-age processing and curve evolution problems. Semi-implicit finite volume-element type schemes are constructed for the general level set like equation (image selective smoothing model) given by Alvarez et al. (Alvarez L, Lions P L, Morel J M. Image selective smoothing and edge detection by nonlinear diffusion II. SIAM J. Numer. Anal., 1992, 29: 845–866). Through the reasonable semi-implicit discretization in time and co-volume method for space approximation, we give finite volume schemes, unconditionally stable in L∞ and W 1,2 (W 1,1) sense in isotropic (anisotropic) diffu-sion domain.

  6. ANALYSIS OF AUGMENTED THREE-FIELD MACRO-HYBRID MIXED FINITE ELEMENT SCHEMES

    Institute of Scientific and Technical Information of China (English)

    Gonzalo Alduncin

    2009-01-01

    On the basis of composition duality principles, augmented three-field macro-hybrid mixed variational problems and finite element schemes are analyzed. The compati-bility condition adopted here, for compositional dualization, is the coupling operator surjec-tivity, property that expresses in a general operator sense the Ladysenskaja-Babuska-Brezzi inf-sup condition. Variational macro-hybridization is performed under the assumption of decomposable primal and dual spaces relative to nonoverlapping domain decompositions. Then, through compositional dualization macro-hybrid mixed problems are obtained, with internal boundary dual traces as Lagrange multipliers. Also, "mass" preconditioned aug-mentation of three-field formulations are derived, stabilizing macro-hybrid mixed finite element schemes and rendering possible speed up of rates of convergence. Dual mixed incompressible Darcy flow problems illustrate the theory throughout the paper.

  7. SIMULATION OF POLLUTANTS IN RIVER SYSTEMS USING FINITE DIFFERENCE METHOD

    Institute of Scientific and Technical Information of China (English)

    ZAHEER Iqbal; CUI Guang Bai

    2002-01-01

    This paper using finite difference scheme for the numerical solution of advection-dispersion equation develops a one-dimensional water quality model. The model algorithm has some modification over other steady state models including QUAL2E, which have been used steady state implementation of implicit backward-difference numerical scheme. The computer program in the developed model contains a special unsteady state implementation of four point implicit upwind numerical schemes using double sweep method. The superiority of this method in the modeling procedure results the simulation efficacy under simplified conditions of effluent discharge from point and non-point sources. The model is helpful for eye view assessment of degree of interaction between model variables for strategic planning purposes. The model has been applied for the water quality simulation of the Hanjiang River basin using flow computation model. Model simulation results have shown the pollutants prediction, dispersion and impact on the existing water quality.Model test shows the model validity comparing with other sophisticated models. Sensitivity analysis was performed to overview the most sensitive parameters followed by calibration and verification process.

  8. Space-time adaptive ADER discontinuous Galerkin finite element schemes with a posteriori sub-cell finite volume limiting

    CERN Document Server

    Zanotti, Olindo; Dumbser, Michael; Hidalgo, Arturo

    2015-01-01

    In this paper we present a novel arbitrary high order accurate discontinuous Galerkin (DG) finite element method on space-time adaptive Cartesian meshes (AMR) for hyperbolic conservation laws in multiple space dimensions, using a high order \\aposteriori sub-cell ADER-WENO finite volume \\emph{limiter}. Notoriously, the original DG method produces strong oscillations in the presence of discontinuous solutions and several types of limiters have been introduced over the years to cope with this problem. Following the innovative idea recently proposed in \\cite{Dumbser2014}, the discrete solution within the troubled cells is \\textit{recomputed} by scattering the DG polynomial at the previous time step onto a suitable number of sub-cells along each direction. Relying on the robustness of classical finite volume WENO schemes, the sub-cell averages are recomputed and then gathered back into the DG polynomials over the main grid. In this paper this approach is implemented for the first time within a space-time adaptive ...

  9. Superconvergence of a New Nonconforming Mixed Finite Element Scheme for Elliptic Problem

    Directory of Open Access Journals (Sweden)

    Lifang Pei

    2013-01-01

    Full Text Available A new nonconforming mixed finite element scheme for the second-order elliptic problem is proposed based on a new mixed variational form. It has the lowest degrees of freedom on rectangular meshes. The superclose property is proven by employing integral identity technique. Then global superconvergence result is derived through interpolation postprocessing operators. At last, some numerical experiments are carried out to verify the theoretical analysis.

  10. Numerical solution of nonlinear partial differential equations of mixed type. [finite difference approximation

    Science.gov (United States)

    Jameson, A.

    1976-01-01

    A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.

  11. A mixed finite element scheme for viscoelastic flows with XPP model

    Institute of Scientific and Technical Information of China (English)

    Xianhong Han; Xikui Li

    2008-01-01

    A mixed finite element formulation for viscoe-lastic flows is derived in this paper, in which the FIC (finite incremental calculus) pressure stabilization process and the DEVSS (discrete elastic viscous stress splitting) method using the Crank-Nicolson-based split are introduced within a general framework of the iterative version of the fractio-nal step algorithm. The SU (streamline-upwind) method is particularly chosen to tackle the convective terms in constitu-tive equations of viscoelastic flows. Thanks to the proposed scheme the finite elements with equal low-order interpola-tion approximations for stress-velocity-pressure variables can be successfully used even for viscoelastic flows with high Weissenberg numbers. The XPP (extended Pom-Pom) consti-tutive model for describing viscoelastic behaviors is particu-larly integrated into the proposed scheme. The numerical results for the 4:1 sudden contraction flow problem demons-trate prominent stability, accuracy and convergence rate of the proposed scheme in both pressure and stress distributions over the flow domain within a wide range of the Weissenberg number, particularly the capability in reproducing the results, which can be used to explain the "die swell" phenomenon observed in the polymer injection molding process.

  12. SH-wave propagation in the whole mantle using high-order finite differences

    OpenAIRE

    H. Igel; Michael Weber;  

    1995-01-01

    Finite-difference approximations to the wave equation in spherical coordinates are used to calculate synthetic seismograms for global Earth models. High-order finite-difference (FD) schemes were employed to obtain accurate waveforms and arrival times. Application to SH-wave propagation in the mantle shows that multiple reflections from the core-mantle boundary (CMB), with travel times of about one hour, can be modeled successfully. FD techniques, which are applicable in generally heterogeneou...

  13. FINITE DIFFERENCE APPROXIMATION FOR PRICING THE AMERICAN LOOKBACK OPTION

    Institute of Scientific and Technical Information of China (English)

    Tie Zhang; Shuhua Zhang; Danmei Zhu

    2009-01-01

    In this paper we are concerned with the pricing of lookback options with American type constrains. Based on the differential linear complementary formula associated with the pricing problem, an implicit difference scheme is constructed and analyzed. We show that there exists a unique difference solution which is unconditionally stable. Using the notion of viscosity solutions, we also prove that the finite difference solution converges uniformly to the viscosity solution of the continuous problem. Furthermore, by means of the variational inequality analysis method, the (O)(△t+△x2)-order error estimate is derived in the discrete L2-norm provided that the continuous problem is sufficiently regular. In addition, a numerical example is provided to illustrate the theoretical results.Mathematics subject classification: 65M12, 65M06, 91B28.

  14. THE UPWIND OPERATOR SPLITTING FINITE DIFFERENCE METHOD FOR COMPRESSIBLE TWO-PHASE DISPLACEMENT PROBLEM AND ANALYSIS

    Institute of Scientific and Technical Information of China (English)

    袁益让

    2002-01-01

    For compressible two-phase displacement problem, a kind of upwind operator splitting finite difference schemes is put forward and make use of operator splitting, of calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estinates in L2 norm are derived to determine the error in the approximate solution.

  15. A comparative study of finite element and finite difference methods for Cauchy-Riemann type equations

    Science.gov (United States)

    Fix, G. J.; Rose, M. E.

    1983-01-01

    A least squares formulation of the system divu = rho, curlu = zeta is surveyed from the viewpoint of both finite element and finite difference methods. Closely related arguments are shown to establish convergence estimates.

  16. ADER-WENO finite volume schemes with space-time adaptive mesh refinement

    Science.gov (United States)

    Dumbser, Michael; Zanotti, Olindo; Hidalgo, Arturo; Balsara, Dinshaw S.

    2013-09-01

    We present the first high order one-step ADER-WENO finite volume scheme with adaptive mesh refinement (AMR) in multiple space dimensions. High order spatial accuracy is obtained through a WENO reconstruction, while a high order one-step time discretization is achieved using a local space-time discontinuous Galerkin predictor method. Due to the one-step nature of the underlying scheme, the resulting algorithm is particularly well suited for an AMR strategy on space-time adaptive meshes, i.e. with time-accurate local time stepping. The AMR property has been implemented 'cell-by-cell', with a standard tree-type algorithm, while the scheme has been parallelized via the message passing interface (MPI) paradigm. The new scheme has been tested over a wide range of examples for nonlinear systems of hyperbolic conservation laws, including the classical Euler equations of compressible gas dynamics and the equations of magnetohydrodynamics (MHD). High order in space and time have been confirmed via a numerical convergence study and a detailed analysis of the computational speed-up with respect to highly refined uniform meshes is also presented. We also show test problems where the presented high order AMR scheme behaves clearly better than traditional second order AMR methods. The proposed scheme that combines for the first time high order ADER methods with space-time adaptive grids in two and three space dimensions is likely to become a useful tool in several fields of computational physics, applied mathematics and mechanics.

  17. Analysis of triangular C-grid finite volume scheme for shallow water flows

    Science.gov (United States)

    Shirkhani, Hamidreza; Mohammadian, Abdolmajid; Seidou, Ousmane; Qiblawey, Hazim

    2015-08-01

    In this paper, a dispersion relation analysis is employed to investigate the finite volume triangular C-grid formulation for two-dimensional shallow-water equations. In addition, two proposed combinations of time-stepping methods with the C-grid spatial discretization are investigated. In the first part of this study, the C-grid spatial discretization scheme is assessed, and in the second part, fully discrete schemes are analyzed. Analysis of the semi-discretized scheme (i.e. only spatial discretization) shows that there is no damping associated with the spatial C-grid scheme, and its phase speed behavior is also acceptable for long and intermediate waves. The analytical dispersion analysis after considering the effect of time discretization shows that the Leap-Frog time stepping technique can improve the phase speed behavior of the numerical method; however it could not damp the shorter decelerated waves. The Adams-Bashforth technique leads to slower propagation of short and intermediate waves and it damps those waves with a slower propagating speed. The numerical solutions of various test problems also conform and are in good agreement with the analytical dispersion analysis. They also indicate that the Adams-Bashforth scheme exhibits faster convergence and more accurate results, respectively, when the spatial and temporal step size decreases. However, the Leap-Frog scheme is more stable with higher CFL numbers.

  18. Finite difference numerical methods for boundary control problems governed by hyperbolic partial differential equations

    Science.gov (United States)

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

    1983-01-01

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

  19. Finite Difference Method for Reaction-Diffusion Equation with Nonlocal Boundary Conditions

    Institute of Scientific and Technical Information of China (English)

    Jianming Liu; Zhizhong Sun

    2007-01-01

    In this paper, we present a numerical approach to a class of nonlinear reactiondiffusion equations with nonlocal Robin type boundary conditions by finite difference methods. A second-order accurate difference scheme is derived by the method of reduction of order. Moreover, we prove that the scheme is uniquely solvable and convergent with the convergence rate of order two in a discrete L2-norm. A simple numerical example is given to illustrate the efficiency of the proposed method.

  20. Abstract Level Parallelization of Finite Difference Methods

    Directory of Open Access Journals (Sweden)

    Edwin Vollebregt

    1997-01-01

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

  1. Hybrid, explicit-implicit, finite-volume schemes on unstructured grids for unsteady compressible flows

    Science.gov (United States)

    Timofeev, Evgeny; Norouzi, Farhang

    2016-06-01

    The motivation for using hybrid, explicit-implicit, schemes rather than fully implicit or explicit methods for some unsteady high-speed compressible flows with shocks is firstly discussed. A number of such schemes proposed in the past are briefly overviewed. A recently proposed hybridization approach is then introduced and used for the development of a hybrid, explicit-implicit, TVD (Total Variation Diminishing) scheme of the second order in space and time on smooth solutions in both, explicit and implicit, modes for the linear advection equation. Further generalizations of this finite-volume method for the Burgers, Euler and Navier-Stokes equations discretized on unstructured grids are mentioned in the concluding remarks.

  2. A parallel finite element scheme for thermo-hydro-mechanical (THM) coupled problems in porous media

    Science.gov (United States)

    Wang, Wenqing; Kosakowski, Georg; Kolditz, Olaf

    2009-08-01

    Many applied problems in geoscience require knowledge about complex interactions between multiple physical and chemical processes in the sub-surface. As a direct experimental investigation is often not possible, numerical simulation is a common approach. The numerical analysis of coupled thermo-hydro-mechanical (THM) problems is computationally very expensive, and therefore the applicability of existing codes is still limited to simplified problems. In this paper we present a novel implementation of a parallel finite element method (FEM) for the numerical analysis of coupled THM problems in porous media. The computational task of the FEM is partitioned into sub-tasks by a priori domain decomposition. The sub-tasks are assigned to the CPU nodes concurrently. Parallelization is achieved by simultaneously establishing the sub-domain mesh topology, synchronously assembling linear equation systems in sub-domains and obtaining the overall solution with a sub-domain linear solver (parallel BiCGStab method with Jacobi pre-conditioner). The present parallelization method is implemented in an object-oriented way using MPI for inter-processor communication. The parallel code was successfully tested with a 2-D example from the international DECOVALEX benchmarking project. The achieved speed-up for a 3-D extension of the test example on different computers demonstrates the advantage of the present parallel scheme.

  3. Finite difference method for the reverse parabolic problem with Neumann condition

    Science.gov (United States)

    Ashyralyyev, Charyyar; Dural, Ayfer; Sozen, Yasar

    2012-08-01

    A finite difference method for the approximate solution of the reverse multidimensional parabolic differential equation with a multipoint boundary condition and Neumann condition is applied. Stability, almost coercive stability, and coercive stability estimates for the solution of the first and second orders of accuracy difference schemes are obtained. The theoretical statements are supported by the numerical example.

  4. Pencil: Finite-difference Code for Compressible Hydrodynamic Flows

    Science.gov (United States)

    Brandenburg, Axel; Dobler, Wolfgang

    2010-10-01

    The Pencil code is a high-order finite-difference code for compressible hydrodynamic flows with magnetic fields. It is highly modular and can easily be adapted to different types of problems. The code runs efficiently under MPI on massively parallel shared- or distributed-memory computers, like e.g. large Beowulf clusters. The Pencil code is primarily designed to deal with weakly compressible turbulent flows. To achieve good parallelization, explicit (as opposed to compact) finite differences are used. Typical scientific targets include driven MHD turbulence in a periodic box, convection in a slab with non-periodic upper and lower boundaries, a convective star embedded in a fully nonperiodic box, accretion disc turbulence in the shearing sheet approximation, self-gravity, non-local radiation transfer, dust particle evolution with feedback on the gas, etc. A range of artificial viscosity and diffusion schemes can be invoked to deal with supersonic flows. For direct simulations regular viscosity and diffusion is being used. The code is written in well-commented Fortran90.

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

    KAUST Repository

    Chu, Chunlei

    2012-05-01

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

  6. Hidden sl$_{2}$-algebra of finite-difference equations

    CERN Document Server

    Smirnov, Yu F; Smirnov, Yuri; Turbiner, Alexander

    1995-01-01

    The connection between polynomial solutions of finite-difference equations and finite-dimensional representations of the sl_2-algebra is established. (Talk presented at the Wigner Symposium, Guadalajara, Mexico, August 1995; to be published in Proceedings)

  7. Cell-Centred Finite Difference Methodology for Solving Partial Differential Equations on an Unstructured Mesh

    Science.gov (United States)

    Situ, J. J.; Barron, R. M.; Higgins, M.

    2011-11-01

    Partial differential equations (PDEs) arise in connection with many physical phenomena involving two or more independent variables. Boundary conditions associated with the PDEs are either Dirichlet, Neumann or mixed conditions. Analytical solutions for most of these problems are not easy to obtain, and may not even be posssible. For such reasons, numerical methodologies for solving PDEs have been developed, such as finite element (FE), finite volume (FV) and finite difference (FD) methods. In the present paper, an innovative finite difference formulation, referred to as the cell-centred finite difference (CCFD) method, is proposed. Instead of applying finite difference approximations at the grid points as in the traditional finite difference method, the new methodology implements a finite difference scheme at each cell centroid in a predefined mesh topology. The prominent advantage of the proposed methodology is that it allows finite differencing to be applied on any arbitrary mesh topology, i.e. structured, unstructured or hybrid. The CCFD formulation is developed in this paper and implemented on a test problem to demonstrate its capabilities.

  8. Finite difference computation of Casimir forces

    Science.gov (United States)

    Pinto, Fabrizio

    2016-09-01

    In this Invited paper, we begin by a historical introduction to provide a motivation for the classical problems of interatomic force computation and associated challenges. This analysis will lead us from early theoretical and experimental accomplishments to the integration of these fascinating interactions into the operation of realistic, next-generation micro- and nanodevices both for the advanced metrology of fundamental physical processes and in breakthrough industrial applications. Among several powerful strategies enabling vastly enhanced performance and entirely novel technological capabilities, we shall specifically consider Casimir force time-modulation and the adoption of non-trivial geometries. As to the former, the ability to alter the magnitude and sign of the Casimir force will be recognized as a crucial principle to implement thermodynamical nano-engines. As to the latter, we shall first briefly review various reported computational approaches. We shall then discuss the game-changing discovery, in the last decade, that standard methods of numerical classical electromagnetism can be retooled to formulate the problem of Casimir force computation in arbitrary geometries. This remarkable development will be practically illustrated by showing that such an apparently elementary method as standard finite-differencing can be successfully employed to numerically recover results known from the Lifshitz theory of dispersion forces in the case of interacting parallel-plane slabs. Other geometries will be also be explored and consideration given to the potential of non-standard finite-difference methods. Finally, we shall introduce problems at the computational frontier, such as those including membranes deformed by Casimir forces and the effects of anisotropic materials. Conclusions will highlight the dramatic transition from the enduring perception of this field as an exotic application of quantum electrodynamics to the recent demonstration of a human climbing

  9. An FCT finite element scheme for ideal MHD equations in 1D and 2D

    Science.gov (United States)

    Basting, Melanie; Kuzmin, Dmitri

    2017-06-01

    This paper presents an implicit finite element (FE) scheme for solving the equations of ideal magnetohydrodynamics in 1D and 2D. The continuous Galerkin approximation is constrained using a flux-corrected transport (FCT) algorithm. The underlying low-order scheme is constructed using a Rusanov-type artificial viscosity operator based on scalar dissipation proportional to the fast wave speed. The accuracy of the low-order solution can be improved using a shock detector which makes it possible to prelimit the added viscosity in a monotonicity-preserving iterative manner. At the FCT correction step, the changes of conserved quantities are limited in a way which guarantees positivity preservation for the density and thermal pressure. Divergence-free magnetic fields are extracted using projections of the FCT predictor into staggered finite element spaces forming exact sequences. In the 2D case, the magnetic field is projected into the space of Raviart-Thomas finite elements. Numerical studies for standard test problems are performed to verify the ability of the proposed algorithms to enforce relevant constraints in applications to ideal MHD flows.

  10. Viscoelastic Finite Difference Modeling Using Graphics Processing Units

    Science.gov (United States)

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

    2014-12-01

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

  11. Accurate finite difference methods for time-harmonic wave propagation

    Science.gov (United States)

    Harari, Isaac; Turkel, Eli

    1994-01-01

    Finite difference methods for solving problems of time-harmonic acoustics are developed and analyzed. Multidimensional inhomogeneous problems with variable, possibly discontinuous, coefficients are considered, accounting for the effects of employing nonuniform grids. A weighted-average representation is less sensitive to transition in wave resolution (due to variable wave numbers or nonuniform grids) than the standard pointwise representation. Further enhancement in method performance is obtained by basing the stencils on generalizations of Pade approximation, or generalized definitions of the derivative, reducing spurious dispersion, anisotropy and reflection, and by improving the representation of source terms. The resulting schemes have fourth-order accurate local truncation error on uniform grids and third order in the nonuniform case. Guidelines for discretization pertaining to grid orientation and resolution are presented.

  12. Digital Waveguides versus Finite Difference Structures: Equivalence and Mixed Modeling

    Directory of Open Access Journals (Sweden)

    Karjalainen Matti

    2004-01-01

    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.

  13. Stability of pseudospectral and finite-difference methods for variable coefficient problems

    Science.gov (United States)

    Gottlieb, D.; Orszag, S. A.; Turkel, E.

    1981-01-01

    It is shown that pseudospectral approximation to a special class of variable coefficient one-dimensional wave equations is stable and convergent even though the wave speed changes sign within the domain. Computer experiments indicate similar results are valid for more general problems. Similarly, computer results indicate that the leapfrog finite-difference scheme is stable even though the wave speed changes sign within the domain. However, both schemes can be asymptotically unstable in time when a fixed spatial mesh is used.

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

    Science.gov (United States)

    Boscheri, Walter; Dumbser, Michael

    2017-10-01

    We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may also include parabolic terms in order to model dissipative transport processes, like molecular viscosity or heat conduction. High order piecewise polynomials of degree N are adopted to represent the discrete solution at each time level and within each spatial control volume of the computational grid, while high order of accuracy in time is achieved by the ADER approach, making use of an element-local space-time Galerkin finite element predictor. A novel nodal solver algorithm based on the HLL flux is derived to compute the velocity for each nodal degree of freedom that describes the current mesh geometry. In our algorithm the spatial mesh configuration can be defined in two different ways: either by an isoparametric approach that generates curved control volumes, or by a piecewise linear decomposition of each spatial control volume into simplex sub-elements. Each technique generates a corresponding number of geometrical degrees of freedom needed to describe the current mesh configuration and which must be considered by the nodal solver for determining the grid velocity. The connection of the old mesh configuration at time tn with the new one at time t n + 1 provides the space-time control volumes on which the governing equations have to be integrated in order to obtain the time evolution of the discrete solution. Our numerical method belongs to the category of so-called direct Arbitrary-Lagrangian-Eulerian (ALE) schemes, where a space-time conservation formulation of the governing PDE system is considered and which already takes into account the new grid geometry (including a possible rezoning step) directly during the computation of the numerical fluxes. We emphasize that our method is a moving mesh method, as opposed to total

  15. DEVELOPMENT AND APPLICATIONS OF WENO SCHEMES IN CONTINUUM PHYSICS

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    This paper briefly presents the general ideas of high order accurate weighted essentially non-oscillatory (WENO) schemes, and describes the similarities and differences of the two classes of WENO schemes: finite volume schemes and finite difference schemes. We also briefly mention a recent development of WENO schemes,namely an adaptive approach within the finite difference framework using smooth time dependent curvilinear coordinates.``

  16. ON FINITE DIFFERENCES ON A STRING PROBLEM

    Directory of Open Access Journals (Sweden)

    J. M. Mango

    2014-01-01

    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.

  17. Secure diversity-multiplexing tradeoff of zero-forcing transmit scheme at finite-SNR

    KAUST Repository

    Rezki, Zouheir

    2012-04-01

    In this paper, we address the finite Signal-to-Noise Ratio (SNR) Diversity-Multiplexing Tradeoff (DMT) of the Multiple Input Multiple Output (MIMO) wiretap channel, where a Zero-Forcing (ZF) transmit scheme, that intends to send the secret information in the orthogonal space of the eavesdropper channel, is used. First, we introduce the secrecy multiplexing gain at finite-SNR that generalizes the definition at high-SNR. Then, we provide upper and lower bounds on the outage probability under secrecy constraint, from which secrecy diversity gain estimates of ZF are derived. Through asymptotic analysis, we show that the upper bound underestimates the secrecy diversity gain, whereas the lower bound is tight at high-SNR, and thus its related diversity gain estimate is equal to the actual asymptotic secrecy diversity gain of the MIMO wiretap channel. © 2012 IEEE.

  18. Secure Diversity-Multiplexing Tradeoff of Zero-Forcing Transmit Scheme at Finite-SNR

    CERN Document Server

    Rezki, Zouheir

    2011-01-01

    In this paper, we address the finite Signal-to-Noise Ratio (SNR) Diversity-Multiplexing Tradeoff (DMT) of the Multiple Input Multiple Output (MIMO) wiretap channel, where a Zero-Forcing (ZF) transmit scheme, that intends to send the secret information in the orthogonal space of the eavesdropper channel, is used. First, we introduce the secrecy multiplexing gain at finite-SNR that generalizes the definition at high-SNR. Then, we provide upper and lower bounds on the outage probability under secrecy constraint, from which secrecy diversity gain estimates of ZF are derived. Through asymptotic analysis, we show that the upper bound underestimates the secrecy diversity gain, whereas the lower bound is tight at high-SNR, and thus its related diversity gain estimate is equal to the actual asymptotic secrecy diversity gain of the MIMO wiretap channel.

  19. FINITE DIFFERENCE FRACTIONAL STEP METHODS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE

    Institute of Scientific and Technical Information of China (English)

    Yuan Yirang

    2005-01-01

    Characteristic finite difference fractional step schemes are put forward. The electric Potential equation is described by a seven-point finite difference scheme, and the electron and hole concentration equations are treated by a kind of characteristic finite difference fractional step methods. The temperature equation is described by a fractional step method. Thick and thin grids are made use of to form a complete set. Piecewise threefold quadratic interpolation, symmetrical extension, calculus of variations, commutativity of operator product, decomposition of high order difference operators and prior estimates are also made use of. Optimal order estimates in l2 norm are derived to determine the error of the approximate solution. The well-known problem is thorongley and completely solred.

  20. A NEW NONCONFORMING MIXED FINITE ELEMENT SCHEME FOR THE STATIONARY NAVIER-STOKES EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    Shi Dongyang; Ren Jincheng; Gong Wei

    2011-01-01

    In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary Navier-Stokes equations, in which a new low order Crouzeix- Raviart type nonconforming rectangular element is taken for approximating space for the velocity and the piecewise constant element for the pressure. The optimal order error estimates for the approximation of both the velocity and the pressure in L2-norm are established, as well as one in broken H1-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis.

  1. A least squares finite element scheme for transonic flow around harmonically oscillating airfoils

    Science.gov (United States)

    Cox, C. L.; Fix, G. J.; Gunzburger, M. D.

    1983-01-01

    The present investigation shows that a finite element scheme with a weighted least squares variational principle is applicable to the problem of transonic flow around a harmonically oscillating airfoil. For the flat plate case, numerical results compare favorably with the exact solution. The obtained numerical results for the transonic problem, for which an exact solution is not known, have the characteristics of known experimental results. It is demonstrated that the performance of the employed numerical method is independent of equation type (elliptic or hyperbolic) and frequency. The weighted least squares principle allows the appropriate modeling of singularities, which such a modeling of singularities is not possible with normal least squares.

  2. Effective condition number for finite difference method

    Science.gov (United States)

    Li, Zi-Cai; Chien, Cheng-Sheng; Huang, Hung-Tsai

    2007-01-01

    For solving the linear algebraic equations Ax=b with the symmetric and positive definite matrix A, from elliptic equations, the traditional condition number in the 2-norm is defined by Cond.=[lambda]1/[lambda]n, where [lambda]1 and [lambda]n are the maximal and minimal eigenvalues of the matrix A, respectively. The condition number is used to provide the bounds of the relative errors from the perturbation of both A and b. Such a Cond. can only be reached by the worst situation of all rounding errors and all b. For the given b, the true relative errors may be smaller, or even much smaller than the Cond., which is called the effective condition number in Chan and Foulser [Effectively well-conditioned linear systems, SIAM J. Sci. Statist. Comput. 9 (1988) 963-969] and Christiansen and Hansen [The effective condition number applied to error analysis of certain boundary collocation methods, J. Comput. Appl. Math. 54(1) (1994) 15-36]. In this paper, we propose the new computational formulas for effective condition number Cond_eff, and define the new simplified effective condition number Cond_E. For the latter, we only need the eigenvector corresponding to the minimal eigenvalue of A, which can be easily obtained by the inverse power method. In this paper, we also apply the effective condition number for the finite difference method for Poisson's equation. The difference grids are not supposed to be quasiuniform. Under a non-orthogonality assumption, the effective condition number is proven to be O(1) for the homogeneous boundary conditions. Such a result is extraordinary, compared with the traditional , where hmin is the minimal meshspacing of the difference grids used. For the non-homogeneous Neumann and Dirichlet boundary conditions, the effective condition number is proven to be O(h-1/2) and , respectively, where h is the maximal meshspacing of the difference grids. Numerical experiments are carried out to verify the analysis made.

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

    KAUST Repository

    El-Amin, Mohamed

    2013-06-01

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

  4. Direct numerical simulation of scalar transport using unstructured finite-volume schemes

    Science.gov (United States)

    Rossi, Riccardo

    2009-03-01

    An unstructured finite-volume method for direct and large-eddy simulations of scalar transport in complex geometries is presented and investigated. The numerical technique is based on a three-level fully implicit time advancement scheme and central spatial interpolation operators. The scalar variable at cell faces is obtained by a symmetric central interpolation scheme, which is formally first-order accurate, or by further employing a high-order correction term which leads to formal second-order accuracy irrespective of the underlying grid. In this framework, deferred-correction and slope-limiter techniques are introduced in order to avoid numerical instabilities in the resulting algebraic transport equation. The accuracy and robustness of the code are initially evaluated by means of basic numerical experiments where the flow field is assigned a priori. A direct numerical simulation of turbulent scalar transport in a channel flow is finally performed to validate the numerical technique against a numerical dataset established by a spectral method. In spite of the linear character of the scalar transport equation, the computed statistics and spectra of the scalar field are found to be significantly affected by the spectral-properties of interpolation schemes. Although the results show an improved spectral-resolution and greater spatial-accuracy for the high-order operator in the analysis of basic scalar transport problems, the low-order central scheme is found superior for high-fidelity simulations of turbulent scalar transport.

  5. ADER-WENO Finite Volume Schemes with Space-Time Adaptive Mesh Refinement

    CERN Document Server

    Dumbser, Michael; Hidalgo, Arturo; Balsara, Dinshaw S

    2012-01-01

    We present the first high order one-step ADER-WENO finite volume scheme with Adaptive Mesh Refinement (AMR) in multiple space dimensions. High order spatial accuracy is obtained through a WENO reconstruction, while a high order one-step time discretization is achieved using a local space-time discontinuous Galerkin predictor method. Due to the one-step nature of the underlying scheme, the resulting algorithm is particularly well suited for an AMR strategy on space-time adaptive meshes, i.e.with time-accurate local time stepping. The AMR property has been implemented 'cell-by-cell', with a standard tree-type algorithm, while the scheme has been parallelized via the Message Passing Interface (MPI) paradigm. The new scheme has been tested over a wide range of examples for nonlinear systems of hyperbolic conservation laws, including the classical Euler equations of compressible gas dynamics and the equations of magnetohydrodynamics (MHD). High order in space and time have been confirmed via a numerical convergenc...

  6. Additive Difference Schemes for Filtration Problems in Multilayer Systems

    CERN Document Server

    Ayrjan, E A; Pavlush, M; Fedorov, A V

    2000-01-01

    In the present paper difference schemes for solution of the plane filtration problem in multilayer systems are analyzed within the framework of difference schemes general theory. Attention is paid to splitting the schemes on physical processes of filtration along water-carring layers and vertical motion between layers. Some absolutely stable additive difference schemes are obtained the realization of which needs no software modification. Parallel algorithm connected with the solving of the filtration problem in every water-carring layer on a single processor is constructed. Program realization on the multi-processor system SPP2000 at JINR is discussed.

  7. High Order Finite Difference Methods, Multidimensional Linear Problems and Curvilinear Coordinates

    Science.gov (United States)

    Nordstrom, Jan; Carpenter, Mark H.

    1999-01-01

    Boundary and interface conditions are derived for high order finite difference methods applied to multidimensional linear problems in curvilinear coordinates. The boundary and interface conditions lead to conservative schemes and strict and strong stability provided that certain metric conditions are met.

  8. On the accuracy of the finite difference method for applications in beam propagating techniques

    NARCIS (Netherlands)

    Hoekstra, Hugo; Krijnen, Gijsbertus J.M.; Lambeck, Paul

    1992-01-01

    In this paper it is shown that the inaccuracy in the beam propagation method based on the finite difference scheme, introduced by the use of the slowly varying envelope approximation, can be overcome in an effective way. By the introduction of a perturbation expansion the accuracy can be improved as

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

    DEFF Research Database (Denmark)

    Dridi, Kim; Hesthaven, J.S.; Ditkowski, A.

    2001-01-01

    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...

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

    Energy Technology Data Exchange (ETDEWEB)

    Hoang, Hai Minh

    2005-07-01

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

  11. An Improved Finite Difference Type Numerical Method for Structural Dynamic Analysis

    Directory of Open Access Journals (Sweden)

    Sung-Hoon Kim

    1994-01-01

    Full Text Available An improved finite difference type numerical method to solve partial differential equations for one-dimensional (1-D structure is proposed. This numerical scheme is a kind of a single-step, second-order accurate and implicit method. The stability, consistency, and convergence are examined analytically with a second-order hyperbolic partial differential equation. Since the proposed numerical scheme automatically satisfies the natural boundary conditions and at the same time, all the partial differential terms at boundary points are directly interpretable to their physical meanings, the proposed numerical scheme has merits in computing 1-D structural dynamic motion over the existing finite difference numeric methods. Using a numerical example, the suggested method was proven to be more accurate and effective than the well-known central difference method. The only limitation of this method is that it is applicable to only 1-D structure.

  12. Memory cost of absorbing conditions for the finite-difference time-domain method.

    Science.gov (United States)

    Chobeau, Pierre; Savioja, Lauri

    2016-07-01

    Three absorbing layers are investigated using standard rectilinear finite-difference schemes. The perfectly matched layer (PML) is compared with basic lossy layers terminated by two types of absorbing boundary conditions, all simulated using equivalent memory consumption. Lossy layers present the advantage of being scalar schemes, whereas the PML relies on a staggered scheme where both velocity and pressure are split. Although the PML gives the lowest reflection magnitudes over all frequencies and incidence angles, the most efficient lossy layer gives reflection magnitudes of the same order as the PML from mid- to high-frequency and for restricted incidence angles.

  13. High order finite difference and multigrid methods for spatially evolving instability in a planar channel

    Science.gov (United States)

    Liu, C.; Liu, Z.

    1993-01-01

    The fourth-order finite-difference scheme with fully implicit time-marching presently used to computationally study the spatial instability of planar Poiseuille flow incorporates a novel treatment for outflow boundary conditions that renders the buffer area as short as one wavelength. A semicoarsening multigrid method accelerates convergence for the implicit scheme at each time step; a line-distributive relaxation is developed as a robust fast solver that is efficient for anisotropic grids. Computational cost is no greater than that of explicit schemes, and excellent agreement with linear theory is obtained.

  14. A quasi-positive family of continuous Darcy-flux finite-volume schemes with full pressure support

    Science.gov (United States)

    Edwards, Michael G.; Zheng, Hongwen

    2008-11-01

    A new family of flux-continuous, locally conservative, finite-volume schemes is presented for solving the general tensor pressure equation of subsurface flow in porous media. The new schemes have full pressure continuity imposed across control-volume faces. Previous families of flux-continuous schemes are point-wise continuous in pressure and flux. When applying the earlier point-wise flux-continuous schemes to strongly anisotropic full-tensor fields their failure to satisfy a maximum principle (as with other FEM and finite-volume methods) can result in loss of local stability for high anisotropy ratios which can cause strong spurious oscillations in the numerical pressure solution. An M-matrix analysis reveals the upper limits for guaranteeing a maximum principle for general 9-point schemes and aids in the design of schemes that minimize the occurrence of spurious oscillations in the discrete pressure field. The full pressure continuity schemes are shown to possess a larger range of flux-continuous schemes, than the previous point-wise counter parts. For strongly anisotropic full-tensor cases it is shown that the full quadrature range possessed by the new schemes permits these schemes to exploit quadrature points (previously out of range) that are shown to minimize spurious oscillations in discrete pressure solutions. The new formulation leads to a more robust quasi-positive family of flux-continuous schemes applicable to general discontinuous full-tensor fields.

  15. Asymptotic preserving IMEX finite volume schemes for low Mach number Euler equations with gravitation

    Science.gov (United States)

    Bispen, Georgij; Lukáčová-Medvid'ová, Mária; Yelash, Leonid

    2017-04-01

    In this paper we will present and analyze a new class of the IMEX finite volume schemes for the Euler equations with a gravity source term. We will in particular concentrate on a singular limit of weakly compressible flows when the Mach number M ≪ 1. In order to efficiently resolve slow dynamics we split the whole nonlinear system in a stiff linear part governing the acoustic and gravity waves and a non-stiff nonlinear part that models nonlinear advection effects. For time discretization we use a special class of the so-called globally stiffly accurate IMEX schemes and approximate the stiff linear operator implicitly and the non-stiff nonlinear operator explicitly. For spatial discretization the finite volume approximation is used with the central and Rusanov/Lax-Friedrichs numerical fluxes for the linear and nonlinear subsystem, respectively. In the case of a constant background potential temperature we prove theoretically that the method is asymptotically consistent and asymptotically stable uniformly with respect to small Mach number. We also analyze experimentally convergence rates in the singular limit when the Mach number tends to zero.

  16. FINITE DIFFERENCE APPROXIMATE SOLUTIONS FOR THE RLW EQUATION%非线性RLW方程的有限差分逼近

    Institute of Scientific and Technical Information of China (English)

    冯民富; 潘璐; 王殿志

    2003-01-01

    A finite difference scheme is proposed to solve the regularized long wave(RLW)equation for computational simplicity compared to finite element methods. Exis-tence and uniqueness of numerical solutions are shown. A priori bound and the error estimates as well as conservation of energy of the finite difference approximate solutions are discussed with theory and numerical examples.

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

    KAUST Repository

    Chu, Chunlei

    2009-01-01

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

  18. On a difference scheme for nonlocal heat transfer boundary-value problem

    Science.gov (United States)

    Akhymbek, Meiram E.; Sadybekov, Makhmud A.

    2016-08-01

    In this paper, we propose a new method of solving nonlocal problems for the heat equation with finite difference method. The main important feature of these problems is their non-self-adjointness. This non-self-adjointness causes major difficulties in their analytical and numerical solving. The problems, which boundary conditions do not possess strong regularity, are less studied. The scope of study of the paper justifies possibility of building a stable difference scheme with weights for abovementioned type of problems.

  19. Second order finite volume scheme for Maxwell's equations with discontinuous electromagnetic properties on unstructured meshes

    Energy Technology Data Exchange (ETDEWEB)

    Ismagilov, Timur Z., E-mail: ismagilov@academ.org

    2015-02-01

    This paper presents a second order finite volume scheme for numerical solution of Maxwell's equations with discontinuous dielectric permittivity and magnetic permeability on unstructured meshes. The scheme is based on Godunov scheme and employs approaches of Van Leer and Lax–Wendroff to increase the order of approximation. To keep the second order of approximation near dielectric permittivity and magnetic permeability discontinuities a novel technique for gradient calculation and limitation is applied near discontinuities. Results of test computations for problems with linear and curvilinear discontinuities confirm second order of approximation. The scheme was applied to modelling propagation of electromagnetic waves inside photonic crystal waveguides with a bend.

  20. Wave Propagation and Stability for Finite Difference Schemes.

    Science.gov (United States)

    1982-05-01

    niod(el possesses anrtahle resonant modes, hout they are generate a rightwardilu ioof enrgi rieo rrrb ite-, -tern easoirt i.e f2 stable. i,t ,ig iuiid...trte’ refteotoit d tr td r-ronotted enrgy . t..1,. .’p .A I fr > r-g t 01- s t si Irnoo.dary foro ta -trW n~fl(6.2.3t I T ine tsPF 1, a’es I eoi it is t

  1. NUMERICAL SIMULATIONS OF SEA ICE WITH DIFFERENT ADVECTION SCHEMES

    Institute of Scientific and Technical Information of China (English)

    LIU Xi-ying

    2011-01-01

    Numerical simulations are carried out for sea ice with four different advection schemes to study their effects on the simulation results.The sea ice model employed here is the Sea Ice Simulator (SIS) of the Geophysical Fluid Dynamics Laboratory (GFDL) Modular Ocean Model version 4b (MOM4b) and the four advection schemes are, the upwind scheme originally used in the SIS, the Multi-Dimensional Positive Advection (MDPA) scheme, the Incremental Remapping Scheme (IRS) and the Two Step Shape Preserving (TSSP) scheme.The latter three schemes are newly introduced.To consider the interactions between sea ice and ocean, a mixed layer ocean model is introduced and coupled to the SIS.The coupled model uses a tri-polar coordinate with 120×65 grids,covering the whole earth globe, in the horizontal plane.Simulation results in the northern high latitudes are analyzed.In all simulations, the model reproduces the seasonal variation of sea ice in the northern high latitudes well.Compared with the results from the observation, the sea ice model produces some extra sea ice coverage in the Greenland Sea and Barents Sea in winter due to the exclusion of ocean current effects and the smaller simulated sea ice thickness in the Arctic basin.There are similar features among the results obtained with the introduced three advection schemes.The simulated sea ice thickness with the three newly introduced schemes are all smaller than that of the upwind scheme and the simulated sea ice velocities of movement are all smaller than that of the upwind scheme.There are more similarities shared in the results obtained with the MPDA and TSSP schemes.

  2. Asymptotic Behavior of the Finite Difference and the Finite Element Methods for Parabolic Equations

    Institute of Scientific and Technical Information of China (English)

    LIU Yang; FENG Hui

    2005-01-01

    The asymptotic convergence of the solution of the parabolic equation is proved. By the eigenvalues estimation, we obtain that the approximate solutions by the finite difference method and the finite element method are asymptotically convergent. Both methods are considered in continuous time.

  3. Compact difference scheme for the fractional sub-diffusion equation with Neumann boundary conditions

    Science.gov (United States)

    Ren, Jincheng; Sun, Zhi-zhong; Zhao, Xuan

    2013-01-01

    An effective finite difference scheme is considered for solving the time fractional sub-diffusion equation with Neumann boundary conditions. A difference scheme combining the compact difference approach the spatial discretization and L1 approximation for the Caputo fractional derivative is proposed and analyzed. Although the spatial approximation order at the Neumann boundary is one order lower than that for interior mesh points, the unconditional stability and the global convergence order O(τ+h4) in discrete L2 norm of the compact difference scheme are proved rigorously, where τ is the temporal grid size and h is the spatial grid size. Numerical experiments are included to support the theoretical results, and comparison with the related works are presented to show the effectiveness of our method.

  4. The characteristic finite difference fractional steps methods for compressible two-phase displacement problem

    Institute of Scientific and Technical Information of China (English)

    袁益让

    1999-01-01

    For compressible two-phase displacement problem, a kind of characteristic finite difference fractional steps schemes is put forward and thick and thin grids are used to form a complete set. Some techniques, such as piecewise biquadratic interpolation, of calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L~2 norm are derived to determine the error in the approximate solution.

  5. Adaptive boundaryless finite-difference method.

    Science.gov (United States)

    Lopez-Mago, Dorilian; Gutiérrez-Vega, Julio C

    2013-02-01

    The boundaryless beam propagation method uses a mapping function to transform the infinite real space into a finite-size computational domain [Opt. Lett.21, 4 (1996)]. This leads to a bounded field that avoids the artificial reflections produced by the computational window. However, the method suffers from frequency aliasing problems, limiting the physical region to be sampled. We propose an adaptive boundaryless method that concentrates the higher density of sampling points in the region of interest. The method is implemented in Cartesian and cylindrical coordinate systems. It keeps the same advantages of the original method but increases accuracy and is not affected by frequency aliasing.

  6. Malware Detection with Different Voting Schemes

    Directory of Open Access Journals (Sweden)

    Ms. Jyoti Landage

    2014-01-01

    Full Text Available A common way of launching the attack in computer system is Malware. It has malicious intent of performing any kind of malicious action to computer system as a result entire system crashes. It comes in different forms like virus, Trojan , Spyware, Scareware, Adware etc. Traditional malware detection techniques viz. signature-based, Heuristic-based and Specification-based detection technique are unable to detect some form of malware and each technique has its own advantages and disadvantages. A new methodology is proposed for malware detection that is based on data mining and machine learning techniques to detect known as well as unknown instances of malware. The new methodology uses disassemble process and three pre -processing techniques as part of feature extraction process to produce three different data sets with different configurations; feature selection technique is used to achieve consistent, reduced feature dataset. Three classification algorithms are used to gener ate and train the classifiers named as Ripper, C4.5 and IBk. The ensemble learning algorithm voting is used to improve the accuracy of result. Here majority voting and veto voting is used, the predicted output is decided on the basis of majority vo ting and veto voting. In veto voting the decision strategy of veto is improved by introducing the trust-based veto voting that definitely helps to improve the detection accuracy.

  7. Malware Detection with Different Voting Schemes

    Directory of Open Access Journals (Sweden)

    Jyoti Landage

    2015-10-01

    Full Text Available A common way of launching the attack in computer system is Malware. It has malicious intent of performing any kind of malicious action to computer system as a result entire system crashes. It comes in different forms like virus, Trojan , Spyware, Scareware, Adware etc. Traditional malware detection techniques viz. signature-based, Heuristic-based and Specification-based detection technique are unable to detect some form of malware and each technique has its own advantages and disadvantages. A new methodology is proposed for malware detection that is based on data mining and machine learning techniques to detect known as well as unknown instances of malware. The new methodology uses disassemble process and three pre -processing techniques as part of feature ext raction process to produce three different data sets with different configurations; feature selection technique is used to achieve consistent, reduced feature dataset. Three classification algorithms are used to gener ate and train the classifiers named as Ripper, C4.5 and IBk. The ensemble learning algorithm voting is used to improve the accuracy of result. Here majority voting and veto voting is used, the predicted output is decided on the basis of majority vo ting and veto voting. In veto voting the decision strategy of veto is improved by introducing the trust -based veto voting that definitely helps to improve the detection accuracy.

  8. Test of two methods for faulting on finite-difference calculations

    Science.gov (United States)

    Andrews, D.J.

    1999-01-01

    Tests of two fault boundary conditions show that each converges with second order accuracy as the finite-difference grid is refined. The first method uses split nodes so that there are disjoint grids that interact via surface traction. The 3D version described here is a generalization of a method I have used extensively in 2D; it is as accurate as the 2D version. The second method represents fault slip as inelastic strain in a fault zone. Offset of stress from its elastic value is seismic moment density. Implementation of this method is quite simple in a finite-difference scheme using velocity and stress as dependent variables.

  9. Adaptive finite-volume WENO schemes on dynamically redistributed grids for compressible Euler equations

    Science.gov (United States)

    Pathak, Harshavardhana S.; Shukla, Ratnesh K.

    2016-08-01

    A high-order adaptive finite-volume method is presented for simulating inviscid compressible flows on time-dependent redistributed grids. The method achieves dynamic adaptation through a combination of time-dependent mesh node clustering in regions characterized by strong solution gradients and an optimal selection of the order of accuracy and the associated reconstruction stencil in a conservative finite-volume framework. This combined approach maximizes spatial resolution in discontinuous regions that require low-order approximations for oscillation-free shock capturing. Over smooth regions, high-order discretization through finite-volume WENO schemes minimizes numerical dissipation and provides excellent resolution of intricate flow features. The method including the moving mesh equations and the compressible flow solver is formulated entirely on a transformed time-independent computational domain discretized using a simple uniform Cartesian mesh. Approximations for the metric terms that enforce discrete geometric conservation law while preserving the fourth-order accuracy of the two-point Gaussian quadrature rule are developed. Spurious Cartesian grid induced shock instabilities such as carbuncles that feature in a local one-dimensional contact capturing treatment along the cell face normals are effectively eliminated through upwind flux calculation using a rotated Hartex-Lax-van Leer contact resolving (HLLC) approximate Riemann solver for the Euler equations in generalized coordinates. Numerical experiments with the fifth and ninth-order WENO reconstructions at the two-point Gaussian quadrature nodes, over a range of challenging test cases, indicate that the redistributed mesh effectively adapts to the dynamic flow gradients thereby improving the solution accuracy substantially even when the initial starting mesh is non-adaptive. The high adaptivity combined with the fifth and especially the ninth-order WENO reconstruction allows remarkably sharp capture of

  10. Wave steering effects in anisotropic composite structures: Direct calculation of the energy skew angle through a finite element scheme.

    Science.gov (United States)

    Chronopoulos, D

    2017-01-01

    A systematic expression quantifying the wave energy skewing phenomenon as a function of the mechanical characteristics of a non-isotropic structure is derived in this study. A structure of arbitrary anisotropy, layering and geometric complexity is modelled through Finite Elements (FEs) coupled to a periodic structure wave scheme. A generic approach for efficiently computing the angular sensitivity of the wave slowness for each wave type, direction and frequency is presented. The approach does not involve any finite differentiation scheme and is therefore computationally efficient and not prone to the associated numerical errors.

  11. A well-balanced finite volume scheme for 1D hemodynamic simulations

    CERN Document Server

    Delestre, Olivier

    2011-01-01

    We are interested in simulating blood flow in arteries with variable elasticity with a one dimensional model. We present a well-balanced finite volume scheme based on the recent developments in shallow water equations context. We thus get a mass conservative scheme which also preserves equilibria of Q=0. This numerical method is tested on analytical tests. Nous nous int\\'eressons \\`a la simulation d'\\'ecoulements sanguins dans des art\\`eres dont les parois sont \\`a \\'elasticit\\'e variable. Ceci est mod\\'elis\\'e \\`a l'aide d'un mod\\`ele unidimensionnel. Nous pr\\'esentons un sch\\'ema "volume fini \\'equilibr\\'e" bas\\'e sur les d\\'eveloppements r\\'ecents effectu\\'es pour la r\\'esolution du syst\\`eme de Saint-Venant. Ainsi, nous obtenons un sch\\'ema qui pr\\'eserve le volume de fluide ainsi que les \\'equilibres au repos: Q=0. Le sch\\'ema introduit est test\\'e sur des solutions analytiques.

  12. A well-balanced finite volume scheme for 1D hemodynamic simulations*

    Directory of Open Access Journals (Sweden)

    Lagrée Pierre-Yves

    2012-04-01

    Full Text Available We are interested in simulating blood flow in arteries with variable elasticity with a one dimensional model. We present a well-balanced finite volume scheme based on the recent developments in shallow water equations context. We thus get a mass conservative scheme which also preserves equilibria of Q = 0. This numerical method is tested on analytical tests. Nous nous intéressons à la simulation d’écoulements sanguins dans des artères dont les parois sont à élasticité variable. Ceci est modélisé à l’aide d’un modèle unidimensionnel. Nous présentons un schéma ”volume fini équilibré” basé sur les développements récents effectués pour la résolution du système de Saint-Venant. Ainsi, nous obtenons un schéma qui préserve le volume de fluide ainsi que les équilibres au repos : Q = 0. Le schéma introduit est testé sur des solutions analytiques.

  13. A toxin-mediated size-structured population model: Finite difference approximation and well-posedness.

    Science.gov (United States)

    Huang, Qihua; Wang, Hao

    2016-08-01

    The question of the effects of environmental toxins on ecological communities is of great interest from both environmental and conservational points of view. Mathematical models have been applied increasingly to predict the effects of toxins on a variety of ecological processes. Motivated by the fact that individuals with different sizes may have different sensitivities to toxins, we develop a toxin-mediated size-structured model which is given by a system of first order fully nonlinear partial differential equations (PDEs). It is very possible that this work represents the first derivation of a PDE model in the area of ecotoxicology. To solve the model, an explicit finite difference approximation to this PDE system is developed. Existence-uniqueness of the weak solution to the model is established and convergence of the finite difference approximation to this unique solution is proved. Numerical examples are provided by numerically solving the PDE model using the finite difference scheme.

  14. Effect of CFRP Schemes on the Flexural Behavior of RC Beams Modeled by Using a Nonlinear Finite-element Analysis

    Science.gov (United States)

    Al-Rousan, R. Z.

    2015-09-01

    The main objective of this study was to assess the effect of the number and schemes of carbon-fiber-reinforced polymer (CFRP) sheets on the capacity of bending moment, the ultimate displacement, the ultimate tensile strain of CFRP, the yielding moment, concrete compression strain, and the energy absorption of RC beams and to provide useful relationships that can be effectively utilized to determine the required number of CFRP sheets for a necessary increase in the flexural strength of the beams without a major loss in their ductility. To accomplish this, various RC beams, identical in their geometric and reinforcement details and having different number and configurations of CFRP sheets, are modeled and analyzed using the ANSYS software and a nonlinear finite-element analysis.

  15. A comparison of finite difference methods for solving Laplace's equation on curvilinear coordinate systems. M.S. Thesis

    Science.gov (United States)

    Mccoy, M. J.

    1980-01-01

    Various finite difference techniques used to solve Laplace's equation are compared. Curvilinear coordinate systems are used on two dimensional regions with irregular boundaries, specifically, regions around circles and airfoils. Truncation errors are analyzed for three different finite difference methods. The false boundary method and two point and three point extrapolation schemes, used when having the Neumann boundary condition are considered and the effects of spacing and nonorthogonality in the coordinate systems are studied.

  16. Optimized difference schemes for multidimensional hyperbolic partial differential equations

    Directory of Open Access Journals (Sweden)

    Adrian Sescu

    2009-04-01

    Full Text Available In numerical solutions to hyperbolic partial differential equations in multidimensions, in addition to dispersion and dissipation errors, there is a grid-related error (referred to as isotropy error or numerical anisotropy that affects the directional dependence of the wave propagation. Difference schemes are mostly analyzed and optimized in one dimension, wherein the anisotropy correction may not be effective enough. In this work, optimized multidimensional difference schemes with arbitrary order of accuracy are designed to have improved isotropy compared to conventional schemes. The derivation is performed based on Taylor series expansion and Fourier analysis. The schemes are restricted to equally-spaced Cartesian grids, so the generalized curvilinear transformation method and Cartesian grid methods are good candidates.

  17. Eigenvalues of singular differential operators by finite difference methods. II.

    Science.gov (United States)

    Baxley, J. V.

    1972-01-01

    Note is made of an earlier paper which defined finite difference operators for the Hilbert space L2(m), and gave the eigenvalues for these operators. The present work examines eigenvalues for higher order singular differential operators by using finite difference methods. The two self-adjoint operators investigated are defined by a particular value in the same Hilbert space, L2(m), and are strictly positive with compact inverses. A class of finite difference operators is considered, with the idea of application to the theory of Toeplitz matrices. The approximating operators consist of a good approximation plus a perturbing operator.

  18. Development of Generic Field Classes for Finite Element and Finite Difference Problems

    Directory of Open Access Journals (Sweden)

    Diane A. Verner

    1993-01-01

    Full Text Available This article considers the development of a reusable object-oriented array library, as well as the use of this library in the construction of finite difference and finite element codes. The classes in this array library are also generic enough to be used to construct other classes specific to finite difference and finite element methods. We demonstrate the usefulness of this library by inserting it into two existing object-oriented scientific codes developed at Sandia National Laboratories. One of these codes is based on finite difference methods, whereas the other is based on finite element methods. Previously, these codes were separately maintained across a variety of sequential and parallel computing platforms. The use of object-oriented programming allows both codes to make use of common base classes. This offers a number of advantages related to optimization and portability. Optimization efforts, particularly important in large scientific codes, can be focused on a single library. Furthermore, by encapsulating machine dependencies within this library, the optimization of both codes on different architec-tures will only involve modification to a single library.

  19. Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation

    Science.gov (United States)

    Kouatchou, Jules

    1999-01-01

    In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.

  20. ANTI-DIFFUSIVE FINITE DIFFERENCE WENO METHODS FOR SHALLOW WATER WITH TRANSPORT OF POLLUTANT

    Institute of Scientific and Technical Information of China (English)

    Zhengfu Xu; Chi-Wang Shu

    2006-01-01

    In this paper we further explore and apply our recent anti-diffusive flux corrected high order finite difference WENO schemes for conservation laws [18]to compute the Saint-Venant system of shallow water equations with pollutant propagation, which is described by a transport equation. The motivation is that the high order anti-diffusive WENOscheme for conservation laws produces sharp resolution of contact discontinuities while keeping high order accuracy for the approximation in the smooth region of the solution.The application of the anti-diffusive high order WENO scheme to the Saint-Venant system of shallow water equations with transport of pollutant achieves high resolution

  1. Finite-Horizon H∞ Consensus for Multiagent Systems With Redundant Channels via An Observer-Type Event-Triggered Scheme.

    Science.gov (United States)

    Xu, Wenying; Wang, Zidong; Ho, Daniel W C

    2017-06-06

    This paper is concerned with the finite-horizon H∞ consensus problem for a class of discrete time-varying multiagent systems with external disturbances and missing measurements. To improve the communication reliability, redundant channels are introduced and the corresponding protocol is constructed for the information transmission over redundant channels. An event-triggered scheme is adopted to determine whether the information of agents should be transmitted to their neighbors. Subsequently, an observer-type event-triggered control protocol is proposed based on the latest received neighbors' information. The purpose of the addressed problem is to design a time-varying controller based on the observed information to achieve the H∞ consensus performance in a finite horizon. By utilizing a constrained recursive Riccati difference equation approach, some sufficient conditions are obtained to guarantee the H∞ consensus performance, and the controller parameters are also designed. Finally, a numerical example is provided to demonstrate the desired reliability of redundant channels and the effectiveness of the event-triggered control protocol.

  2. A quasi-vector finite difference mode solver for optical waveguides with step-index profiles

    Institute of Scientific and Technical Information of China (English)

    Jinbiao Xiao; Mingde Zhang; Xiaohan Sun

    2006-01-01

    @@ A finite difference scheme based on the polynomial interpolation is constructed to solve the quasi-vector equations for optical waveguides with step-index profiles. The discontinuities of the normal components of the electric field across abrupt dielectric interfaces are taken into account. The numerical results include the polarization effects, but the memory requirement is the same as in solving the scalar wave equation. Moreover, the proposed finite difference scheme can be applied to both uniform and non-uniform mesh grids. The modal propagation constants and field distributions for a buried rectangular waveguide and a rib waveguide are presented. Solutions are compared favorably with those obtained by the numerical approaches published earlier.

  3. Radiation boundary condition and anisotropy correction for finite difference solutions of the Helmholtz equation

    Science.gov (United States)

    Tam, Christopher K. W.; Webb, Jay C.

    1994-01-01

    In this paper finite-difference solutions of the Helmholtz equation in an open domain are considered. By using a second-order central difference scheme and the Bayliss-Turkel radiation boundary condition, reasonably accurate solutions can be obtained when the number of grid points per acoustic wavelength used is large. However, when a smaller number of grid points per wavelength is used excessive reflections occur which tend to overwhelm the computed solutions. Excessive reflections are due to the incompability between the governing finite difference equation and the Bayliss-Turkel radiation boundary condition. The Bayliss-Turkel radiation boundary condition was developed from the asymptotic solution of the partial differential equation. To obtain compatibility, the radiation boundary condition should be constructed from the asymptotic solution of the finite difference equation instead. Examples are provided using the improved radiation boundary condition based on the asymptotic solution of the governing finite difference equation. The computed results are free of reflections even when only five grid points per wavelength are used. The improved radiation boundary condition has also been tested for problems with complex acoustic sources and sources embedded in a uniform mean flow. The present method of developing a radiation boundary condition is also applicable to higher order finite difference schemes. In all these cases no reflected waves could be detected. The use of finite difference approximation inevita bly introduces anisotropy into the governing field equation. The effect of anisotropy is to distort the directional distribution of the amplitude and phase of the computed solution. It can be quite large when the number of grid points per wavelength used in the computation is small. A way to correct this effect is proposed. The correction factor developed from the asymptotic solutions is source independent and, hence, can be determined once and for all. The

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

    Energy Technology Data Exchange (ETDEWEB)

    Mishev, I.D.

    1996-12-31

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

  5. A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension

    Energy Technology Data Exchange (ETDEWEB)

    Garrick, Daniel P. [Department of Aerospace Engineering, Iowa State University, Ames, IA (United States); Owkes, Mark [Department of Mechanical and Industrial Engineering, Montana State University, Bozeman, MT (United States); Regele, Jonathan D., E-mail: jregele@iastate.edu [Department of Aerospace Engineering, Iowa State University, Ames, IA (United States)

    2017-06-15

    Shock waves are often used in experiments to create a shear flow across liquid droplets to study secondary atomization. Similar behavior occurs inside of supersonic combustors (scramjets) under startup conditions, but it is challenging to study these conditions experimentally. In order to investigate this phenomenon further, a numerical approach is developed to simulate compressible multiphase flows under the effects of surface tension forces. The flow field is solved via the compressible multicomponent Euler equations (i.e., the five equation model) discretized with the finite volume method on a uniform Cartesian grid. The solver utilizes a total variation diminishing (TVD) third-order Runge–Kutta method for time-marching and second order TVD spatial reconstruction. Surface tension is incorporated using the Continuum Surface Force (CSF) model. Fluxes are upwinded with a modified Harten–Lax–van Leer Contact (HLLC) approximate Riemann solver. An interface compression scheme is employed to counter numerical diffusion of the interface. The present work includes modifications to both the HLLC solver and the interface compression scheme to account for capillary force terms and the associated pressure jump across the gas–liquid interface. A simple method for numerically computing the interface curvature is developed and an acoustic scaling of the surface tension coefficient is proposed for the non-dimensionalization of the model. The model captures the surface tension induced pressure jump exactly if the exact curvature is known and is further verified with an oscillating elliptical droplet and Mach 1.47 and 3 shock-droplet interaction problems. The general characteristics of secondary atomization at a range of Weber numbers are also captured in a series of simulations.

  6. A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension

    Science.gov (United States)

    Garrick, Daniel P.; Owkes, Mark; Regele, Jonathan D.

    2017-06-01

    Shock waves are often used in experiments to create a shear flow across liquid droplets to study secondary atomization. Similar behavior occurs inside of supersonic combustors (scramjets) under startup conditions, but it is challenging to study these conditions experimentally. In order to investigate this phenomenon further, a numerical approach is developed to simulate compressible multiphase flows under the effects of surface tension forces. The flow field is solved via the compressible multicomponent Euler equations (i.e., the five equation model) discretized with the finite volume method on a uniform Cartesian grid. The solver utilizes a total variation diminishing (TVD) third-order Runge-Kutta method for time-marching and second order TVD spatial reconstruction. Surface tension is incorporated using the Continuum Surface Force (CSF) model. Fluxes are upwinded with a modified Harten-Lax-van Leer Contact (HLLC) approximate Riemann solver. An interface compression scheme is employed to counter numerical diffusion of the interface. The present work includes modifications to both the HLLC solver and the interface compression scheme to account for capillary force terms and the associated pressure jump across the gas-liquid interface. A simple method for numerically computing the interface curvature is developed and an acoustic scaling of the surface tension coefficient is proposed for the non-dimensionalization of the model. The model captures the surface tension induced pressure jump exactly if the exact curvature is known and is further verified with an oscillating elliptical droplet and Mach 1.47 and 3 shock-droplet interaction problems. The general characteristics of secondary atomization at a range of Weber numbers are also captured in a series of simulations.

  7. A Finite Difference Approximation for a Coupled System of Nonlinear Size-Structured Populations

    Science.gov (United States)

    2000-01-01

    We study a quasilinear nonlocal hyperbolic initial-boundary value problem that models the evolution of N size-structured subpopulations competing for common resources. We develop an implicit finite difference scheme to approximate the solution of this model. The convergence of this approximation to a unique bounded variation weak solution is obtained. The numerical results for a special case of this model suggest that when subpopulations are closed under reproduction, one subpopulation survives and the others go to extinction. Moreover

  8. Accurate finite-difference time-domain simulation of anisotropic media by subpixel smoothing.

    Science.gov (United States)

    Oskooi, Ardavan F; Kottke, Chris; Johnson, Steven G

    2009-09-15

    Finite-difference time-domain methods suffer from reduced accuracy when discretizing discontinuous materials. We previously showed that accuracy can be significantly improved by using subpixel smoothing of the isotropic dielectric function, but only if the smoothing scheme is properly designed. Using recent developments in perturbation theory that were applied to spectral methods, we extend this idea to anisotropic media and demonstrate that the generalized smoothing consistently reduces the errors and even attains second-order convergence with resolution.

  9. Implicit finite-difference simulations of seismic wave propagation

    KAUST Repository

    Chu, Chunlei

    2012-03-01

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

  10. The standard upwind compact difference schemes for incompressible flow simulations

    Science.gov (United States)

    Fan, Ping

    2016-10-01

    Compact difference schemes have been used extensively for solving the incompressible Navier-Stokes equations. However, the earlier formulations of the schemes are of central type (called central compact schemes, CCS), which are dispersive and susceptible to numerical instability. To enhance stability of CCS, the optimal upwind compact schemes (OUCS) are developed recently by adding high order dissipative terms to CCS. In this paper, it is found that OUCS are essentially not of the upwind type because they do not use upwind-biased but central type of stencils. Furthermore, OUCS are not the most optimal since orders of accuracy of OUCS are at least one order lower than the maximum achievable orders. New upwind compact schemes (called standard upwind compact schemes, SUCS) are developed in this paper. In contrast to OUCS, SUCS are constructed based completely on upwind-biased stencils and hence can gain adequate numerical dissipation with no need for introducing optimization calculations. Furthermore, SUCS can achieve the maximum achievable orders of accuracy and hence be more compact than OUCS. More importantly, SUCS have prominent advantages on combining the stable and high resolution properties which are demonstrated from the global spectral analyses and typical numerical experiments.

  11. Finite element simulation of laser tube bending: Effect of scanning schemes on bending angle, distortions and stress distribution

    Science.gov (United States)

    Safdar, Shakeel; Li, Lin; Sheikh, M. A.; Zhu Liu

    2007-09-01

    Laser forming has received considerable attention in recent years. Within laser forming, tube bending is an important industrial activity, with applications in critical engineering systems like micro-machines, heat exchangers, hydraulic systems, boilers, etc. Laser tube bending utilizes the thermal stresses generated during laser scanning to achieve the desired bends. The parameters to control the process are usually laser power, beam diameter, scanning velocity and number of scans. Recently axial scanning has been used for tube bending instead of commonly used circumferential scans. However the comparison between the scanning schemes has involved dissimilar laser beam geometries with circular beam used for circumferential scanning and a rectangular beam for the axial scan. Thermal stresses generated during laser scanning are strongly dependent upon laser beam geometry and scanning direction and hence it is difficult to isolate the contribution made by these two variables. It has recently been established at the Corrosion and Protection Centre, University of Manchester, that corrosion properties of material during laser forming are affected by the number of laser passes. Depending on the material, the corrosion behaviour is either adversely or favourably affected by number of passes. Thus it is of great importance to know how different scanning schemes would affect laser tube bending. Moreover, any scanning scheme which results in greater bending angle would eliminate the need for higher number of passes, making the process faster. However, it is not only the bending angle which is critical, distortions in other planes are also extremely important. Depending on the use of the final product, unwanted distortions may be the final selection criteria. This paper investigates the effect of scanning direction on laser tube bending. Finite-element modelling has been used for the study of the process with some results also validated by experiments.

  12. The upwind finite difference fractional steps method for combinatorial system of dynamics of fluids in porous media and its application

    Institute of Scientific and Technical Information of China (English)

    YUAN; Yiran(袁益让)

    2002-01-01

    For combinatorial system of multilayer dynamics of fluids in porous media, the second order and first order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques,such as implicit-explicit difference scheme, calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates, are adopted. Optimal order estimates in L2 norm are derived to determine the error in the second order approximate solution. This method has already been applied to the numerical simulation of migration-accumulation of oil resources.

  13. 正则长波方程的一个新的差分方法%A NEW FINITE DIFFERENCE METHOD FOR REGULARIZED LONG-WAVE EQUATION

    Institute of Scientific and Technical Information of China (English)

    张鲁明; 常谦顺

    2000-01-01

    In this paper, a finite difference method for a initial-boundary valueproblem of regularized long-wave equation was considered. A energyconservative finite difference scheme of three levels was proposed.Convergence and stability of difference solution were proved. The schemeneedn't iterate, thus, requires less CPU time. Numerical experimentresults demonstrate that the method is efficient and reliable.

  14. Numerical solution of the one-dimensional Burgers’ equation: Implicit and fully implicit exponential finite difference methods

    Indian Academy of Sciences (India)

    Bilge Inan; Ahmet Refik Bahadir

    2013-10-01

    This paper describes two new techniques which give improved exponential finite difference solutions of Burgers’ equation. These techniques are called implicit exponential finite difference method and fully implicit exponential finite difference method for solving Burgers’ equation. As the Burgers’ equation is nonlinear, the scheme leads to a system of nonlinear equations. At each time-step, Newton’s method is used to solve this nonlinear system. The results are compared with exact values and it is clearly shown that results obtained using both the methods are precise and reliable.

  15. Single Alternating Group Explicit (SAGE) Method for Electrochemical Finite Difference Digital Simulation

    Institute of Scientific and Technical Information of China (English)

    DENG,Zhao-Xiang(邓兆祥); LIN,Xiang-Qin(林祥钦); TONG,Zhong-Hua(童中华)

    2002-01-01

    The four different schemes of Group Explicit Method (GEM): GER, GEL, SAGE and DAGE have been claimed to be unstable when employed for electrochemical digital simulations with large model diffusion coefficient DM@ However, in this investigation, in spite of the conditional stability of GER and GEL, the SAGE scheme, which is a combination of GEL and GER, was found to be unconditionally stable when used for simulations of electrochemical reaction-diffusions and had a performance comparable with or even better than the Fast Quasi Explicit Finite Difference Method (FQEFD) in srme aspects. Corresponding differential equations of SAGE scheme for digital simulations of various electrochemical mechanisms with both uniform and exponentially expanded space units were established. The effectiveness of the SAGE method was further demonstrated by the simulations of an EC and a catalytic mechanism with very large homogoneous rate constants.

  16. Solving difference equations in finite terms

    NARCIS (Netherlands)

    Hendriks, Peter; Singer, MF

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

  17. Solving difference equations in finite terms

    NARCIS (Netherlands)

    Hendriks, Peter; Singer, MF

    1999-01-01

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

  18. SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES.

    Science.gov (United States)

    Wan, Xiaohai; Li, Zhilin

    2012-06-01

    Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size.

  19. Hybrid finite volume scheme for a two-phase flow in heterogeneous porous media*

    Directory of Open Access Journals (Sweden)

    Brenner Konstantin

    2012-04-01

    Full Text Available We propose a finite volume method on general meshes for the numerical simulation of an incompressible and immiscible two-phase flow in porous media. We consider the case that can be written as a coupled system involving a degenerate parabolic convection-diffusion equation for the saturation together with a uniformly elliptic equation for the global pressure. The numerical scheme, which is implicit in time, allows computations in the case of a heterogeneous and anisotropic permeability tensor. The convective fluxes, which are non monotone with respect to the unknown saturation and discontinuous with respect to the space variables, are discretized by means of a special Godunov scheme. We prove the existence of a discrete solution which converges, along a subsequence, to a solution of the continuous problem. We present a number of numerical results in space dimension two, which confirm the efficiency of the numerical method. Nous proposons un schéma de volumes finis hybrides pour la discrétisation d’un problème d’écoulement diphasique incompressible et immiscible en milieu poreux. On suppose que ce problème a la forme d’une équation parabolique dégénérée de convection-diffusion en saturation couplée à une équation uniformément elliptique en pression. On considère un schéma implicite en temps, où les flux diffusifs sont discrétisés par la méthode des volumes finis hybride, ce qui permet de pouvoir traiter le cas d’un tenseur de perméabilité anisotrope et hétérogène sur un maillage très général, et l’on s’appuie sur un schéma de Godunov pour la discrétisation des flux convectifs, qui peuvent être non monotones et discontinus par rapport aux variables spatiales. On démontre l’existence d’une solution discrète, dont une sous-suite converge vers une solution faible du problème continu. On présente finalement des cas test bidimensionnels.

  20. FINITE DIFFERENCE SIMULATION OF LOW CARBON STEEL MANUAL ARC WELDING

    Directory of Open Access Journals (Sweden)

    Laith S Al-Khafagy

    2011-01-01

    Full Text Available This study discusses the evaluation and simulation of angular distortion in welding joints, and the ways of controlling and treating them, while welding plates of (low carbon steel type (A-283-Gr-C through using shielded metal arc welding. The value of this distortion is measured experimentally and the results are compared with the suggested finite difference method computer program. Time dependent temperature distributions are obtained using finite difference method. This distribution is used to obtain the shrinkage that causes the distortions accompanied with structural forces that act to modify these distortions. Results are compared with simple empirical models and experimental results. Different thickness of plates and welding parameters is manifested to illustrate its effect on angular distortions. Results revealed the more accurate results of finite difference method that match experimental results in comparison with empirical formulas. Welding parameters include number of passes, current, electrode type and geometry of the welding process.

  1. Numerical simulation of standing wave with 3D predictor-corrector finite difference method for potential flow equations

    Institute of Scientific and Technical Information of China (English)

    罗志强; 陈志敏

    2013-01-01

    A three-dimensional (3D) predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa-tions with a free surface. The 3D irregular tank is mapped onto a fixed cubic tank through the proper coordinate transform schemes. The cubic tank is distributed by the staggered meshgrid, and the staggered meshgrid is used to denote the variables of the flow field. The predictor-corrector finite difference method is given to develop the difference equa-tions of the dynamic boundary equation and kinematic boundary equation. Experimental results show that, using the finite difference method of the predictor-corrector scheme, the numerical solutions agree well with the published results. The wave profiles of the standing wave with different amplitudes and wave lengths are studied. The numerical solutions are also analyzed and presented graphically.

  2. The mimetic finite difference method for the Landau-Lifshitz equation

    Science.gov (United States)

    Kim, Eugenia; Lipnikov, Konstantin

    2017-01-01

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

  3. A comparison of the finite difference and finite element methods for heat transfer calculations

    Science.gov (United States)

    Emery, A. F.; Mortazavi, H. R.

    1982-01-01

    The finite difference method and finite element method for heat transfer calculations are compared by describing their bases and their application to some common heat transfer problems. In general it is noted that neither method is clearly superior, and in many instances, the choice is quite arbitrary and depends more upon the codes available and upon the personal preference of the analyst than upon any well defined advantages of one method. Classes of problems for which one method or the other is better suited are defined.

  4. Compact finite difference method for American option pricing

    Science.gov (United States)

    Zhao, Jichao; Davison, Matt; Corless, Robert M.

    2007-09-01

    A compact finite difference method is designed to obtain quick and accurate solutions to partial differential equation problems. The problem of pricing an American option can be cast as a partial differential equation. Using the compact finite difference method this problem can be recast as an ordinary differential equation initial value problem. The complicating factor for American options is the existence of an optimal exercise boundary which is jointly determined with the value of the option. In this article we develop three ways of combining compact finite difference methods for American option price on a single asset with methods for dealing with this optimal exercise boundary. Compact finite difference method one uses the implicit condition that solutions of the transformed partial differential equation be nonnegative to detect the optimal exercise value. This method is very fast and accurate even when the spatial step size h is large (h[greater-or-equal, slanted]0.1). Compact difference method two must solve an algebraic nonlinear equation obtained by Pantazopoulos (1998) at every time step. This method can obtain second order accuracy for space x and requires a moderate amount of time comparable with that required by the Crank Nicolson projected successive over relaxation method. Compact finite difference method three refines the free boundary value by a method developed by Barone-Adesi and Lugano [The saga of the American put, 2003], and this method can obtain high accuracy for space x. The last two of these three methods are convergent, moreover all the three methods work for both short term and long term options. Through comparison with existing popular methods by numerical experiments, our work shows that compact finite difference methods provide an exciting new tool for American option pricing.

  5. On the Torsion Units of Integral Adjacency Algebras of Finite Association Schemes

    Directory of Open Access Journals (Sweden)

    Allen Herman

    2014-01-01

    Full Text Available Torsion units of group rings have been studied extensively since the 1960s. As association schemes are generalization of groups, it is natural to ask about torsion units of association scheme rings. In this paper we establish some results about torsion units of association scheme rings analogous to basic results for torsion units of group rings.

  6. Perfectly matched layer stability in 3-D finite-difference time-domain simulation of electroacoustic wave propagation in piezoelectric crystals with different symmetry class.

    Science.gov (United States)

    Nova, Omar; Peña, Néstor; Ney, Michel

    2015-03-01

    Perfectly matched layer stability in 3-D finite-difference 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.

  7. Finite-Difference Frequency-Domain Method in Nanophotonics

    DEFF Research Database (Denmark)

    Ivinskaya, Aliaksandra

    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...

  8. The Modified Upwind Finite Difference Fractional Steps Method for Compressible Two-phase Displacement Problem

    Institute of Scientific and Technical Information of China (English)

    Yi-rang Yuan

    2004-01-01

    For compressible two-phase displacement problem,the modified upwind finite difference fractional steps schemes are put forward.Some techniques,such as calculus of variations,commutative law of multiplication of difference operators,decomposition of high order difference operators,the theory of prior estimates and techniques are used.Optimal order estimates in L 2 norm are derived for the error in the approximate solution.This method has already been applied to the numerical simulation of seawater intrusion and migration-accumulation of oil resources.

  9. An implicit finite volume scheme for a scalar hyperbolic problem with measure data related to piecewise deterministic Markov processes

    Science.gov (United States)

    Eymard, Robert; Mercier, Sophie; Prignet, Alain

    2008-12-01

    We are interested here in the numerical approximation of a family of probability measures, solution of the Chapman-Kolmogorov equation associated to some non-diffusion Markov process with uncountable state space. Such an equation contains a transport term and another term, which implies redistribution of the probability mass on the whole space. An implicit finite volume scheme is proposed, which is intermediate between an upstream weighting scheme and a modified Lax-Friedrichs one. Due to the seemingly unusual probability framework, a new weak bounded variation inequality had to be developed, in order to prove the convergence of the discretised transport term. Such an inequality may be used in other contexts, such as for the study of finite volume approximations of scalar linear or nonlinear hyperbolic equations with initial data in L1. Also, due to the redistribution term, the tightness of the family of approximate probability measures had to be proven. Numerical examples are provided, showing the efficiency of the implicit finite volume scheme and its potentiality to be helpful in an industrial reliability context.

  10. Solving parabolic and hyperbolic equations by the generalized finite difference method

    Science.gov (United States)

    Benito, J. J.; Urena, F.; Gavete, L.

    2007-12-01

    Classical finite difference schemes are in wide use today for approximately solving partial differential equations of mathematical physics. An evolution of the method of finite differences has been the development of generalized finite difference (GFD) method, that can be applied to irregular grids of points. In this paper the extension of the GFD to the explicit solution of parabolic and hyperbolic equations has been developed for partial differential equations with constant coefficients in the cases of considering one, two or three space dimensions. The convergence of the method has been studied and the truncation errors over irregular grids are given. Different examples have been solved using the explicit finite difference formulae and the criterion of stability. This has been expressed in function of the coefficients of the star equation for irregular clouds of nodes in one, two or three space dimensions. The numerical results show the accuracy obtained over irregular grids. This paper also includes the study of the maximum local error and the global error for different examples of parabolic and hyperbolic time-dependent equations.

  11. A new finite element and finite difference hybrid method for computing electrostatics of ionic solvated biomolecule

    Science.gov (United States)

    Ying, Jinyong; Xie, Dexuan

    2015-10-01

    The Poisson-Boltzmann equation (PBE) is one widely-used implicit solvent continuum model for calculating electrostatics of ionic solvated biomolecule. In this paper, a new finite element and finite difference hybrid method is presented to solve PBE efficiently based on a special seven-overlapped box partition with one central box containing the solute region and surrounded by six neighboring boxes. In particular, an efficient finite element solver is applied to the central box while a fast preconditioned conjugate gradient method using a multigrid V-cycle preconditioning is constructed for solving a system of finite difference equations defined on a uniform mesh of each neighboring box. Moreover, the PBE domain, the box partition, and an interface fitted tetrahedral mesh of the central box can be generated adaptively for a given PQR file of a biomolecule. This new hybrid PBE solver is programmed in C, Fortran, and Python as a software tool for predicting electrostatics of a biomolecule in a symmetric 1:1 ionic solvent. Numerical results on two test models with analytical solutions and 12 proteins validate this new software tool, and demonstrate its high performance in terms of CPU time and memory usage.

  12. A positive and entropy-satisfying finite volume scheme for the Baer-Nunziato model

    Science.gov (United States)

    Coquel, Frédéric; Hérard, Jean-Marc; Saleh, Khaled

    2017-02-01

    We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer-Nunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in [16] for the isentropic Baer-Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing scheme for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound are also proven to be maintained by the numerical scheme. It is also the only scheme for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the numerical method, is satisfied for any admissible equation of state. We provide a numerical study for the convergence of the approximate solutions towards some exact Riemann solutions. The numerical simulations show that the relaxation scheme compares well with two of the most popular existing schemes available for the Baer-Nunziato model, namely Schwendeman-Wahle-Kapila's Godunov-type scheme [39] and Tokareva-Toro's HLLC scheme [44]. The relaxation scheme also shows a higher precision and a lower computational cost (for comparable accuracy) than a standard numerical scheme used in the nuclear industry, namely Rusanov's scheme. Finally, we assess the good behavior of the scheme when approximating vanishing phase solutions.

  13. PRISMATIC END ITEM ON THE BASIS OF MOMENT FINITE ELEMENTS SCHEMES

    Directory of Open Access Journals (Sweden)

    Guliar A.І

    2014-12-01

    Full Text Available Based on the semianalytical finite element method, a new finite element with a variable crosssectional area along a generator, which is due to take fully into account the numerical integration of the variability of all the variables in cross-section. It is shown that the resulting variant finite element allows to obtain reliable results for the prismatic bodies with variable cross-sectional area along a generatrix.

  14. A Pipelined Non-Deterministic Finite Automaton-Based String Matching Scheme Using Merged State Transitions in an FPGA.

    Science.gov (United States)

    Kim, HyunJin; Choi, Kang-Il

    2016-01-01

    This paper proposes a pipelined non-deterministic finite automaton (NFA)-based string matching scheme using field programmable gate array (FPGA) implementation. The characteristics of the NFA such as shared common prefixes and no failure transitions are considered in the proposed scheme. In the implementation of the automaton-based string matching using an FPGA, each state transition is implemented with a look-up table (LUT) for the combinational logic circuit between registers. In addition, multiple state transitions between stages can be performed in a pipelined fashion. In this paper, it is proposed that multiple one-to-one state transitions, called merged state transitions, can be performed with an LUT. By cutting down the number of used LUTs for implementing state transitions, the hardware overhead of combinational logic circuits is greatly reduced in the proposed pipelined NFA-based string matching scheme.

  15. Weak convergence of finite element approximations of linear stochastic evolution equations with additive noise II. Fully discrete schemes

    CERN Document Server

    Kovács, M; Lindgren, F

    2012-01-01

    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.

  16. A new coupled computational method in conjunction with three-dimensional finite volume schemes for nonlinear coupled constitutive relations

    CERN Document Server

    Jiang, Zhongzheng; Zhao, Wenwen

    2016-01-01

    Non-equilibrium effects play a vital role in high-speed and rarefied gas flows and the accurate simulation of these flow regimes are far beyond the capability of near-local-equilibrium Navier-Stokes-Fourier equations. Eu proposed generalized hydrodynamic equations which are consistent with the laws of irreversible thermodynamics to solve this problem. Based on Eu's generalized hydrodynamics equations, a computational model, namely the nonlinear coupled constitutive relations(NCCR),was developed by R.S.Myong and applied successfully to one-dimensional shock wave structure and two-dimensional rarefied flows. In this paper, finite volume schemes, including LU-SGS time advance scheme, MUSCL interpolation and AUSMPW+ scheme, are fistly adopted to investigate NCCR model's validity and potential in three-dimensional complex hypersonic rarefied gas flows. Moreover, in order to solve the computational stability problems in 3D complex flows,a modified solution is developed for the NCCR model. Finally, the modified solu...

  17. Energy- and enstrophy-conserving schemes for the shallow-water equations, based on mimetic finite elements

    CERN Document Server

    McRae, Andrew T T

    2013-01-01

    This paper presents a family of spatial discretisations of the nonlinear rotating shallow-water equations that conserve both energy and potential enstrophy. These are based on two-dimensional mixed finite element methods, and hence, unlike some finite difference methods, do not require an orthogonal grid. Numerical verification of the aforementioned properties is also provided.

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

    KAUST Repository

    Radwan, Ahmed G.

    2011-08-01

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

  19. The modified equation approach to the stability and accuracy analysis of finite-difference methods

    Science.gov (United States)

    Warming, R. F.; Hyett, B. J.

    1974-01-01

    The stability and accuracy of finite-difference approximations to simple linear partial differential equations are analyzed by studying the modified partial differential equation. Aside from round-off error, the modified equation represents the actual partial differential equation solved when a numerical solution is computed using a finite-difference equation. The modified equation is derived by first expanding each term of a difference scheme in a Taylor series and then eliminating time derivatives higher than first order by certain algebraic manipulations. The connection between 'heuristic' stability theory based on the modified equation approach and the von Neumann (Fourier) method is established. In addition to the determination of necessary and sufficient conditions for computational stability, a truncated version of the modified equation can be used to gain insight into the nature of both dissipative and dispersive errors.

  20. High order sub-cell finite volume schemes for solving hyperbolic conservation laws I: basic formulation and one-dimensional analysis

    Science.gov (United States)

    Pan, JianHua; Ren, YuXin

    2017-08-01

    In this paper, a family of sub-cell finite volume schemes for solving the hyperbolic conservation laws is proposed and analyzed in one-dimensional cases. The basic idea of this method is to subdivide a control volume (main cell) into several sub-cells and the finite volume discretization is applied to each of the sub-cells. The averaged values on the sub-cells of current and face neighboring main cells are used to reconstruct the polynomial distributions of the dependent variables. This method can achieve arbitrarily high order of accuracy using a compact stencil. It is similar to the spectral volume method incorporating with PNPM technique but with fundamental differences. An elaborate utilization of these differences overcomes some shortcomings of the spectral volume method and results in a family of accurate and robust schemes for solving the hyperbolic conservation laws. In this paper, the basic formulation of the proposed method is presented. The Fourier analysis is performed to study the properties of the one-dimensional schemes. A WENO limiter based on the secondary reconstruction is constructed.

  1. Different radiation impedance models for finite porous materials

    DEFF Research Database (Denmark)

    Nolan, Melanie; Jeong, Cheol-Ho; Brunskog, Jonas;

    2015-01-01

    coupled to the transfer matrix method (TMM). These methods are found to yield comparable results when predicting the Sabine absorption coefficients of finite porous materials. Discrepancies with measurement results can essentially be explained by the unbalance between grazing and non-grazing sound field...... the infinite case. Thus, in order to predict the Sabine absorption coefficients of finite porous samples, one can incorporate models of the radiation impedance. In this study, different radiation impedance models are compared with two experimental examples. Thomasson’s model is compared to Rhazi’s method when...

  2. Chebyshev Finite Difference Method for Fractional Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Boundary

    2015-09-01

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

  3. Eigenvalues of singular differential operators by finite difference methods. I.

    Science.gov (United States)

    Baxley, J. V.

    1972-01-01

    Approximation of the eigenvalues of certain self-adjoint operators defined by a formal differential operator in a Hilbert space. In general, two problems are studied. The first is the problem of defining a suitable Hilbert space operator that has eigenvalues. The second problem concerns the finite difference operators to be used.

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

    NARCIS (Netherlands)

    van Linde, Hendrik Jan

    1971-01-01

    In this thesis finite-difference approximations to the three boundary value problems for Poisson’s equation are given, with discretization errors of O(H^3) for the mixed boundary value problem, O(H^3 |ln(h)| for the Neumann problem and O(H^4)for the Dirichlet problem respectively . First an operator

  5. Finite Difference Solution for Biopotentials of Axially Symmetric Cells

    Science.gov (United States)

    Klee, Maurice; Plonsey, Robert

    1972-01-01

    The finite difference equations necessary for calculating the three-dimensional, time-varying biopotentials within and surrounding axially symmetric cells are presented. The method of sucessive overrelaxation is employed to solve these equations and is shown to be rapidly convergent and accurate for the exemplary problem of a spheroidal cell under uniform field stimulation. PMID:4655665

  6. A new 9-point sixth-order accurate compact finite-difference method for the Helmholtz equation

    Science.gov (United States)

    Nabavi, Majid; Siddiqui, M. H. Kamran; Dargahi, Javad

    2007-11-01

    A new 9-point sixth-order accurate compact finite-difference method for solving the Helmholtz equation in one and two dimensions, is developed and analyzed. This scheme is based on sixth-order approximation to the derivative calculated from the Helmholtz equation. A sixth-order accurate symmetrical representation for the Neumann boundary condition was also developed. The efficiency and accuracy of the scheme is validated by its application to two test problems which have exact solutions. Numerical results show that this sixth-order scheme has the expected accuracy and behaves robustly with respect to the wave number.

  7. Flux vector splitting of the inviscid equations with application to finite difference methods

    Science.gov (United States)

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

    1979-01-01

    The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one. This property readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum. As a consequence of flux vector splitting, new explicit and implicit dissipative finite-difference schemes are developed for first-order hyperbolic systems of equations. Appropriate one-sided spatial differences for each split flux vector are used throughout the computational field even if the flow is locally subsonic. The results of some preliminary numerical computations are included.

  8. Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods

    Science.gov (United States)

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

    1981-01-01

    The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one. This property readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum. As a consequence of flux vector splitting, new explicit and implicit dissipative finite-difference schemes are developed for first-order hyperbolic systems of equations. Appropriate one-sided spatial differences for each split flux vector are used throughout the computational field even if the flow is locally subsonic. The results of some preliminary numerical computations are included.

  9. Transporter taxonomy - a comparison of different transport protein classification schemes.

    Science.gov (United States)

    Viereck, Michael; Gaulton, Anna; Digles, Daniela; Ecker, Gerhard F

    2014-06-01

    Currently, there are more than 800 well characterized human membrane transport proteins (including channels and transporters) and there are estimates that about 10% (approx. 2000) of all human genes are related to transport. Membrane transport proteins are of interest as potential drug targets, for drug delivery, and as a cause of side effects and drug–drug interactions. In light of the development of Open PHACTS, which provides an open pharmacological space, we analyzed selected membrane transport protein classification schemes (Transporter Classification Database, ChEMBL, IUPHAR/BPS Guide to Pharmacology, and Gene Ontology) for their ability to serve as a basis for pharmacology driven protein classification. A comparison of these membrane transport protein classification schemes by using a set of clinically relevant transporters as use-case reveals the strengths and weaknesses of the different taxonomy approaches.

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2008-07-01

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

  11. Linear finite-difference bond graph model of an ionic polymer actuator

    Science.gov (United States)

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

    2017-09-01

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

  12. A Review of High-Order and Optimized Finite-Difference Methods for Simulating Linear Wave Phenomena

    Science.gov (United States)

    Zingg, David W.

    1996-01-01

    This paper presents a review of high-order and optimized finite-difference methods for numerically simulating the propagation and scattering of linear waves, such as electromagnetic, acoustic, or elastic waves. The spatial operators reviewed include compact schemes, non-compact schemes, schemes on staggered grids, and schemes which are optimized to produce specific characteristics. The time-marching methods discussed include Runge-Kutta methods, Adams-Bashforth methods, and the leapfrog method. In addition, the following fourth-order fully-discrete finite-difference methods are considered: a one-step implicit scheme with a three-point spatial stencil, a one-step explicit scheme with a five-point spatial stencil, and a two-step explicit scheme with a five-point spatial stencil. For each method studied, the number of grid points per wavelength required for accurate simulation of wave propagation over large distances is presented. Recommendations are made with respect to the suitability of the methods for specific problems and practical aspects of their use, such as appropriate Courant numbers and grid densities. Avenues for future research are suggested.

  13. WLS-ENO: Weighted-least-squares based essentially non-oscillatory schemes for finite volume methods on unstructured meshes

    Science.gov (United States)

    Liu, Hongxu; Jiao, Xiangmin

    2016-06-01

    ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes are widely used high-order schemes for solving partial differential equations (PDEs), especially hyperbolic conservation laws with piecewise smooth solutions. For structured meshes, these techniques can achieve high order accuracy for smooth functions while being non-oscillatory near discontinuities. For unstructured meshes, which are needed for complex geometries, similar schemes are required but they are much more challenging. We propose a new family of non-oscillatory schemes, called WLS-ENO, in the context of solving hyperbolic conservation laws using finite-volume methods over unstructured meshes. WLS-ENO is derived based on Taylor series expansion and solved using a weighted least squares formulation. Unlike other non-oscillatory schemes, the WLS-ENO does not require constructing sub-stencils, and hence it provides a more flexible framework and is less sensitive to mesh quality. We present rigorous analysis of the accuracy and stability of WLS-ENO, and present numerical results in 1-D, 2-D, and 3-D for a number of benchmark problems, and also report some comparisons against WENO.

  14. A finite volume upwind scheme for the solution of the linear advection diffusion equation with sharp gradients in multiple dimensions

    Science.gov (United States)

    Badrot-Nico, Fabiola; Brissaud, François; Guinot, Vincent

    2007-09-01

    A finite volume upwind numerical scheme for the solution of the linear advection equation in multiple dimensions on Cartesian grids is presented. The small-stencil, Modified Discontinuous Profile Method (MDPM) uses a sub-cell piecewise constant reconstruction and additional information at the cell interfaces, rather than a spatial extension of the stencil as in usual methods. This paper presents the MDPM profile reconstruction method in one dimension and its generalization and algorithm to two- and three-dimensional problems. The method is extended to the advection-diffusion equation in multiple dimensions. The MDPM is tested against the MUSCL scheme on two- and three-dimensional test cases. It is shown to give high-quality results for sharp gradients problems, although some scattering appears. For smooth gradients, extreme values are best preserved with the MDPM than with the MUSCL scheme, while the MDPM does not maintain the smoothness of the original shape as well as the MUSCL scheme. However the MDPM is proved to be more efficient on coarse grids in terms of error and CPU time, while on fine grids the MUSCL scheme provides a better accuracy at a lower CPU.

  15. THE UPWIND FINITE DIFFERENCE METHOD FOR MOVING BOUNDARY VALUE PROBLEM OF COUPLED SYSTEM

    Institute of Scientific and Technical Information of China (English)

    Yuan Yirang

    2011-01-01

    Coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution. It is of great value in rational evaluation of prospecting and exploiting oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. The upwind finite difference schemes applicable to parallel arith- metic are put forward and two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as change of variables, calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order dif- ference operators and prior estimates, are adopted. The estimates in 12 norm are derived to determine the error in the approximate solution. This method was already applied to the numerical simulation of migration-accumulation of oil resources.

  16. Finite-volume method with lattice Boltzmann flux scheme for incompressible porous media flow at the representative-elementary-volume scale

    Science.gov (United States)

    Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong

    2016-02-01

    Based on the Darcy-Brinkman-Forchheimer equation, a finite-volume computational model with lattice Boltzmann flux scheme is proposed for incompressible porous media flow in this paper. The fluxes across the cell interface are calculated by reconstructing the local solution of the generalized lattice Boltzmann equation for porous media flow. The time-scaled midpoint integration rule is adopted to discretize the governing equation, which makes the time step become limited by the Courant-Friedricks-Lewy condition. The force term which evaluates the effect of the porous medium is added to the discretized governing equation directly. The numerical simulations of the steady Poiseuille flow, the unsteady Womersley flow, the circular Couette flow, and the lid-driven flow are carried out to verify the present computational model. The obtained results show good agreement with the analytical, finite-difference, and/or previously published solutions.

  17. Accurate convergent finite difference approximations for viscosity solutions of the elliptic Monge-Amp\\`ere partial differential equation

    CERN Document Server

    Froese, Brittany D

    2012-01-01

    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.

  18. Hybrid Spectral Difference/Embedded Finite Volume Method for Conservation Laws

    CERN Document Server

    Choi, Jung J

    2014-01-01

    A novel hybrid spectral difference/embedded finite volume method is introduced in order to apply a discontinuous high-order method for large scale engineering applications involving discontinuities in flows with complex geometries. In the proposed hybrid approach, structured finite volume (FV) cells are embedded in hexahedral SD elements containing discontinuities, and FV based high-order shock-capturing scheme is employed to overcome Gibbs phenomenon. Thus, discontinuities are captured at the resolution of embedded FV cells within an SD element. In smooth flow regions, the SD method is chosen for its low numerical dissipation and computational efficiency preserving spectral-like solutions. The coupling between the SD elements and the elements with embedded FV cells are achieved by the mortar method. In this paper, the 5th-order WENO scheme with characteristic decomposition is employed as the shock-capturing scheme in the embedded FV cells, and the 5th-order SD method is used in the smooth flow field. The ord...

  19. Time dependent wave envelope finite difference analysis of sound propagation

    Science.gov (United States)

    Baumeister, K. J.

    1984-01-01

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

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

    Energy Technology Data Exchange (ETDEWEB)

    MINKOFF,SUSAN E.

    1999-12-09

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

  1. Spatial parallelism of a 3D finite difference, velocity-stress elastic wave propagation code

    Energy Technology Data Exchange (ETDEWEB)

    Minkoff, S.E.

    1999-12-01

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

  2. A spectral Finite Difference Analysis of Natural Convection in a Rectangular Equilateral Triangle Cavity

    Institute of Scientific and Technical Information of China (English)

    Yoshihiromochimaru

    2000-01-01

    A steady-state two-dimensional natural convection in a rectangular equlateral triangle cavity is analyzed numercally,using a spectral finite difference scheme,where a conformal mapping coordinate system is adopted with a unit circle for the boundary.Vorticity-stream function formulation is used in conjunction with an energy equation.Time marching algorithm in a diagonal dominant form under a Fourier series decomposition is used to give a steady-state field for a mixed(Neumann and Dirichlet) thermal boundary condition even at a Grashof number of 106.

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

    DEFF Research Database (Denmark)

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

    2012-01-01

    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...... 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....

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

    DEFF Research Database (Denmark)

    Ducrozet, Guillaume; Bingham, Harry B.; Engsig-Karup, Allan Peter;

    2010-01-01

    This contribution presents our recent progress on developing an efficient fully-nonlinear potential flow model for simulating 3D wave-wave and wave-structure interaction over arbitrary depths (i.e. in coastal and offshore environment). The model is based on a high-order finite difference scheme...... 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...

  5. Characteristic finite difference method and application for moving boundary value problem of coupled system

    Institute of Scientific and Technical Information of China (English)

    YUAN Yi-rang; LI Chang-feng; YANG Cheng-shun; HAN Yu-ji

    2008-01-01

    The coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution. It is of great value in rational evaluation of prospecting and exploiting oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. A kind of characteristic finite difference schemes is put forward, from which optimal order estimates in l2 norm are derived for the error in the approximate solutions. The research is important both theoretically and practically for the model analysis in the field, the model numerical method and software development.

  6. A novel incompressible finite-difference lattice Boltzmann equation for particle-laden flow

    Institute of Scientific and Technical Information of China (English)

    Sheng Chen; Zhaohui Liu; Baochang Shi; Zhu He; Chuguang Zheng

    2005-01-01

    In this paper, we propose a novel incompressible finite-difference lattice Boltzmann Equation (FDLBE). Because source terms that reflect the interaction between phases can be accurately described, the new model is suitable for simulating two-way coupling incompressible multiphase flow.The 2-D particle-laden flow over a backward-facing step is chosen as a test case to validate the present method. Favorable results are obtained and the present scheme is shown to have good prospects in practical applications.

  7. Characteristic Finite Difference Methods for Moving Boundary Value Problem of Numerical Simulation of Oil Deposit

    Institute of Scientific and Technical Information of China (English)

    袁益让

    1994-01-01

    The software for oil-gas transport and accumulation is to describe the history of oil-gas transport and accumulation in basin evolution. It is of great value in rational evaluation of prospecting and exploiting oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary value problem. This paper puts forward a kind of characteristic finite difference schemes, and derives from them optimal order estimates in l~2 norm for the error in the approximate solutions. The research is important both theoretically and practically for the model analysis in the field, for model numerical method and for software development.

  8. Different acceptance functions for Multiple Try Metropolis schemes

    CERN Document Server

    Martino, Luca

    2012-01-01

    The Multiple Try Metropolis method is an extension of the classical Metropolis algorithm in which the next state of the chain is chosen among a set of samples, according to normalized weights. In literature, a generalization of this technique has been proposed in Pandolfi et al. (2010) where the weight functions are not analytically specified. In this work, we propose different Multiple Try Metropolis schemes where the analytic form of weight functions can be chosen arbitrarily. The resulting algorithms fulfill the detailed balance condition.

  9. The Laguerre finite difference one-way equation solver

    Science.gov (United States)

    Terekhov, Andrew V.

    2017-05-01

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

  10. On the finite-SNR diversity-multiplexing tradeoff of zero-forcing transmit scheme under secrecy constraint

    KAUST Repository

    Rezki, Zouheir

    2011-06-01

    In this paper, we address the finite Signal-to-Noise Ratio (SNR) Diversity-Multiplexing Tradeoff (DMT) of the Multiple Input Multiple Output (MIMO) wiretap channel, where a Zero-Forcing (ZF) transmit scheme, that intends to send the secret information in the orthogonal space of the eavesdropper channel, is used. First, we introduce the secret multiplexing gain at finite-SNR that generalizes the definition at high-SNR. Then, we provide upper and lower bounds on the outage probability under secrecy constraint, from which secret diversity gain estimates of ZF are derived. Through asymptotic analysis, we show that the upper bound underestimates the secret diversity gain, whereas the lower bound is tight at high-SNR, and thus its related diversity gain estimate is equal to the actual asymptotic secret diversity gain of the Multiple-Input Multiple-Output (MIMO) wiretap channel. © 2011 IEEE.

  11. The mimetic finite difference method for elliptic problems

    CERN Document Server

    Veiga, Lourenço Beirão; Manzini, Gianmarco

    2014-01-01

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

  12. Multi-Dimensional High Order Essentially Non-Oscillatory Finite Difference Methods in Generalized Coordinates

    Science.gov (United States)

    Shu, Chi-Wang

    1998-01-01

    This project is about the development of high order, non-oscillatory type schemes for computational fluid dynamics. Algorithm analysis, implementation, and applications are performed. Collaborations with NASA scientists have been carried out to ensure that the research is relevant to NASA objectives. The combination of ENO finite difference method with spectral method in two space dimension is considered, jointly with Cai [3]. The resulting scheme behaves nicely for the two dimensional test problems with or without shocks. Jointly with Cai and Gottlieb, we have also considered one-sided filters for spectral approximations to discontinuous functions [2]. We proved theoretically the existence of filters to recover spectral accuracy up to the discontinuity. We also constructed such filters for practical calculations.

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

    Science.gov (United States)

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

    2012-09-01

    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.

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

    CERN Document Server

    Bachiri, H; Vázquez, L

    1997-01-01

    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.

  15. THE UPWIND FINITE DIFFERENCE FRACTIONAL STEPS METHOD FOR NONLINEAR COUPLED SYSTEM OF DYNAMICS OF FLUIDS IN POROUS MEDIA

    Institute of Scientific and Technical Information of China (English)

    Yirang YUAN

    2006-01-01

    For nonlinear coupled system of multilayer dynamics of fluids in porous media, the second order and first order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward, and two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates, are adopted. Optimal order estimates in L2 norm are derived to determine the error in the second order approximate solution.This method has already been applied to the numerical simulation of migration-accumulation of oil resources.

  16. Finite Volume schemes on unstructured grids for non-local models: Application to the simulation of heat transport in plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Goudon, Thierry, E-mail: thierry.goudon@inria.fr [Team COFFEE, INRIA Sophia Antipolis Mediterranee (France); Labo. J.A. Dieudonne CNRS and Univ. Nice-Sophia Antipolis (UMR 7351), Parc Valrose, 06108 Nice cedex 02 (France); Parisot, Martin, E-mail: martin.parisot@gmail.com [Project-Team SIMPAF, INRIA Lille Nord Europe, Park Plazza, 40 avenue Halley, F-59650 Villeneuve d' Ascq cedex (France)

    2012-10-15

    In the so-called Spitzer-Haerm regime, equations of plasma physics reduce to a nonlinear parabolic equation for the electronic temperature. Coming back to the derivation of this limiting equation through hydrodynamic regime arguments, one is led to construct a hierarchy of models where the heat fluxes are defined through a non-local relation which can be reinterpreted as well by introducing coupled diffusion equations. We address the question of designing numerical methods to simulate these equations. The basic requirement for the scheme is to be asymptotically consistent with the Spitzer-Haerm regime. Furthermore, the constraints of physically realistic simulations make the use of unstructured meshes unavoidable. We develop a Finite Volume scheme, based on Vertex-Based discretization, which reaches these objectives. We discuss on numerical grounds the efficiency of the method, and the ability of the generalized models in capturing relevant phenomena missed by the asymptotic problem.

  17. The Partition of Unity Method for High-Order Finite Volume Schemes Using Radial Basis Functions Reconstruction

    Institute of Scientific and Technical Information of China (English)

    Serena Morigi; Fiorella Sgallari

    2009-01-01

    This paper introduces the use of partition of unity method for the develop-ment of a high order finite volume discretization scheme on unstructured grids for solv-ing diffusion models based on partial differential equations. The unknown function and its gradient can be accurately reconstructed using high order optimal recovery based on radial basis functions. The methodology proposed is applied to the noise removal prob-lem in functional surfaces and images. Numerical results demonstrate the effectiveness of the new numerical approach and provide experimental order of convergence.

  18. Benchmark Numerical Simulations of Viscoelastic Fluid Flows with an Efficient Integrated Lattice Boltzmann and Finite Volume Scheme

    Directory of Open Access Journals (Sweden)

    Shun Zou

    2015-02-01

    Full Text Available An efficient IBLF-dts scheme is proposed to integrate the bounce-back LBM and FVM scheme to solve the Navier-Stokes equations and the constitutive equation, respectively, for the simulation of viscoelastic fluid flows. In order to improve the efficiency, the bounce-back boundary treatment for LBM is introduced in to improve the grid mapping of LBM and FVM, and the two processes are also decoupled in different time scales according to the relaxation time of polymer and the time scale of solvent Newtonian effect. Critical numerical simulations have been carried out to validate the integrated scheme in various benchmark flows at vanishingly low Reynolds number with open source CFD toolkits. The results show that the numerical solution with IBLF-dts scheme agrees well with the exact solution and the numerical solution with FVM PISO scheme and the efficiency and scalability could be remarkably improved under equivalent configurations.

  19. A method of solving the stiffness problem in Biot's poroelastic equations using a staggered high-order finite-difference

    Institute of Scientific and Technical Information of China (English)

    Zhao Hai-Bo; Wang Xiu-Ming; Chen Hao

    2006-01-01

    In modelling elastic wave propagation in a porous medium, when the ratio between the fluid viscosity and the medium permeability is comparatively large, the stiffness problem of Biot's poroelastic equations will be encountered. In the paper, a partition method is developed to solve the stiffness problem with a staggered high-order finite-difference. The method splits the Biot equations into two systems. One is stiff, and solved analytically, the other is nonstiff,and solved numerically by using a high-order staggered-grid finite-difference scheme. The time step is determined by the staggered finite-difference algorithm in solving the nonstiff equations, thus a coarse time step 05 be employed.Therefore, the computation efficiency and computational stability are improved greatly. Also a perfect by matched layer technology is used in the split method as absorbing boundary conditions. The numerical results are compared with the analytical results and those obtained from the conventional staggered-grid finite-difference method in a homogeneous model, respectively. They are in good agreement with each other. Finally, a slightly more complex model is investigated and compared with related equivalent model to illustrate the good performance of the staggered-grid finite-difference scheme in the partition method.

  20. Crab biodiversity under different management schemes of mangrove ecosystems

    Directory of Open Access Journals (Sweden)

    M. Bandibas

    2016-01-01

    Full Text Available Reforestation is one of the Philippines’ government efforts to restore and rehabilitate degraded mangrove ecosystems. Although there is recovery of the ecosystem in terms of vegetation, the recovery of closely-linked faunal species in terms of community structure is still understudied. This research investigates the community structure of mangrove crabs under two different management schemes: protected mangroves and reforested mangroves. The transect-plot method was employed in each management scheme to quantify the vegetation, crab assemblages and environmental variables. Community composition of crabs and mangrove trees were compared between protected and reforested mangroves using non-metric multi-dimensional scaling and analysis of similarity in PRIMER 6. Chi-squared was used to test the variance of sex ration of the crabs. Canonical Correspondence Analysis was used to determine the relationship between crabs and environmental parameters. A total of twelve species of crabs belonging to six families were identified in protected mangroves while only four species were documented in reforested mangroves. Perisesarma indiarum and Baptozius vinosus were the most dominant species in protected and reforested mangrove, respectively.  Univariate analysis of variance of crab assemblage data revealed significant differences in crab composition and abundance between protected mangroves and from reforested mangroves (P

  1. Difference schemes for fully nonlinear pseudo-parabolic systems with two space dimensions

    Institute of Scientific and Technical Information of China (English)

    周毓麟; 袁光伟

    1996-01-01

    The first boundary value problem for the fully nonlinear pseudoparabolic systems of partial differential equations with two space dimensions by the finite difference method is studied. The existence and uniqueness of the discrete vector solutions for the difference systems are established by the fixed point technique. The stability and convergence of the discrete vector solutions of the difference schemes to the vector solutions of the original boundary problem of the fully nonlinear pseudo-parabolic system are obtained by way of a priori estimation. Here the unique smooth vector solution of the original problems for the fully nonlinear pseudo-parabolic system is assumed. Moreover, by the method used here, it can be proved that analogous results hold for fully nonlinear pseudo-parabolic system with three space dimensions, and improve the known results in the case of one space dimension.

  2. Phase cycling schemes for finite-pulse-RFDR MAS solid state NMR experiments.

    Science.gov (United States)

    Zhang, Rongchun; Nishiyama, Yusuke; Sun, Pingchuan; Ramamoorthy, Ayyalusamy

    2015-03-01

    The finite-pulse radio frequency driven dipolar recoupling (fp-RFDR) pulse sequence is used in 2D homonuclear chemical shift correlation experiments under magic angle spinning (MAS). A recent study demonstrated the advantages of using a short phase cycle, XY4, and its super-cycle, XY4(1)4, for the fp-RFDR pulse sequence employed in 2D (1)H/(1)H single-quantum/single-quantum correlation experiments under ultrafast MAS conditions. In this study, we report a comprehensive analysis on the dipolar recoupling efficiencies of XY4, XY4(1)2, XY4(1)3, XY4(1)4, and XY8(1)4 phase cycles under different spinning speeds ranging from 10 to 100 kHz. The theoretical calculations reveal the presence of second-order terms (T(10)T(2,±2), T(1,±1)T(2,±1), etc.) in the recoupled homonuclear dipolar coupling Hamiltonian only when the basic XY4 phase cycle is utilized, making it advantageous for proton-proton magnetization transfer under ultrafast MAS conditions. It is also found that the recoupling efficiency of fp-RFDR is quite dependent on the duty factor (τ180/τR) as well as on the strength of homonuclear dipolar couplings. The rate of longitudinal magnetization transfer increases linearly with the duty factor of fp-RFDR for all the XY-based phase cycles investigated in this study. Examination of the performances of different phase cycles against chemical shift offset and RF field inhomogeneity effects revealed that XY4(1)4 is the most tolerant phase cycle, while the shortest phase cycle XY4 suppressed the RF field inhomogeneity effects most efficiently under slow spinning speeds. Our results suggest that the difference in the fp-RFDR recoupling efficiencies decreases with the increasing MAS speed, while ultrafast (>60 kHz) spinning speed is advantageous as it recouples a large amount of homonuclear dipolar couplings and therefore enable fast magnetization exchange. The effects of higher-order terms and cross terms between various interactions in the effective Hamiltonian of fp

  3. Energy levels of interacting curved nanomagnets in a frustrated geometry: increasing accuracy when using finite difference methods.

    Science.gov (United States)

    Riahi, H; Montaigne, F; Rougemaille, N; Canals, B; Lacour, D; Hehn, M

    2013-07-24

    The accuracy of finite difference methods is related to the mesh choice and cell size. Concerning the micromagnetism of nano-objects, we show here that discretization issues can drastically affect the symmetry of the problem and therefore the resulting computed properties of lattices of interacting curved nanomagnets. In this paper, we detail these effects for the multi-axis kagome lattice. Using the OOMMF finite difference method, we propose an alternative way of discretizing the nanomagnet shape via a variable moment per cell scheme. This method is shown to be efficient in reducing discretization effects.

  4. Performance Evaluation of Different Data Value Prediction Schemes

    Institute of Scientific and Technical Information of China (English)

    Yong Xiao; Xing-Ming Zhou

    2005-01-01

    Data value prediction has been widely accepted as an effective mechanism to break data hazards for high performance processor design. Several works have reported promising performance potential. However, there is hardly enough information that is presented in a clear way about performance comparison of these prediction mechanisms. This paper investigates the performance impact of four previously proposed value predictors, namely last value predictor, stride value predictor, two-level value predictor and hybrid (stride+two-level) predictor. The impact of misprediction penalty,which has been frequently ignored, is discussed in detail. Several other implementation issues, including instruction window size, issue width and branch predictor are also addressed and simulated. Simulation results indicate that data value predictors act differently under different configurations. In some cases, simpler schemes may be more beneficial than complicated ones.In some particular cases, value prediction may have negative impact on performance.

  5. Conservative high-order-accurate finite-difference methods for curvilinear grids

    Science.gov (United States)

    Rai, Man M.; Chakrvarthy, Sukumar

    1993-01-01

    Two fourth-order-accurate finite-difference methods for numerically solving hyperbolic systems of conservation equations on smooth curvilinear grids are presented. The first method uses the differential form of the conservation equations; the second method uses the integral form of the conservation equations. Modifications to these schemes, which are required near boundaries to maintain overall high-order accuracy, are discussed. An analysis that demonstrates the stability of the modified schemes is also provided. Modifications to one of the schemes to make it total variation diminishing (TVD) are also discussed. Results that demonstrate the high-order accuracy of both schemes are included in the paper. In particular, a Ringleb-flow computation demonstrates the high-order accuracy and the stability of the boundary and near-boundary procedures. A second computation of supersonic flow over a cylinder demonstrates the shock-capturing capability of the TVD methodology. An important contribution of this paper is the dear demonstration that higher order accuracy leads to increased computational efficiency.

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

    NARCIS (Netherlands)

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

    2008-01-01

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

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

    NARCIS (Netherlands)

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

    2008-01-01

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

  8. A Symmetric Characteristic Finite Volume Element Scheme for Nonlinear Convection-Diffusion Problems

    Institute of Scientific and Technical Information of China (English)

    Min Yang; Yi-rang Yuan

    2008-01-01

    In this paper, we implement alternating direction strategy and construct a symmetric FVE scheme for nonlinear convection-diffusion problems. Comparing to general FVE methods, our method has two advantages. First, the coefficient matrices of the discrete schemes will be symmetric even for nonlinear problems.Second, since the solution of the algebraic equations at each time step can be inverted into the solution of several one-dimensional problems, the amount of computation work is smaller. We prove the optimal H1-norm error estimates of order O(△t2 + h) and present some numerical examples at the end of the paper.

  9. A finite area scheme for shallow granular flows on three-dimensional surfaces

    Science.gov (United States)

    Rauter, Matthias

    2017-04-01

    Shallow granular flow models have become a popular tool for the estimation of natural hazards, such as landslides, debris flows and avalanches. The shallowness of the flow allows to reduce the three-dimensional governing equations to a quasi two-dimensional system. Three-dimensional flow fields are replaced by their depth-integrated two-dimensional counterparts, which yields a robust and fast method [1]. A solution for a simple shallow granular flow model, based on the so-called finite area method [3] is presented. The finite area method is an adaption of the finite volume method [4] to two-dimensional curved surfaces in three-dimensional space. This method handles the three dimensional basal topography in a simple way, making the model suitable for arbitrary (but mildly curved) topography, such as natural terrain. Furthermore, the implementation into the open source software OpenFOAM [4] is shown. OpenFOAM is a popular computational fluid dynamics application, designed so that the top-level code mimics the mathematical governing equations. This makes the code easy to read and extendable to more sophisticated models. Finally, some hints on how to get started with the code and how to extend the basic model will be given. I gratefully acknowledge the financial support by the OEAW project "beyond dense flow avalanches". Savage, S. B. & Hutter, K. 1989 The motion of a finite mass of granular material down a rough incline. Journal of Fluid Mechanics 199, 177-215. Ferziger, J. & Peric, M. 2002 Computational methods for fluid dynamics, 3rd edn. Springer. Tukovic, Z. & Jasak, H. 2012 A moving mesh finite volume interface tracking method for surface tension dominated interfacial fluid flow. Computers & fluids 55, 70-84. Weller, H. G., Tabor, G., Jasak, H. & Fureby, C. 1998 A tensorial approach to computational continuum mechanics using object-oriented techniques. Computers in physics 12(6), 620-631.

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

    Directory of Open Access Journals (Sweden)

    Vineet K. Srivastava

    2014-03-01

    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.

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2009-12-19

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

  12. SEISMIC PROPAGATION SIMULATION IN COMPLEX MEDIA WITH NON-RECTANGULAR IRREGULAR-GRID FINITE-DIFFERENCE

    Institute of Scientific and Technical Information of China (English)

    SUN Weitao; YANG Huizhu

    2004-01-01

    This paper presents a finite-difference (FD) method with spatially non-rectangular irregular grids to simulate the elastic wave propagation. Staggered irregular grid finite difference operators with a second-order time and spatial accuracy are used to approximate the velocity-stress elastic wave equations. This method is very simple and the cost of computing time is not much. Complicated geometries like curved thin layers, cased borehole and nonplanar interfaces may be treated with nonrectangular irregular grids in a more flexible way. Unlike the multi-grid scheme, this method requires no interpolation between the fine and coarse grids and all grids are computed at the same spatial iteration. Compared with the rectangular irregular grid FD, the spurious diffractions from "staircase"interfaces can easily be eliminated without using finer grids. Dispersion and stability conditions of the proposed method can be established in a similar form as for the rectangular irregular grid scheme. The Higdon's absorbing boundary condition is adopted to eliminate boundary reflections. Numerical simulations show that this method has satisfactory stability and accuracy in simulating wave propagation near rough solid-fluid interfaces. The computation costs are less than those using a regular grid and rectangular grid FD method.

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

    CERN Document Server

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

    2015-01-01

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

  14. Synchronization of Boolean Networks with Different Update Schemes.

    Science.gov (United States)

    Zhang, Hao; Wang, Xingyuan; Lin, Xiaohui

    2014-01-01

    In this paper, the synchronizations of Boolean networks with different update schemes (synchronized Boolean networks and asynchronous Boolean networks) are investigated. All nodes in Boolean network are represented in terms of semi-tensor product. First, we give the concept of inner synchronization and observe that all nodes in a Boolean network are synchronized with each other. Second, we investigate the outer synchronization between a driving Boolean network and a corresponding response Boolean network. We provide not only the concept of traditional complete synchronization, but also the anti-synchronization and get the anti-synchronization in simulation. Third, we extend the outer synchronization to asynchronous Boolean network and get the complete synchronization between an asynchronous Boolean network and a response Boolean network. Consequently, theorems for synchronization of Boolean networks and asynchronous Boolean networks are derived. Examples are provided to show the correctness of our theorems.

  15. Seismic imaging using finite-differences and parallel computers

    Energy Technology Data Exchange (ETDEWEB)

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

    1997-12-31

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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2009-01-01

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

  17. Acoustic radiation force analysis using finite difference time domain method.

    Science.gov (United States)

    Grinenko, A; Wilcox, P D; Courtney, C R P; Drinkwater, B W

    2012-05-01

    Acoustic radiation force exerted by standing waves on particles is analyzed using a finite difference time domain Lagrangian method. This method allows the acoustic radiation force to be obtained directly from the solution of nonlinear fluid equations, without any assumptions on size or geometry of the particles, boundary conditions, or acoustic field amplitude. The model converges to analytical results in the limit of small particle radii and low field amplitudes, where assumptions within the analytical models apply. Good agreement with analytical and numerical models based on solutions of linear scattering problems is observed for compressible particles, whereas some disagreement is detected when the compressibility of the particles decreases.

  18. A review of current finite difference rotor flow methods

    Science.gov (United States)

    Caradonna, F. X.; Tung, C.

    1986-01-01

    Rotary-wing computational fluid dynamics is reaching a point where many three-dimensional, unsteady, finite-difference codes are becoming available. This paper gives a brief review of five such codes, which treat the small disturbance, conservative and nonconservative full-potential, and Euler flow models. A discussion of the methods of applying these codes to the rotor environment (including wake and trim considerations) is followed by a comparison with various available data. These data include tests of advancing lifting and nonlifting, and hovering model rotors with significant supercritical flow regions. The codes are also compared for computational efficiency.

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

    KAUST Repository

    Al-Hinai, Omar

    2015-01-01

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

  20. A SECOND ORDER DIFFERENCE SCHEME WITH NONUNIFORM MESHES FOR NONLINEAR PARABOLIC SYSTEM

    Institute of Scientific and Technical Information of China (English)

    WAN Zhengsu; CHEN Guangnan

    2003-01-01

    In this paper, a difference scheme with nonuniform meshes is established for the initial-boundary problem of the nonlinear parabolic system. It is proved that the difference scheme is second order convergent in spacestep and timestep.

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

    NARCIS (Netherlands)

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

    2013-01-01

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

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

    NARCIS (Netherlands)

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

    2013-01-01

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

  3. Generalized Subtraction Schemes for the Difference Formulation in Radiation Transport

    Energy Technology Data Exchange (ETDEWEB)

    Luu, T; Brooks, E; Szoke, A

    2008-07-25

    In the difference formulation for the transport of thermally emitted photons, the photon intensity is defined relative to a reference field, the black body at the local material temperature. This choice of reference field removes the cancellation between thermal emission and absorption that is responsible for noise in the Monte Carlo solution of thick systems, but introduces time and space derivative source terms that can not be determined until the end of the time step. It can also lead to noise induced crashes under certain conditions where the real physical photon intensity differs strongly from a black body at the local material temperature. In this report, we consider a difference formulation relative to the material temperature at the beginning of the time step, and in the situations where the radiation intensity more closely follows a temperature other than the local material temperature, that temperature. The result is a method where iterative solution of the material energy equation is efficient and noise induced crashes are avoided. To support our contention that the resulting generalized subtraction scheme is robust, and therefore suitable for practical use, we perform a stability analysis in the thick limit where instabilities usually occur.

  4. Analysis of developing laminar flows in circular pipes using a higher-order finite-difference technique

    Science.gov (United States)

    Gladden, Herbert J.; Ko, Ching L.; Boddy, Douglas E.

    1995-01-01

    A higher-order finite-difference technique is developed to calculate the developing-flow field of steady incompressible laminar flows in the entrance regions of circular pipes. Navier-Stokes equations governing the motion of such a flow field are solved by using this new finite-difference scheme. This new technique can increase the accuracy of the finite-difference approximation, while also providing the option of using unevenly spaced clustered nodes for computation such that relatively fine grids can be adopted for regions with large velocity gradients. The velocity profile at the entrance of the pipe is assumed to be uniform for the computation. The velocity distribution and the surface pressure drop of the developing flow then are calculated and compared to existing experimental measurements reported in the literature. Computational results obtained are found to be in good agreement with existing experimental correlations and therefore, the reliability of the new technique has been successfully tested.

  5. OPTIMIZATION OF THE TEMPERATURE CONTROL SCHEME FOR ROLLER COMPACTED CONCRETE DAMS BASED ON FINITE ELEMENT AND SENSITIVITY ANALYSIS METHODS

    Directory of Open Access Journals (Sweden)

    Huawei Zhou

    2016-10-01

    Full Text Available Achieving an effective combination of various temperature control measures is critical for temperature control and crack prevention of concrete dams. This paper presents a procedure for optimizing the temperature control scheme of roller compacted concrete (RCC dams that couples the finite element method (FEM with a sensitivity analysis method. In this study, seven temperature control schemes are defined according to variations in three temperature control measures: concrete placement temperature, water-pipe cooling time, and thermal insulation layer thickness. FEM is employed to simulate the equivalent temperature field and temperature stress field obtained under each of the seven designed temperature control schemes for a typical overflow dam monolith based on the actual characteristics of a RCC dam located in southwestern China. A sensitivity analysis is subsequently conducted to investigate the degree of influence each of the three temperature control measures has on the temperature field and temperature tensile stress field of the dam. Results show that the placement temperature has a substantial influence on the maximum temperature and tensile stress of the dam, and that the placement temperature cannot exceed 15 °C. The water-pipe cooling time and thermal insulation layer thickness have little influence on the maximum temperature, but both demonstrate a substantial influence on the maximum tensile stress of the dam. The thermal insulation thickness is significant for reducing the probability of cracking as a result of high thermal stress, and the maximum tensile stress can be controlled under the specification limit with a thermal insulation layer thickness of 10 cm. Finally, an optimized temperature control scheme for crack prevention is obtained based on the analysis results.

  6. Finite-difference calculation of traveltimes based on rectangular grid

    Institute of Scientific and Technical Information of China (English)

    李振春; 刘玉莲; 张建磊; 马在田; 王华忠

    2004-01-01

    To the most of velocity fields, the traveltimes of the first break that seismic waves propagate along rays can be computed on a 2-D or 3-D numerical grid by finite-difference extrapolation. Under ensuring accuracy, to improve calculating efficiency and adaptability, the calculation method of first-arrival traveltime of finite-difference is derived based on any rectangular grid and a local plane wavefront approximation. In addition, head waves and scattering waves are properly treated and shadow and caustic zones cannot be encountered, which appear in traditional ray-tracing. The testes of two simple models and the complex Marmousi model show that the method has higher accuracy and adaptability to complex structure with strong vertical and lateral velocity variation, and Kirchhoff prestack depth migration based on this method can basically achieve the position imaging effects of wave equation prestack depth migration in major structures and targets. Because of not taking account of the later arrivals energy, the effect of its amplitude preservation is worse than that by wave equation method, but its computing efficiency is higher than that by total Green's function method and wave equation method.

  7. Least-squares finite-element scheme for the lattice Boltzmann method on an unstructured mesh.

    Science.gov (United States)

    Li, Yusong; LeBoeuf, Eugene J; Basu, P K

    2005-10-01

    A numerical model of the lattice Boltzmann method (LBM) utilizing least-squares finite-element method in space and the Crank-Nicolson method in time is developed. This method is able to solve fluid flow in domains that contain complex or irregular geometric boundaries by using the flexibility and numerical stability of a finite-element method, while employing accurate least-squares optimization. Fourth-order accuracy in space and second-order accuracy in time are derived for a pure advection equation on a uniform mesh; while high stability is implied from a von Neumann linearized stability analysis. Implemented on unstructured mesh through an innovative element-by-element approach, the proposed method requires fewer grid points and less memory compared to traditional LBM. Accurate numerical results are presented through two-dimensional incompressible Poiseuille flow, Couette flow, and flow past a circular cylinder. Finally, the proposed method is applied to estimate the permeability of a randomly generated porous media, which further demonstrates its inherent geometric flexibility.

  8. On the difference between permutation poynomials over finite fields

    DEFF Research Database (Denmark)

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

    2017-01-01

    The well-known Chowla and Zassenhaus conjecture, proven by Cohen in 1990, states that if p > (d 2 − 3d + 4)2 , then there is no complete mapping polynomial f in Fp[x] of degree d ≥ 2. For arbitrary finite fields Fq, a similar non-existence result is obtained recently by I¸sık, Topuzo˘glu and Wint......The well-known Chowla and Zassenhaus conjecture, proven by Cohen in 1990, states that if p > (d 2 − 3d + 4)2 , then there is no complete mapping polynomial f in Fp[x] of degree d ≥ 2. For arbitrary finite fields Fq, a similar non-existence result is obtained recently by I¸sık, Topuzo......˘glu and Winterhof in terms of the Carlitz rank of f. Cohen, Mullen and Shiue generalized the Chowla-Zassenhaus-Cohen Theorem significantly in 1995, by considering differences of permutation polynomials. More precisely, they showed that if f and f + g are both permutation polynomials of degree d ≥ 2 over Fp, with p...

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

    Science.gov (United States)

    Itzá, Reymundo; Iturrarán-Viveros, Ursula; Parra, Jorge O.

    2016-08-01

    Numerical modeling of seismic waves in heterogeneous porous reservoir rocks is an important tool for the interpretation of seismic surveys in reservoir engineering. We apply globally optimal implicit staggered-grid finite differences (FD) to model 2-D wave propagation in heterogeneous poroelastic media at a low-frequency range (<10 kHz). We validate the numerical solution by comparing it to an analytical-transient solution obtaining clear seismic wavefields including fast P and slow P and S waves (for a porous media saturated with fluid). The numerical dispersion and stability conditions are derived using von Neumann analysis, showing that over a wide range of porous materials the Courant condition governs the stability and this optimal implicit scheme improves the stability of explicit schemes. High-order explicit FD can be replaced by some lower order optimal implicit FD so computational cost will not be as expensive while maintaining the accuracy. Here, we compute weights for the optimal implicit FD scheme to attain an accuracy of γ = 10-8. The implicit spatial differentiation involves solving tridiagonal linear systems of equations through Thomas' algorithm.

  10. Finite-difference modeling of Biot's poroelastic equations across all frequencies

    Energy Technology Data Exchange (ETDEWEB)

    Masson, Y.J.; Pride, S.R.

    2009-10-22

    An explicit time-stepping finite-difference scheme is presented for solving Biot's equations of poroelasticity across the entire band of frequencies. In the general case for which viscous boundary layers in the pores must be accounted for, the time-domain version of Darcy's law contains a convolution integral. It is shown how to efficiently and directly perform the convolution so that the Darcy velocity can be properly updated at each time step. At frequencies that are low enough compared to the onset of viscous boundary layers, no memory terms are required. At higher frequencies, the number of memory terms required is the same as the number of time points it takes to sample accurately the wavelet being used. In practice, we never use more than 20 memory terms and often considerably fewer. Allowing for the convolution makes the scheme even more stable (even larger time steps might be used) than it is when the convolution is entirely neglected. The accuracy of the scheme is confirmed by comparing numerical examples to exact analytic results.

  11. Comparing Sediment Yield Predictions from Different Hydrologic Modeling Schemes

    Science.gov (United States)

    Dahl, T. A.; Kendall, A. D.; Hyndman, D. W.

    2015-12-01

    Sediment yield, or the delivery of sediment from the landscape to a river, is a difficult process to accurately model. It is primarily a function of hydrology and climate, but influenced by landcover and the underlying soils. These additional factors make it much more difficult to accurately model than water flow alone. It is not intuitive what impact different hydrologic modeling schemes may have on the prediction of sediment yield. Here, two implementations of the Modified Universal Soil Loss Equation (MUSLE) are compared to examine the effects of hydrologic model choice. Both the Soil and Water Assessment Tool (SWAT) and the Landscape Hydrology Model (LHM) utilize the MUSLE for calculating sediment yield. SWAT is a lumped parameter hydrologic model developed by the USDA, which is commonly used for predicting sediment yield. LHM is a fully distributed hydrologic model developed primarily for integrated surface and groundwater studies at the watershed to regional scale. SWAT and LHM models were developed and tested for two large, adjacent watersheds in the Great Lakes region; the Maumee River and the St. Joseph River. The models were run using a variety of single model and ensemble downscaled climate change scenarios from the Coupled Model Intercomparison Project 5 (CMIP5). The initial results of this comparison are discussed here.

  12. Mapping of the Universe of Knowledge in Different Classification Schemes

    Directory of Open Access Journals (Sweden)

    M. P. Satija

    2017-06-01

    Full Text Available Given the variety of approaches to mapping the universe of knowledge that have been presented and discussed in the literature, the purpose of this paper is to systematize their main principles and their applications in the major general modern library classification schemes. We conducted an analysis of the literature on classification and the main classification systems, namely Dewey/Universal Decimal Classification, Cutter’s Expansive Classification, Subject Classification of J.D. Brown, Colon Classification, Library of Congress Classification, Bibliographic Classification, Rider’s International Classification, Bibliothecal Bibliographic Klassification (BBK, and Broad System of Ordering (BSO. We conclude that the arrangement of the main classes can be done following four principles that are not mutually exclusive: ideological principle, social purpose principle, scientific order, and division by discipline. The paper provides examples and analysis of each system. We also conclude that as knowledge is ever-changing, classifications also change and present a different structure of knowledge depending upon the society and time of their design.

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

    Energy Technology Data Exchange (ETDEWEB)

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

    1994-12-31

    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.

  14. Computationally efficient finite-difference modal method for the solution of Maxwell's equations.

    Science.gov (United States)

    Semenikhin, Igor; Zanuccoli, Mauro

    2013-12-01

    In this work, a new implementation of the finite-difference (FD) modal method (FDMM) based on an iterative approach to calculate the eigenvalues and corresponding eigenfunctions of the Helmholtz equation is presented. Two relevant enhancements that significantly increase the speed and accuracy of the method are introduced. First of all, the solution of the complete eigenvalue problem is avoided in favor of finding only the meaningful part of eigenmodes by using iterative methods. Second, a multigrid algorithm and Richardson extrapolation are implemented. Simultaneous use of these techniques leads to an enhancement in terms of accuracy, which allows a simple method such as the FDMM with a typical three-point difference scheme to be significantly competitive with an analytical modal method.

  15. Weighted Average Finite Difference Methods for Fractional Reaction-Subdiffusion Equation

    Directory of Open Access Journals (Sweden)

    Nasser Hassen SWEILAM

    2014-04-01

    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

  16. Incompressible turbulent flow calculation in body-fitted coordinates using block-implicit finite difference method

    Science.gov (United States)

    Hu, Zeming; Chen, Xuechun; Wu, Yulin

    The block-implicit finite-difference method is used to calculate 3D incompressible turbulent flows in the body-fitted coordinate system. In the numerical discretization the hybrid difference scheme is used to treat Reynolds-averaged Navier-Stokes equations. The iterative solution of velocities and pressure on the flow field is obtained by solving simultaneously the Reynolds-averaged N-S equations and continuity equation for each cell. In the iterative process the Gauss-Seidel method is used to solve nonlinear algebraic equations. The turbulent flow is simulated by the k-epsilon turbulence modeling in conjunction with Reynolds equations. The turbulent flow of a curved duct with square cross sections is treated in detail.

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

    Energy Technology Data Exchange (ETDEWEB)

    Saas, L.

    2004-05-01

    This Thesis deals with sedimentary basin modeling whose goal is the prediction through geological times of the localizations and appraisal of hydrocarbons quantities present in the ground. Due to the natural and evolutionary decomposition of the sedimentary basin in blocks and stratigraphic layers, domain decomposition methods are requested to simulate flows of waters and of hydrocarbons in the ground. Conservations laws are used to model the flows in the ground and form coupled partial differential equations which must be discretized by finite volume method. In this report we carry out a study on finite volume methods on non-matching grids solved by domain decomposition methods. We describe a family of finite volume schemes on non-matching grids and we prove that the associated global discretized problem is well posed. Then we give an error estimate. We give two examples of finite volume schemes on non matching grids and the corresponding theoretical results (Constant scheme and Linear scheme). Then we present the resolution of the global discretized problem by a domain decomposition method using arbitrary interface conditions (for example Robin conditions). Finally we give numerical results which validate the theoretical results and study the use of finite volume methods on non-matching grids for basin modeling. (author)

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

    Energy Technology Data Exchange (ETDEWEB)

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

    1994-11-15

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

  19. Finite-difference modeling of commercial aircraft using TSAR

    Energy Technology Data Exchange (ETDEWEB)

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

    1994-11-15

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

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

    CERN Document Server

    Taflove, Allen

    2005-01-01

    This extensively revised and expanded third edition of the Artech House bestseller, Computational Electrodynamics: The Finite-Difference Time-Domain Method, offers engineers the most up-to-date and definitive resource on this critical method for solving Maxwell's equations. The method helps practitioners design antennas, wireless communications devices, high-speed digital and microwave circuits, and integrated optical devices with unsurpassed efficiency. There has been considerable advancement in FDTD computational technology over the past few years, and the third edition brings professionals the very latest details with entirely new chapters on important techniques, major updates on key topics, and new discussions on emerging areas such as nanophotonics. What's more, to supplement the third edition, the authors have created a Web site with solutions to problems, downloadable graphics and videos, and updates, making this new edition the ideal textbook on the subject as well.

  1. A finite-difference method for transonic airfoil design.

    Science.gov (United States)

    Steger, J. L.; Klineberg, J. M.

    1972-01-01

    This paper describes an inverse method for designing transonic airfoil sections or for modifying existing profiles. Mixed finite-difference procedures are applied to the equations of transonic small disturbance theory to determine the airfoil shape corresponding to a given surface pressure distribution. The equations are solved for the velocity components in the physical domain and flows with embedded shock waves can be calculated. To facilitate airfoil design, the method allows alternating between inverse and direct calculations to obtain a profile shape that satisfies given geometric constraints. Examples are shown of the application of the technique to improve the performance of several lifting airfoil sections. The extension of the method to three dimensions for designing supercritical wings is also indicated.

  2. Parallel finite-difference time-domain method

    CERN Document Server

    Yu, Wenhua

    2006-01-01

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

  3. Application of a new finite difference algorithm for computational aeroacoustics

    Science.gov (United States)

    Goodrich, John W.

    1995-01-01

    Acoustic problems have become extremely important in recent years because of research efforts such as the High Speed Civil Transport program. Computational aeroacoustics (CAA) requires a faithful representation of wave propagation over long distances, and needs algorithms that are accurate and boundary conditions that are unobtrusive. This paper applies a new finite difference method and boundary algorithm to the Linearized Euler Equations (LEE). The results demonstrate the ability of a new fourth order propagation algorithm to accurately simulate the genuinely multidimensional wave dynamics of acoustic propagation in two space dimensions with the LEE. The results also show the ability of a new outflow boundary condition and fourth order algorithm to pass the evolving solution from the computational domain with no perceptible degradation of the solution remaining within the domain.

  4. Finite difference methods for coupled flow interaction transport models

    Directory of Open Access Journals (Sweden)

    Shelly McGee

    2009-04-01

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

  5. A comparison of finite-difference and finite-element methods for calculating free edge stresses in composites

    Science.gov (United States)

    Bauld, N. R., Jr.; Goree, J. G.; Tzeng, L.-S.

    1985-01-01

    It is pointed out that edge delamination is a serious failure mechanism for laminated composite materials. Various numerical methods have been utilized in attempts to calculate the interlaminar stress components which precede delamination in a laminate. There are, however, discrepancies regarding the results provided by different methods, taking into account a finite-difference procedure, a perturbation procedure, and finite element approaches. The present investigation has the objective to assess the capacity of a finite difference method to predict the character and magnitude of the interlaminar stress distributions near an interface corner. A second purpose of the investigation is to determine if predictions by finite element method in-plane, interlaminar stress components near an interface corner represent actual laminate behavior.

  6. A NURBS-based generalized finite element scheme for 3D simulation of heterogeneous materials

    Science.gov (United States)

    Safdari, Masoud; Najafi, Ahmad R.; Sottos, Nancy R.; Geubelle, Philippe H.

    2016-08-01

    A 3D NURBS-based interface-enriched generalized finite element method (NIGFEM) is introduced to solve problems with complex discontinuous gradient fields observed in the analysis of heterogeneous materials. The method utilizes simple structured meshes of hexahedral elements that do not necessarily conform to the material interfaces in heterogeneous materials. By avoiding the creation of conforming meshes used in conventional FEM, the NIGFEM leads to significant simplification of the mesh generation process. To achieve an accurate solution in elements that are crossed by material interfaces, the NIGFEM utilizes Non-Uniform Rational B-Splines (NURBS) to enrich the solution field locally. The accuracy and convergence of the NIGFEM are tested by solving a benchmark problem. We observe that the NIGFEM preserves an optimal rate of convergence, and provides additional advantages including the accurate capture of the solution fields in the vicinity of material interfaces and the built-in capability for hierarchical mesh refinement. Finally, the use of the NIGFEM in the computational analysis of heterogeneous materials is discussed.

  7. A Drift-Diffusion-Reaction Model for Excitonic Photovoltaic Bilayers: Asymptotic Analysis and A 2-D HDG Finite-Element Scheme

    CERN Document Server

    Brinkman, Daniel; Markowich, Peter A; Wolfram, Marie-Therese

    2012-01-01

    We present and discuss a mathematical model for the operation of bilayer organic photovoltaic devices. Our model couples drift-diffusion-recombination equations for the charge carriers (specifically, electrons and holes) with a reaction-diffusion equation for the excitons/ polaron pairs and Poisson's equation for the self-consistent electrostatic potential. The material difference (i.e. the HOMO/LUMO gap) of the two organic substrates forming the bilayer device are included as a work-function potential. Firstly, we perform an asymptotic analysis of the scaled one-dimensional stationary state system i) with focus on the dynamics on the interface and ii) with the goal of simplifying the bulk dynamics away for the interface. Secondly, we present a twodimensional Hybrid Discontinuous Galerkin Finite Element numerical scheme which is very well suited to resolve i) the material changes ii) the resulting strong variation over the interface and iii) the necessary upwinding in the discretization of drift-diffusion equ...

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

    Science.gov (United States)

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

    2013-01-01

    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.

  9. High-order weighted essentially nonoscillatory finite-difference formulation of the lattice Boltzmann method in generalized curvilinear coordinates

    Science.gov (United States)

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

    2017-02-01

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

  10. High-order weighted essentially nonoscillatory finite-difference formulation of the lattice Boltzmann method in generalized curvilinear coordinates.

    Science.gov (United States)

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

    2017-02-01

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

  11. Algorithm composition scheme for problems in composite domains based on the difference potential method

    Science.gov (United States)

    Ryaben'kii, V. S.; Turchaninov, V. I.; Epshteyn, Ye. Yu.

    2006-10-01

    An algorithm composition scheme for the numerical solution of boundary value problems in composite domains is proposed and illustrated using an example. The scheme requires neither difference approximations of the boundary conditions nor matching conditions on the boundary between the subdomains. The scheme is suited for multiprocessor computers.

  12. Full-vectorial analysis of optical waveguides by the finite difference method based on polynomial interpolation

    Institute of Scientific and Technical Information of China (English)

    Xiao Jin-Biao; Zhang Ming-De; Sun Xiao-Han

    2006-01-01

    Based on the polynomial interpolation, a new finite difference (FD) method in solving the full-vectorial guidedmodes for step-index optical waveguides is proposed. The discontinuities of the normal components of the electric field across abrupt dielectric interfaces are considered in the absence of the limitations of scalar and semivectorial approximation, and the present FD scheme can be applied to both uniform and non-uniform mesh grids. The modal propagation constants and field distributions for buried rectangular waveguides and optical rib waveguides are presented. The hybrid nature of the vectorial modes is demonstrated and the singular behaviours of the minor field components in the corners are observed. Moreover, solutions are in good agreement with those published early, which tests the validity of the present approach.

  13. Upwind finite difference method for miscible oil and water displacement problem with moving boundary values

    Institute of Scientific and Technical Information of China (English)

    Yi-rang YUAN; Chang-feng LI; Cheng-shun YANG; Yu-ji HAN

    2009-01-01

    The research of the miscible oil and water displacement problem with moving boundary values is of great value to the history of oil-gas transport and accumulation in the basin evolution as well as to the rational evaluation in prospecting and exploiting oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. For the two-dimensional bounded region, the upwind finite difference schemes are proposed. Some techniques, such as the calculus of variations, the change of variables, and the theory of a priori estimates, are used. The optimal order l2-norm estimates are derived for the errors in the approximate solutions. The research is important both theoretically and practically for the model analysis in the field, the model numerical method, and the software development.

  14. Finite difference method and analysis for three-dimensional semiconductor device of heat conduction

    Institute of Scientific and Technical Information of China (English)

    袁益让

    1996-01-01

    The mathematical model of the three-dimensional semiconductor devices of heat conduction is described by a system of four quasilinear partial differential equations for initial boundary value problem. One equation in elliptic form is for the electric potential; two equations of convection-dominated diffusion type are for the electron and hole concentration; and one heat conduction equation is for temperature. Characteristic finite difference schemes for two kinds of boundary value problems are put forward. By using the thick and thin grids to form a complete set and treating the product threefold-quadratic interpolation, variable time step method with the boundary condition, calculus of variations and the theory of prior estimates and techniques, the optimal error estimates in L2 norm are derived in the approximate solutions.

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

    Directory of Open Access Journals (Sweden)

    M.A. Maâtoug

    2016-09-01

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

  16. Parallel Adaptive Mesh Refinement for High-Order Finite-Volume Schemes in Computational Fluid Dynamics

    Science.gov (United States)

    Schwing, Alan Michael

    For computational fluid dynamics, the governing equations are solved on a discretized domain of nodes, faces, and cells. The quality of the grid or mesh can be a driving source for error in the results. While refinement studies can help guide the creation of a mesh, grid quality is largely determined by user expertise and understanding of the flow physics. Adaptive mesh refinement is a technique for enriching the mesh during a simulation based on metrics for error, impact on important parameters, or location of important flow features. This can offload from the user some of the difficult and ambiguous decisions necessary when discretizing the domain. This work explores the implementation of adaptive mesh refinement in an implicit, unstructured, finite-volume solver. Consideration is made for applying modern computational techniques in the presence of hanging nodes and refined cells. The approach is developed to be independent of the flow solver in order to provide a path for augmenting existing codes. It is designed to be applicable for unsteady simulations and refinement and coarsening of the grid does not impact the conservatism of the underlying numerics. The effect on high-order numerical fluxes of fourth- and sixth-order are explored. Provided the criteria for refinement is appropriately selected, solutions obtained using adapted meshes have no additional error when compared to results obtained on traditional, unadapted meshes. In order to leverage large-scale computational resources common today, the methods are parallelized using MPI. Parallel performance is considered for several test problems in order to assess scalability of both adapted and unadapted grids. Dynamic repartitioning of the mesh during refinement is crucial for load balancing an evolving grid. Development of the methods outlined here depend on a dual-memory approach that is described in detail. Validation of the solver developed here against a number of motivating problems shows favorable

  17. A coarse-mesh nodal method-diffusive-mesh finite difference method

    Energy Technology Data Exchange (ETDEWEB)

    Joo, H.; Nichols, W.R.

    1994-05-01

    Modern nodal methods have been successfully used for conventional light water reactor core analyses where the homogenized, node average cross sections (XSs) and the flux discontinuity factors (DFs) based on equivalence theory can reliably predict core behavior. For other types of cores and other geometries characterized by tightly-coupled, heterogeneous core configurations, the intranodal flux shapes obtained from a homogenized nodal problem may not accurately portray steep flux gradients near fuel assembly interfaces or various reactivity control elements. This may require extreme values of DFs (either very large, very small, or even negative) to achieve a desired solution accuracy. Extreme values of DFs, however, can disrupt the convergence of the iterative methods used to solve for the node average fluxes, and can lead to a difficulty in interpolating adjacent DF values. Several attempts to remedy the problem have been made, but nothing has been satisfactory. A new coarse-mesh nodal scheme called the Diffusive-Mesh Finite Difference (DMFD) technique, as contrasted with the coarse-mesh finite difference (CMFD) technique, has been developed to resolve this problem. This new technique and the development of a few-group, multidimensional kinetics computer program are described in this paper.

  18. Finite difference methods for option pricing under Lévy processes: Wiener-Hopf factorization approach.

    Science.gov (United States)

    Kudryavtsev, Oleg

    2013-01-01

    In the paper, we consider the problem of pricing options in wide classes of Lévy processes. We propose a general approach to the numerical methods based on a finite difference approximation for the generalized Black-Scholes equation. The goal of the paper is to incorporate the Wiener-Hopf factorization into finite difference methods for pricing options in Lévy models with jumps. The method is applicable for pricing barrier and American options. The pricing problem is reduced to the sequence of linear algebraic systems with a dense Toeplitz matrix; then the Wiener-Hopf factorization method is applied. We give an important probabilistic interpretation based on the infinitely divisible distributions theory to the Laurent operators in the correspondent factorization identity. Notice that our algorithm has the same complexity as the ones which use the explicit-implicit scheme, with a tridiagonal matrix. However, our method is more accurate. We support the advantage of the new method in terms of accuracy and convergence by using numerical experiments.

  19. Two-dimensional time-domain finite-difference modeling for viscoelastic seismic wave propagation

    Science.gov (United States)

    Fan, Na; Zhao, Lian-Feng; Xie, Xiao-Bi; Ge, Zengxi; Yao, Zhen-Xing

    2016-09-01

    Real Earth media are not perfectly elastic. Instead, they attenuate propagating mechanical waves. This anelastic phenomenon in wave propagation can be modeled by a viscoelastic mechanical model consisting of several standard linear solids. Using this viscoelastic model, we approximate a constant Q over a frequency band of interest. We use a four-element viscoelastic model with a trade-off between accuracy and computational costs to incorporate Q into 2-D time-domain first-order velocity-stress wave equations. To improve the computational efficiency, we limit the Q in the model to a list of discrete values between 2 and 1000. The related stress and strain relaxation times that characterize the viscoelastic model are pre-calculated and stored in a database for use by the finite-difference calculation. A viscoelastic finite-difference scheme that is second order in time and fourth order in space is developed based on the MacCormack algorithm. The new method is validated by comparing the numerical result with analytical solutions that are calculated using the generalized reflection/transmission coefficient method. The synthetic seismograms exhibit greater than 95 per cent consistency in a two-layer viscoelastic model. The dispersion generated from the simulation is consistent with the Kolsky-Futterman dispersion relationship.

  20. Direct method of solving finite difference nonlinear equations for multicomponent diffusion in a gas centrifuge

    Energy Technology Data Exchange (ETDEWEB)

    Potemki, Valeri G. [Moscow State Engineering Physics Institute (Technical University), Moscow (Russian Federation). Dept. of Automatics and Electronics; Borisevich, Valentine D.; Yupatov, Sergei V. [Moscow State Enineering Physics Institute (Technical University), Moscow (Russian Federation). Dept. of Technical Physics

    1996-12-31

    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) 7 refs., 10 figs.

  1. Simple High-order Galerkin Finite Element Scheme for the Investigation of Both Guided and Leaky Modes in Anisotropic Planar Waveguides

    NARCIS (Netherlands)

    Uranus, H.P.; Hoekstra, H.J.W.M.; Groesen, van E.

    2004-01-01

    A simple high-order Galerkin finite element scheme is formulated to compute both the guided and leaky modes of anisotropic planar waveguides with a diagonal permittivity tensor. Transparent boundary conditions derived from the Sommerfield radiation conditions are used to model the fields at the comp

  2. A finite difference model for free surface gravity drainage

    Energy Technology Data Exchange (ETDEWEB)

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

    1993-09-01

    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.

  3. Experiments with explicit filtering for LES using a finite-difference method

    Science.gov (United States)

    Lund, T. S.; Kaltenbach, H. J.

    1995-01-01

    The equations for large-eddy simulation (LES) are derived formally by applying a spatial filter to the Navier-Stokes equations. The filter width as well as the details of the filter shape are free parameters in LES, and these can be used both to control the effective resolution of the simulation and to establish the relative importance of different portions of the resolved spectrum. An analogous, but less well justified, approach to filtering is more or less universally used in conjunction with LES using finite-difference methods. In this approach, the finite support provided by the computational mesh as well as the wavenumber-dependent truncation errors associated with the finite-difference operators are assumed to define the filter operation. This approach has the advantage that it is also 'automatic' in the sense that no explicit filtering: operations need to be performed. While it is certainly convenient to avoid the explicit filtering operation, there are some practical considerations associated with finite-difference methods that favor the use of an explicit filter. Foremost among these considerations is the issue of truncation error. All finite-difference approximations have an associated truncation error that increases with increasing wavenumber. These errors can be quite severe for the smallest resolved scales, and these errors will interfere with the dynamics of the small eddies if no corrective action is taken. Years of experience at CTR with a second-order finite-difference scheme for high Reynolds number LES has repeatedly indicated that truncation errors must be minimized in order to obtain acceptable simulation results. While the potential advantages of explicit filtering are rather clear, there is a significant cost associated with its implementation. In particular, explicit filtering reduces the effective resolution of the simulation compared with that afforded by the mesh. The resolution requirements for LES are usually set by the need to capture

  4. The finite difference method for the three-dimensional nonlinear coupled system of dynamics of fluids in porous media

    Institute of Scientific and Technical Information of China (English)

    YUAN; Yirang

    2006-01-01

    For the three-dimensional coupled system of multilayer dynamics of fluids in porous media, the second-order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Some techniques, such as calculus of variations, energy method,multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in l2 norm are derived to determine the error in the second-order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources.

  5. Crank-Nicholson difference scheme for a stochastic parabolic equation with a dependent operator coefficient

    Science.gov (United States)

    Ashyralyev, Allaberen; Okur, Ulker

    2016-08-01

    In the present paper, the Crank-Nicolson difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is considered. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, convergence estimates for the solution of difference schemes for the numerical solution of three mixed problems for parabolic equations are obtained. The numerical results are given.

  6. QED multi-dimensional vacuum polarization finite-difference solver

    Science.gov (United States)

    Carneiro, Pedro; Grismayer, Thomas; Silva, Luís; Fonseca, Ricardo

    2015-11-01

    The Extreme Light Infrastructure (ELI) is expected to deliver peak intensities of 1023 - 1024 W/cm2 allowing to probe nonlinear Quantum Electrodynamics (QED) phenomena in an unprecedented regime. Within the framework of QED, the second order process of photon-photon scattering leads to a set of extended Maxwell's equations [W. Heisenberg and H. Euler, Z. Physik 98, 714] effectively creating nonlinear polarization and magnetization terms that account for the nonlinear response of the vacuum. To model this in a self-consistent way, we present a multi dimensional generalized Maxwell equation finite difference solver with significantly enhanced dispersive properties, which was implemented in the OSIRIS particle-in-cell code [R.A. Fonseca et al. LNCS 2331, pp. 342-351, 2002]. We present a detailed numerical analysis of this electromagnetic solver. As an illustration of the properties of the solver, we explore several examples in extreme conditions. We confirm the theoretical prediction of vacuum birefringence of a pulse propagating in the presence of an intense static background field [arXiv:1301.4918 [quant-ph

  7. Contraction preconditioner in finite-difference electromagnetic modeling

    Science.gov (United States)

    Yavich, Nikolay; Zhdanov, Michael S.

    2016-06-01

    This paper introduces a novel approach to constructing an effective preconditioner for finite-difference (FD) electromagnetic modeling in geophysical applications. This approach is based on introducing an FD contraction operator, similar to one developed for integral equation formulation of Maxwell's equation. The properties of the FD contraction operator were established using an FD analog of the energy equality for the anomalous electromagnetic field. A new preconditioner uses a discrete Green's function of a 1D layered background conductivity. We also developed the formulas for an estimation of the condition number of the system of FD equations preconditioned with the introduced FD contraction operator. Based on this estimation, we have established that for high contrasts, the condition number is bounded by the maximum conductivity contrast between the background conductivity and actual conductivity. When there are both resistive and conductive anomalies relative to the background, the new preconditioner is advantageous over using the 1D discrete Green's function directly. In our numerical experiments with both resistive and conductive anomalies, for a land geoelectrical model with 1:10 contrast, the method accelerates convergence of an iterative method (BiCGStab) by factors of 2 to 2.5, and in a marine example with 1:50 contrast, by a factor of 4.6, compared to direct use of the discrete 1D Green's function as a preconditioner.

  8. Contraction pre-conditioner in finite-difference electromagnetic modelling

    Science.gov (United States)

    Yavich, Nikolay; Zhdanov, Michael S.

    2016-09-01

    This paper introduces a novel approach to constructing an effective pre-conditioner for finite-difference (FD) electromagnetic modelling in geophysical applications. This approach is based on introducing an FD contraction operator, similar to one developed for integral equation formulation of Maxwell's equation. The properties of the FD contraction operator were established using an FD analogue of the energy equality for the anomalous electromagnetic field. A new pre-conditioner uses a discrete Green's function of a 1-D layered background conductivity. We also developed the formulae for an estimation of the condition number of the system of FD equations pre-conditioned with the introduced FD contraction operator. Based on this estimation, we have established that the condition number is bounded by the maximum conductivity contrast between the background conductivity and actual conductivity. When there are both resistive and conductive anomalies relative to the background, the new pre-conditioner is advantageous over using the 1-D discrete Green's function directly. In our numerical experiments with both resistive and conductive anomalies, for a land geoelectrical model with 1:10 contrast, the method accelerates convergence of an iterative method (BiCGStab) by factors of 2-2.5, and in a marine example with 1:50 contrast, by a factor of 4.6, compared to direct use of the discrete 1-D Green's function as a pre-conditioner.

  9. LONG-TIME BEHAVIOR OF FINITE DIFFERENCE SOLUTIONS OF THREE-DIMENSIONAL NONLINEAR SCHR(O)DINGER EQUATION WITH WEAKLY DAMPED

    Institute of Scientific and Technical Information of China (English)

    Fa-yong Zhang

    2004-01-01

    The three-dimensional nonlinear Schrodinger equation with weakly damped that possesses a global attractor are considered. The dynamical properties of the discrete dynamical system which generate by a class of finite difference scheme are analysed. The existence of global attractor is proved for the discrete dynamical system.

  10. On a finite-difference method for solving transient viscous flow problems

    Science.gov (United States)

    Li, C. P.

    1983-01-01

    A method has been developed to solve the unsteady, compressible Navier-Stokes equation with the property of consistency and the ability of minimizing the equation stiffness. It relies on innovative extensions of the state-of-the-art finite-difference techniques and is composed of: (1) the upwind scheme for split-flux and the central scheme for conventional flux terms in the inviscid and viscous regions, respectively; (2) the characteristic treatment of both inviscid and viscous boundaries; (3) an ADI procedure compatible with interior and boundary points; and (4) a scalar matrix coefficient including viscous terms. The performance of this method is assessed with four sample problems; namely, a standing shock in the Laval duct, a shock reflected from the wall, the shock-induced boundary-layer separation, and a transient internal nozzle flow. The results from the present method, an existing hybrid block method, and a well-known two-step explicit method are compared and discussed. It is concluded that this method has an optimal trade-off between the solution accuracy and computational economy, and other desirable properties for analyzing transient viscous flow problems.

  11. Unconditionally stable finite-difference time-domain methods for modeling the Sagnac effect.

    Science.gov (United States)

    Novitski, Roman; Scheuer, Jacob; Steinberg, Ben Z

    2013-02-01

    We present two unconditionally stable finite-difference time-domain (FDTD) methods for modeling the Sagnac effect in rotating optical microsensors. The methods are based on the implicit Crank-Nicolson scheme, adapted to hold in the rotating system reference frame-the rotating Crank-Nicolson (RCN) methods. The first method (RCN-2) is second order accurate in space whereas the second method (RCN-4) is fourth order accurate. Both methods are second order accurate in time. We show that the RCN-4 scheme is more accurate and has better dispersion isotropy. The numerical results show good correspondence with the expression for the classical Sagnac resonant frequency splitting when using group refractive indices of the resonant modes of a microresonator. Also we show that the numerical results are consistent with the perturbation theory for the rotating degenerate microcavities. We apply our method to simulate the effect of rotation on an entire Coupled Resonator Optical Waveguide (CROW) consisting of a set of coupled microresonators. Preliminary results validate the formation of a rotation-induced gap at the center of a transfer function of a CROW.

  12. Matched interface and boundary (MIB) for the implementation of boundary conditions in high-order central finite differences.

    Science.gov (United States)

    Zhao, Shan; Wei, G W

    2009-03-19

    High-order central finite difference schemes encounter great difficulties in implementing complex boundary conditions. This paper introduces the matched interface and boundary (MIB) method as a novel boundary scheme to treat various general boundary conditions in arbitrarily high-order central finite difference schemes. To attain arbitrarily high order, the MIB method accurately extends the solution beyond the boundary by repeatedly enforcing only the original set of boundary conditions. The proposed approach is extensively validated via boundary value problems, initial-boundary value problems, eigenvalue problems, and high-order differential equations. Successful implementations are given to not only Dirichlet, Neumann, and Robin boundary conditions, but also more general ones, such as multiple boundary conditions in high-order differential equations and time-dependent boundary conditions in evolution equations. Detailed stability analysis of the MIB method is carried out. The MIB method is shown to be able to deliver high-order accuracy, while maintaining the same or similar stability conditions of the standard high-order central difference approximations. The application of the proposed MIB method to the boundary treatment of other non-standard high-order methods is also considered.

  13. Optimization of lumping schemes for plane square quadratic finite element in elastodynamics

    Directory of Open Access Journals (Sweden)

    Kolman R.

    2007-10-01

    Full Text Available The effectiveness of explicit direct time-integration methods is conditioned by using diagonal mass matrix which entails significant computational savings and storage advantages. In recent years many procedures that produced diagonally lumped mass matrices were developed. For example, the row sum method and diagonal scaling method (HRZ procedure can be mentioned. In this paper, the dispersive properties of different lumping matrices with variable mass distribution for the plane square 8-node serendipity elements are investigated. The dispersion diagrams for such lumping matrices are derived for various Courant numbers, wavelengths and the directions of wave propagation.

  14. Comparison Experiments of Different Model Error Schemes in Ensemble Kalman Filter Soil Moisture Assimilation

    Science.gov (United States)

    Nie, Suping; Zhu, Jiang; Luo, Yong

    2010-05-01

    The purpose of this study is to explore the performances of different model error scheme in soil moisture data assimilation. Based on the ensemble Kalman filter (EnKF) and the atmosphere-vegetation interaction model (AVIM), point-scale analysis results for three schemes, 1) covariance inflation (CI), 2) direct random disturbance (DRD), and 3) error source random disturbance (ESRD), are combined under conditions of different observational error estimations, different observation layers, and different observation intervals using a series of idealized experiments. The results shows that all these schemes obtain good assimilation results when the assumed observational error is an accurate statistical representation of the actual error used to perturb the original truth value, and the ESRD scheme has the least root mean square error (RMSE). Overestimation or underestimation of the observational errors can affect the assimilation results of CI and DRD schemes sensitively. The performances of these two schemes deteriorate obviously while the ESRD scheme keeps its capability well. When the observation layers or observation interval increase, the performances of both CI and DRD schemes decline evidently. But for the ESRD scheme, as it can assimilate multi-layer observations coordinately, the increased observations improve the assimilation results further. Moreover, as the ESRD scheme contains a certain amount of model error estimation functions in its assimilation process, it also has a good performance in assimilating sparse-time observations.

  15. A Comparison of Boundary-Layer Characteristics Simulated Using Different Parametrization Schemes

    Science.gov (United States)

    Wang, Weiguo; Shen, Xinyong; Huang, Wenyan

    2016-06-01

    We compare daytime planetary boundary-layer (PBL) characteristics under fair-weather conditions simulated using a single column version of the Weather Research and Forecasting model with different PBL parametrization schemes. The model is driven only by prescribed surface heat fluxes and horizontal pressure gradient forcing. Parametrizations for all physical processes except for turbulence and transport in the PBL are turned off in the simulations to ensure the discrepancies in the simulated PBL flow are due only to differences in the PBL schemes. A large-eddy simulation (LES) of the evolution of a daytime PBL is performed as a benchmark to examine how well a PBL parametrization scheme reproduces the LES results, and performance statistics are compared to rank those schemes. In general, hybrid local and non-local schemes such as the Yonsei University and Asymmetrical Convective Model (version 2) schemes perform better in reproducing the LES results, particularly well-mixed features, than do local schemes. Among local schemes, the University of Washington scheme produces the results closest to the LES. Local schemes, such as those of Mellor-Yamada-Janjic and Mellor-Yamada-Nakanishi-Niino, simulate too low an entrainment flux, while PBL heights diagnosed from the simulations using local schemes are lower than those from the LES results. Hybrid local and non-local schemes are more sensitive to vertical grid resolution than local schemes. With a higher vertical resolution in the PBL, the schemes using the eddy-diffusivity and mass-flux methods perform better. Differences in the values of eddy diffusivity, length scale, and turbulence kinetic energy and their vertical distributions are large.

  16. A Comparison of Boundary-Layer Characteristics Simulated Using Different Parametrization Schemes

    Science.gov (United States)

    Wang, Weiguo; Shen, Xinyong; Huang, Wenyan

    2016-11-01

    We compare daytime planetary boundary-layer (PBL) characteristics under fair-weather conditions simulated using a single column version of the Weather Research and Forecasting model with different PBL parametrization schemes. The model is driven only by prescribed surface heat fluxes and horizontal pressure gradient forcing. Parametrizations for all physical processes except for turbulence and transport in the PBL are turned off in the simulations to ensure the discrepancies in the simulated PBL flow are due only to differences in the PBL schemes. A large-eddy simulation (LES) of the evolution of a daytime PBL is performed as a benchmark to examine how well a PBL parametrization scheme reproduces the LES results, and performance statistics are compared to rank those schemes. In general, hybrid local and non-local schemes such as the Yonsei University and Asymmetrical Convective Model (version 2) schemes perform better in reproducing the LES results, particularly well-mixed features, than do local schemes. Among local schemes, the University of Washington scheme produces the results closest to the LES. Local schemes, such as those of Mellor-Yamada-Janjic and Mellor-Yamada-Nakanishi-Niino, simulate too low an entrainment flux, while PBL heights diagnosed from the simulations using local schemes are lower than those from the LES results. Hybrid local and non-local schemes are more sensitive to vertical grid resolution than local schemes. With a higher vertical resolution in the PBL, the schemes using the eddy-diffusivity and mass-flux methods perform better. Differences in the values of eddy diffusivity, length scale, and turbulence kinetic energy and their vertical distributions are large.

  17. Comparison of different incremental analysis update schemes in a realistic assimilation system with Ensemble Kalman Filter

    Science.gov (United States)

    Yan, Y.; Barth, A.; Beckers, J. M.; Brankart, J. M.; Brasseur, P.; Candille, G.

    2017-07-01

    In this paper, three incremental analysis update schemes (IAU 0, IAU 50 and IAU 100) are compared in the same assimilation experiments with a realistic eddy permitting primitive equation model of the North Atlantic Ocean using the Ensemble Kalman Filter. The difference between the three IAU schemes lies on the position of the increment update window. The relevance of each IAU scheme is evaluated through analyses on both thermohaline and dynamical variables. The validation of the assimilation results is performed according to both deterministic and probabilistic metrics against different sources of observations. For deterministic validation, the ensemble mean and the ensemble spread are compared to the observations. For probabilistic validation, the continuous ranked probability score (CRPS) is used to evaluate the ensemble forecast system according to reliability and resolution. The reliability is further decomposed into bias and dispersion by the reduced centred random variable (RCRV) score. The obtained results show that 1) the IAU 50 scheme has the same performance as the IAU 100 scheme 2) the IAU 50/100 schemes outperform the IAU 0 scheme in error covariance propagation for thermohaline variables in relatively stable region, while the IAU 0 scheme outperforms the IAU 50/100 schemes in dynamical variables estimation in dynamically active region 3) in case with sufficient number of observations and good error specification, the impact of IAU schemes is negligible. The differences between the IAU 0 scheme and the IAU 50/100 schemes are mainly due to different model integration time and different instability (density inversion, large vertical velocity, etc.) induced by the increment update. The longer model integration time with the IAU 50/100 schemes, especially the free model integration, on one hand, allows for better re-establishment of the equilibrium model state, on the other hand, smooths the strong gradients in dynamically active region.

  18. The Numerical Solution of Underwater Acoustic Propagation Problems Using Finite Difference and Finite Element Methods

    Science.gov (United States)

    1984-07-09

    State and /IP Code i Arlington, VA 22217 10. SOURCE OF FUNDING NOS. PROGRAM E LEMENT NO. 61153N 11 TITLE ilnclude SeGur \\ly Classificationi... CYBER 205. We observe in this connection that the finite-element algorithm, we described previously is, for the most part, vectorizable. The main...words. We understand that it is scheduled to be available before the end of 1985. We also understand that CDC is planning a successor to the CYBER 205

  19. 3D Finite Difference Modelling of Basaltic Region

    Science.gov (United States)

    Engell-Sørensen, L.

    2003-04-01

    The main purpose of the work was to generate realistic data to be applied for testing of processing and migration tools for basaltic regions. The project is based on the three - dimensional finite difference code (FD), TIGER, made by Sintef. The FD code was optimized (parallelized) by the author, to run on parallel computers. The parallel code enables us to model large-scale realistic geological models and to apply traditional seismic and micro seismic sources. The parallel code uses multiple processors in order to manipulate subsets of large amounts of data simultaneously. The general anisotropic code uses 21 elastic coefficients. Eight independent coefficients are needed as input parameters for the general TI medium. In the FD code, the elastic wave field computation is implemented by a higher order FD solution to the elastic wave equation and the wave fields are computed on a staggered grid, shifted half a node in one or two directions. The geological model is a gridded basalt model, which covers from 24 km to 37 km of a real shot line in horizontal direction and from the water surface to the depth of 3.5 km. The 2frac {1}{2}D model has been constructed using the compound modeling software from Norsk Hydro. The vertical parameter distribution is obtained from observations in two wells. At The depth of between 1100 m to 1500 m, a basalt horizon covers the whole sub surface layers. We have shown that it is possible to simulate a line survey in realistic (3D) geological models in reasonable time by using high performance computers. The author would like to thank Norsk Hydro, Statoil, GEUS, and SINTEF for very helpful discussions and Parallab for being helpful with the new IBM, p690 Regatta system.

  20. PCS: an Euler--Lagrange method for treating convection in pulsating stars using finite difference techniques in two spatial dimensions. [Finite difference method, time dependence

    Energy Technology Data Exchange (ETDEWEB)

    Deupree, R.G.

    1977-01-01

    Finite difference techniques were used to examine the coupling of radial pulsation and convection in stellar models having comparable time scales. Numerical procedures are emphasized, including diagnostics to help determine the range of free parameters.

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

    Directory of Open Access Journals (Sweden)

    Taohua Liu

    2017-01-01

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

  2. Accurate finite difference beam propagation method for complex integrated optical structures

    DEFF Research Database (Denmark)

    Rasmussen, Thomas; Povlsen, Jørn Hedegaard; Bjarklev, Anders Overgaard

    1993-01-01

    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......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...

  3. On Third Order Stable Difference Scheme for Hyperbolic Multipoint Nonlocal Boundary Value Problem

    Directory of Open Access Journals (Sweden)

    Ozgur Yildirim

    2015-01-01

    Full Text Available This paper presents a third order of accuracy stable difference scheme for the approximate solution of multipoint nonlocal boundary value problem of the hyperbolic type in a Hilbert space with self-adjoint positive definite operator. Stability estimates for solution of the difference scheme are obtained. Some results of numerical experiments that support theoretical statements are presented.

  4. Stability of Difference Schemes for Fractional Parabolic PDE with the Dirichlet-Neumann Conditions

    Directory of Open Access Journals (Sweden)

    Zafer Cakir

    2012-01-01

    boundary conditions are presented. Stability estimates and almost coercive stability estimates with ln (1/(+|ℎ| for the solution of these difference schemes are obtained. A procedure of modified Gauss elimination method is used for solving these difference schemes of one-dimensional fractional parabolic partial differential equations.

  5. A Difference Scheme for the Coupled KdV Equation 14

    Institute of Scientific and Technical Information of China (English)

    ShaohongZHU

    1999-01-01

    In this paper,a difference scheme for the periodic initial-boundary problem of the coupled KdV equation is given.The scheme keeps the first two conserved quantities which the differential equation possesses.The catch-ran iterative method is used to solve the difference equations.The numerical simulation exhibits the existence of two-soliton solutions.

  6. THE UNCONDITIONAL STABILITY OF PARALLEL DIFFERENCE SCHEMES WITH SECOND ORDER CONVERGENCE FOR NONLINEAR PARABOLIC SYSTEM

    Institute of Scientific and Technical Information of China (English)

    Yuan Guangwei; Sheng Zhiqiang; Hang Xudeng

    2007-01-01

    For solving nonlinear parabolic equation on massive parallel computers,the construction of parallel difference schemes with simple design, high parallelism and unconditional stability and second order global accuracy in space, has long been desired.In the present work, a new kind of general parallel difference schemes for the nonlinear parabolic system is proposed. The general parallel difference schemes include, among others, two new parallel schemes. In one of them, to obtain the interface values on the interface of sub-domains an explicit scheme of Jacobian type is employed, and then the fully implicit scheme is used in the sub-domains. Here, in the explicit scheme of Jacobian type, the values at the points being adjacent to the interface points are taken as the linear combination of values of previous two time layers at the adjoining points of the inner interface. For the construction of another new parallel difference scheme,the main procedure is as follows. Firstly the linear combination of values of previous two time layers at the interface points among the sub-domains is used as the (Dirichlet)boundary condition for solving the sub-domain problems. Then the values in the subdomains are calculated by the fully implicit scheme. Finally the interface values are computed by the fully implicit scheme, and in fact these calculations of the last step are explicit since the values adjacent to the interface points have been obtained in the previous step. The existence, uniqueness, unconditional stability and the second order accuracy of the discrete vector solutions for the parallel difference schemes are proved.Numerical results are presented to examine the stability, accuracy and parallelism of the parallel schemes.

  7. IMPROVED LOCALLY CONFORMAL FINITE-DIFFERENCE TIME-DOMAIN METHOD FOR EDGE INCLINED SLOTS IN A FINITE WALL THICKNESS WAVEGUIDE

    Institute of Scientific and Technical Information of China (English)

    Li Long; Zhang Yu; Liang Changhong

    2004-01-01

    An Improved Locally Conformal Finite-Difference Time-Domain (ILC-FDTD) method is presented in this paper, which is used to analyze the edge inclined slots penetrating adjacent broadwalls of a finite wall thickness waveguide. ILC-FDTD not only removes the instability of the original locally conformal FDTD algorithm, but also improves the computational accuracy by locally modifying magnetic field update equations and the virtual iterative electric fields according to the complexity of the slot fringe fields. The mutual coupling between two edge inclined slots can also be analyzed by ILC-FDTD effectively.

  8. Analysis of regular and chaotic dynamics of the Euler-Bernoulli beams using finite difference and finite element methods

    Institute of Scientific and Technical Information of China (English)

    J. Awrejcewicz; A.V. Krysko; J. Mrozowski; O.A. Saltykova; M.V. Zhigalov

    2011-01-01

    Chaotic vibrations of flexible non-linear EulerBernoulli beams subjected to harmonic load and with various boundary conditions (symmetric and non-symmetric) are studied in this work. Reliability of the obtained results is verified by the finite difference method (FDM) and the finite element method (FEM) with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes (regular and non-regular). The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly, dynamic behavior vs. control parameters {ωp, q0} is reported, and scenarios of the system transition into chaos are illustrated.

  9. A Multifunctional Interface Method for Coupling Finite Element and Finite Difference Methods: Two-Dimensional Scalar-Field Problems

    Science.gov (United States)

    Ransom, Jonathan B.

    2002-01-01

    A multifunctional interface method with capabilities for variable-fidelity modeling and multiple method analysis is presented. The methodology provides an effective capability by which domains with diverse idealizations can be modeled independently to exploit the advantages of one approach over another. The multifunctional method is used to couple independently discretized subdomains, and it is used to couple the finite element and the finite difference methods. The method is based on a weighted residual variational method and is presented for two-dimensional scalar-field problems. A verification test problem and a benchmark application are presented, and the computational implications are discussed.

  10. Assessment on Different Schemes of Industrial Structure Adjustment Based on DEA

    Institute of Scientific and Technical Information of China (English)

    FU Li-fang; MENG Jun

    2004-01-01

    DEA is a new research field in operations research. It has unique virtues in dealing with assessment problem with multi-inputs especially multi-outputs, In this paper, DEA model of Dεc2R has been applied to evaluate the relative efficiency of several different schemes of industrial structure adjustment of agriculture and finally select the optimal scheme. Furthermore, the inferior scheme has been improved according to some useful insights got from DEA model.

  11. Nonstandard Finite Difference Variational Integrators for Multisymplectic PDEs

    Directory of Open Access Journals (Sweden)

    Cuicui Liao

    2012-01-01

    discretization and a square discretization, respectively. These methods are naturally multisymplectic. Their discrete multisymplectic structures are presented by the multisymplectic form formulas. The convergence of the discretization schemes is discussed. The effectiveness and efficiency of the proposed methods are verified by the numerical experiments.

  12. Comparison of a Reaction Front Model and a Finite Difference Model for the Simulation of Solid Absorption Process

    Institute of Scientific and Technical Information of China (English)

    ZikangWu; ArneJakobsen; 等

    1994-01-01

    The pupose of this paper is to investigate the validity of a lumped model,i.e.a reaction front model,for the simulation of solid absorption process.A distributed model is developed for solid absorption process,and a dimensionless RF number is suggested to predict the qualitative shape of reaction degree profile.The simulation results from the reaction front model are compared with those from the distributed model solved by a finite difference scheme,and it is shown that they are in good agreement in almost all cased.no matter whether there is reaction front or not.

  13. An object-oriented designed finite-difference time-domain simulator for electromagnetic analysis and design in MRI.

    Science.gov (United States)

    Wei, Q; Crozier, S; Xia, L; Liu, F

    2004-01-01

    This paper presents a finite-difference time-domain (FDTD) simulator for electromagnetic analysis and design applications in magnetic resonance imaging (MRI). It is intended to be a complete FDTD model of an MRI system including all RF and low frequency field generating units and electrical models of the patient. The framework has been constructed with the assistance of object-oriented concepts. The detailed design procedure is described and the numerical method has been verified against analytical solutions for simple cases and also applied to real field calculations. The simulated results demonstrated that the proposed FDTD scheme can be used to analyze large-scale computational electromagnetic problems in MRI engineering.

  14. A Finite Difference-Augmented Peridynamics Method for Wave Dispersion

    Science.gov (United States)

    2014-10-21

    model using a blending function in 1D, though again, the focus is on preset, unchang- ing local/ nonlocal regions. In contrast, this work will focus on...Fracture. 2014; 190:39-52. 14. ABSTRACT A method is presented for the modeling of brittle elastic fracture which combines peridynamics and a finite...propagation modeling , while peridynamics is automatically inserted in high strain areas to model crack initiation and growth. The dispersion

  15. Optimized explicit Runge-Kutta schemes for the spectral difference method applied to wave propagation problems

    CERN Document Server

    Parsani, M; Deconinck, W

    2012-01-01

    Explicit Runge-Kutta schemes with large stable step sizes are developed for integration of high order spectral difference spatial discretization on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard explicit Runge-Kutta schemes available in literature. Furthermore, they have a small principal error norm and admit a low-storage implementation. The advantages of the new schemes are demonstrated through application to the Euler equations and the linearized Euler equations.

  16. Optimized Explicit Runge--Kutta Schemes for the Spectral Difference Method Applied to Wave Propagation Problems

    KAUST Repository

    Parsani, Matteo

    2013-04-10

    Explicit Runge--Kutta schemes with large stable step sizes are developed for integration of high-order spectral difference spatial discretizations on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard explicit Runge--Kutta schemes available in the literature. Furthermore, they have a small principal error norm and admit a low-storage implementation. The advantages of the new schemes are demonstrated through application to the Euler equations and the linearized Euler equations.

  17. Numerical simulation of particulate flows using a hybrid of finite difference and boundary integral methods.

    Science.gov (United States)

    Bhattacharya, Amitabh; Kesarkar, Tejas

    2016-10-01

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

  18. Finite-difference modeling of Bragg fibers with ultrathin cladding layers via adaptive coordinate transformation

    DEFF Research Database (Denmark)

    Shyroki, Dzmitry; Lægsgaard, Jesper; Bang, Ole

    As an alternative to the finite-element analysis or subgridding, coordinate transformation is used to “stretch” the fine-structured cladding of a Bragg fiber, and then the fullvector, equidistant-grid finite-difference computations of the modal structure are performed.......As an alternative to the finite-element analysis or subgridding, coordinate transformation is used to “stretch” the fine-structured cladding of a Bragg fiber, and then the fullvector, equidistant-grid finite-difference computations of the modal structure are performed....

  19. Finite-difference modeling of Bragg fibers with ultrathin cladding layers via adaptive coordinate transformation

    DEFF Research Database (Denmark)

    Shyroki, Dzmitry; Lægsgaard, Jesper; Bang, Ole;

    As an alternative to the finite-element analysis or subgridding, coordinate transformation is used to “stretch” the fine-structured cladding of a Bragg fiber, and then the fullvector, equidistant-grid finite-difference computations of the modal structure are performed.......As an alternative to the finite-element analysis or subgridding, coordinate transformation is used to “stretch” the fine-structured cladding of a Bragg fiber, and then the fullvector, equidistant-grid finite-difference computations of the modal structure are performed....

  20. On stability of difference schemes for hyperbolic multipoint NBVP with Neumann conditions

    Science.gov (United States)

    Yildirim, Ozgur; Uzun, Meltem

    2016-08-01

    In this work, a multipoint nonlocal boundary value problem (NBVP) for hyperbolic equations with Neumann conditions is considered. Third and fourth order of accuracy stable difference schemes for solving this problem are presented. Efficiency of these schemes are tested via MATLAB implementation.

  1. [Farmacoeconomical estimation of efficiency of different schemes of eradication therapy of Helicobacter pylori infection in children].

    Science.gov (United States)

    Kashnikova, S N; Shcherbakov, P L; Kashnikov, V V; Tatarinov, P A; Shcherbakova, M Iu

    2008-01-01

    In this article farmakoekonomical analysis of efficiency of various, the most common in Russia schemes of eradication therapy disoders, associated with H. pylori infection is given to by authors basis on their private experience. All-round studying of the different economical factors influencing on a cost of used schemes is realized, and result of spent complex efficiency eradication therapy is estimated.

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

    NARCIS (Netherlands)

    Quiney, H. M.; Glushkov, V. N.; Wilson, S.; Sabin,; Brandas, E

    2001-01-01

    A comparison is made of the accuracy achieved in finite difference and finite basis set approximations to the Dirac equation for the ground state of the hydrogen molecular ion. The finite basis set calculations are carried out using a distributed basis set of Gaussian functions the exponents and pos

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

    NARCIS (Netherlands)

    Quiney, H. M.; Glushkov, V. N.; Wilson, S.; Sabin,; Brandas, E

    2001-01-01

    A comparison is made of the accuracy achieved in finite difference and finite basis set approximations to the Dirac equation for the ground state of the hydrogen molecular ion. The finite basis set calculations are carried out using a distributed basis set of Gaussian functions the exponents and

  4. An investigation of the accuracy of finite difference methods in the solution of linear elasticity problems

    Science.gov (United States)

    Bauld, N. R., Jr.; Goree, J. G.

    1983-01-01

    The accuracy of the finite difference method in the solution of linear elasticity problems that involve either a stress discontinuity or a stress singularity is considered. Solutions to three elasticity problems are discussed in detail: a semi-infinite plane subjected to a uniform load over a portion of its boundary; a bimetallic plate under uniform tensile stress; and a long, midplane symmetric, fiber reinforced laminate subjected to uniform axial strain. Finite difference solutions to the three problems are compared with finite element solutions to corresponding problems. For the first problem a comparison with the exact solution is also made. The finite difference formulations for the three problems are based on second order finite difference formulas that provide for variable spacings in two perpendicular directions. Forward and backward difference formulas are used near boundaries where their use eliminates the need for fictitious grid points.

  5. Finite difference modeling of sinking stage curved beam based on revised Vlasov equations

    Institute of Scientific and Technical Information of China (English)

    张磊; 朱真才; 沈刚; 曹国华

    2015-01-01

    For the static analysis of the sinking stage curved beam, a finite difference model was presented based on the proposed revised Vlasov equations. First, revised Vlasov equations for thin-walled curved beams with closed sections were deduced considering the shear strain on the mid-surface of the cross-section. Then, the finite difference formulation of revised Vlasov equations was implemented with the parabolic interpolation based on Taylor series. At last, the finite difference model was built by substituting geometry and boundary conditions of the sinking stage curved beam into the finite difference formulation. The validity of present work is confirmed by the published literature and ANSYS simulation results. It can be concluded that revised Vlasov equations are more accurate than the original one in the analysis of thin-walled beams with closed sections, and that present finite difference model is applicable in the evaluation of the sinking stage curved beam.

  6. True Concurrent Thermal Engineering Integrating CAD Model Building with Finite Element and Finite Difference Methods

    Science.gov (United States)

    Panczak, Tim; Ring, Steve; Welch, Mark

    1999-01-01

    Thermal engineering has long been left out of the concurrent engineering environment dominated by CAD (computer aided design) and FEM (finite element method) software. Current tools attempt to force the thermal design process into an environment primarily created to support structural analysis, which results in inappropriate thermal models. As a result, many thermal engineers either build models "by hand" or use geometric user interfaces that are separate from and have little useful connection, if any, to CAD and FEM systems. This paper describes the development of a new thermal design environment called the Thermal Desktop. This system, while fully integrated into a neutral, low cost CAD system, and which utilizes both FEM and FD methods, does not compromise the needs of the thermal engineer. Rather, the features needed for concurrent thermal analysis are specifically addressed by combining traditional parametric surface based radiation and FD based conduction modeling with CAD and FEM methods. The use of flexible and familiar temperature solvers such as SINDA/FLUINT (Systems Improved Numerical Differencing Analyzer/Fluid Integrator) is retained.

  7. Time-Dependent Parabolic Finite Difference Formulation for Harmonic Sound Propagation in a Two-Dimensional Duct with Flow

    Science.gov (United States)

    Kreider, Kevin L.; Baumeister, Kenneth J.

    1996-01-01

    An explicit finite difference real time iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for future large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable for a harmonic monochromatic sound field, a parabolic (in time) approximation is introduced to reduce the order of the governing equation. The analysis begins with a harmonic sound source radiating into a quiescent duct. This fully explicit iteration method then calculates stepwise in time to obtain the 'steady state' harmonic solutions of the acoustic field. For stability, applications of conventional impedance boundary conditions requires coupling to explicit hyperbolic difference equations at the boundary. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

  8. Implicit finite-difference methods for the Euler equations

    Science.gov (United States)

    Pulliam, T. H.

    1985-01-01

    The present paper is concerned with two-dimensional Euler equations and with schemes which are in use of the time of this writing. Most of the development presented carries over directly to three dimensions. The characteristics of the two-dimensional Euler equations in Cartesian coordinates are considered along with generalized curvilinear coordinate transformations, metric relations, invariants of the transformation, flux Jacobian matrices and eigensystems, numerical algorithms, flux split algorithms, implicit and explicit nonlinear control (smoothing), upwind differencing in supersonic regions, unsteady and steady-state computation, the diagonal form of implicit algorithm, metric differencing and invariants, boundary conditions, geometry and mesh generation, and sample solutions.

  9. Features and implications of different LHC crossing schemes

    CERN Document Server

    Herr, Werner

    2003-01-01

    To avoid unwanted beam-beam interactions, the two LHC beams cross at an angle in all experimental interaction points. The choice of the crossing plane in the different areas has fundamental consequences on the effects of the long range beam-beam interaction. Recent changes to the hardware, i.e. introduction of a beam screen into the triplet quadrupoles, may limit this choice or reduce the flexibility. The consequences of different crossing scenarios are presented in this report. Other implications such as limitations to the correction possibilities and the flexibility of the crossing geometry are addressed.

  10. Well-posedness of the difference schemes of the high order of accuracy for elliptic equations

    Directory of Open Access Journals (Sweden)

    2006-01-01

    Full Text Available It is well known the differential equation − u ″ ( t +Au( t =f( t ( −∞difference schemes generated by an exact difference scheme or by Taylor's decomposition on three points for the approximate solutions of this differential equation. The well-posedness of these difference schemes in the difference analogy of the smooth functions is obtained. The exact almost coercive inequality for solutions in C( τ,E of these difference schemes is established.

  11. A drift-diffusion-reaction model for excitonic photovoltaic bilayers: Photovoltaic bilayers: Asymptotic analysis and a 2D hdg finite element scheme

    KAUST Repository

    Brinkman, Daniel

    2013-05-01

    We present and discuss a mathematical model for the operation of bilayer organic photovoltaic devices. Our model couples drift-diffusion-recombination equations for the charge carriers (specifically, electrons and holes) with a reaction-diffusion equation for the excitons/polaron pairs and Poisson\\'s equation for the self-consistent electrostatic potential. The material difference (i.e. the HOMO/LUMO gap) of the two organic substrates forming the bilayer device is included as a work-function potential. Firstly, we perform an asymptotic analysis of the scaled one-dimensional stationary state system: (i) with focus on the dynamics on the interface and (ii) with the goal of simplifying the bulk dynamics away from the interface. Secondly, we present a two-dimensional hybrid discontinuous Galerkin finite element numerical scheme which is very well suited to resolve: (i) the material changes, (ii) the resulting strong variation over the interface, and (iii) the necessary upwinding in the discretization of drift-diffusion equations. Finally, we compare the numerical results with the approximating asymptotics. © 2013 World Scientific Publishing Company.

  12. Finite difference methods for reducing numerical diffusion in TEACH-type calculations. [Teaching Elliptic Axisymmetric Characteristics Heuristically

    Science.gov (United States)

    Syed, S. A.; Chiappetta, L. M.

    1985-01-01

    A methodological evaluation for two-finite differencing schemes for computer-aided gas turbine design is presented. The two computational schemes include; a Bounded Skewed Finite Differencing Scheme (BSUDS); and a Quadratic Upwind Differencing Scheme (QSDS). In the evaluation, the derivations of the schemes were incorporated into two-dimensional and three-dimensional versions of the Teaching Axisymmetric Characteristics Heuristically (TEACH) computer code. Assessments were made according to performance criteria for the solution of problems of turbulent, laminar, and coannular turbulent flow. The specific performance criteria used in the evaluation were simplicity, accuracy, and computational economy. It is found that the BSUDS scheme performed better with respect to the criteria than the QUDS. Some of the reasons for the more successful performance BSUDS are discussed.

  13. Finite difference methods for reducing numerical diffusion in TEACH-type calculations. [Teaching Elliptic Axisymmetric Characteristics Heuristically

    Science.gov (United States)

    Syed, S. A.; Chiappetta, L. M.

    1985-01-01

    A methodological evaluation for two-finite differencing schemes for computer-aided gas turbine design is presented. The two computational schemes include; a Bounded Skewed Finite Differencing Scheme (BSUDS); and a Quadratic Upwind Differencing Scheme (QSDS). In the evaluation, the derivations of the schemes were incorporated into two-dimensional and three-dimensional versions of the Teaching Axisymmetric Characteristics Heuristically (TEACH) computer code. Assessments were made according to performance criteria for the solution of problems of turbulent, laminar, and coannular turbulent flow. The specific performance criteria used in the evaluation were simplicity, accuracy, and computational economy. It is found that the BSUDS scheme performed better with respect to the criteria than the QUDS. Some of the reasons for the more successful performance BSUDS are discussed.

  14. Parallel difference schemes with interface extrapolation terms for quasi-linear parabolic systems

    Institute of Scientific and Technical Information of China (English)

    Guang-wei YUAN; Xu-deng HANG; Zhi-qiang SHENG

    2007-01-01

    In this paper some new parallel difference schemes with interface extrapolation terms for a quasi-linear parabolic system of equations are constructed. Two types of time extrapolations are proposed to give the interface values on the interface of sub-domains or the values adjacent to the interface points, so that the unconditional stable parallel schemes with the second accuracy are formed.Without assuming heuristically that the original boundary value problem has the unique smooth vector solution, the existence and uniqueness of the discrete vector solutions of the parallel difference schemes constructed are proved. Moreover the unconditional stability of the parallel difference schemes is justified in the sense of the continuous dependence of the discrete vector solution of the schemes on the discrete known data of the original problems in the discrete W2(2,1) (Q△) norms. Finally the convergence of the discrete vector solutions of the parallel difference schemes with interface extrapolation terms to the unique generalized solution of the original quasi-linear parabolic problem is proved. Numerical results are presented to show the good performance of the parallel schemes, including the unconditional stability, the second accuracy and the high parallelism.

  15. Comparison between different encoding schemes for synthetic aperture imaging

    DEFF Research Database (Denmark)

    Nikolov, Svetoslav; Jensen, Jørgen Arendt

    2002-01-01

    have solved the first problem by building a scanner capable of acquiring data using STAU in real-time. The SNR is increased by using encoded signals, which make it possible to send more energy in the body, while reserving the spatial and contrast resolution. The performance of temporal, spatial...... and spatio-temporal encoding was investigated. Experiments on wire phantom in water were carried out to quantify the gain from the different encodings. The gain in SNR using an FM modulated pulse is 12 dB. The penetration depth of the images was studied using tissue mimicking phantom with frequency dependent...... influence the performance of the STAU....

  16. Artificial Bee Colony with Different Mutation Schemes: A comparative study

    Directory of Open Access Journals (Sweden)

    Iyad Abu Doush

    2014-03-01

    Full Text Available Artificial Bee Colony (ABC is a swarm-based metaheuristic for continuous optimization. Recent work hybridized this algorithm with other metaheuristics in order to improve performance. The work in this paper, experimentally evaluates the use of different mutation operators with the ABC algorithm. The introduced operator is activated according to a determined probability called mutation rate (MR. The results on standard benchmark function suggest that the use of this operator improves performance in terms of convergence speed and quality of final obtained solution. It shows that Power and Polynomial mutations give best results. The fastest convergence was for the mutation rate value (MR=0.2.

  17. Parallel Solvers for Finite-Difference Modeling of Large-Scale, High-Resolution Electromagnetic Problems in MRI

    Directory of Open Access Journals (Sweden)

    Hua Wang

    2008-01-01

    Full Text Available With the movement of magnetic resonance imaging (MRI technology towards higher field (and therefore frequency systems, the interaction of the fields generated by the system with patients, healthcare workers, and internally within the system is attracting more attention. Due to the complexity of the interactions, computational modeling plays an essential role in the analysis, design, and development of modern MRI systems. As a result of the large computational scale associated with most of the MRI models, numerical schemes that rely on a single computer processing unit often require a significant amount of memory and long computational times, which makes modeling of these problems quite inefficient. This paper presents dedicated message passing interface (MPI, OPENMP parallel computing solvers for finite-difference time-domain (FDTD, and quasistatic finite-difference (QSFD schemes. The FDTD and QSFD methods have been widely used to model/ analyze the induction of electric fields/ currents in voxel phantoms and MRI system components at high and low frequencies, respectively. The power of the optimized parallel computing architectures is illustrated by distinct, large-scale field calculation problems and shows significant computational advantages over conventional single processing platforms.

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

    CERN Document Server

    Itkin, Andrey

    2017-01-01

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

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

    Directory of Open Access Journals (Sweden)

    B. Godongwana

    2015-01-01

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

  20. Eddy Current Tomography Based on a Finite Difference Forward Model with Additive Regularization

    Science.gov (United States)

    Trillon, A.; Girard, A.; Idier, J.; Goussard, Y.; Sirois, F.; Dubost, S.; Paul, N.

    2010-02-01

    Eddy current tomography is a nondestructive evaluation technique used for characterization of metal components. It is an inverse problem acknowledged as difficult to solve since it is both ill-posed and nonlinear. Our goal is to derive an inversion technique with improved tradeoff between quality of the results, computational requirements and ease of implementation. This is achieved by fully accounting for the nonlinear nature of the forward problem by means of a system of bilinear equations obtained through a finite difference modeling of the problem. The bilinear character of equations with respect to the electric field and the relative conductivity is taken advantage of through a simple contrast source inversion-like scheme. The ill-posedness is dealt with through the addition of regularization terms to the criterion, the form of which is determined according to computational constraints and the piecewise constant nature of the medium. Therefore an edge-preserving functional is selected. The performance of the resulting method is illustrated using 2D synthetic data examples.

  1. A Difference Scheme for Solving the Timoshenko Beam Equations with Tip Body

    Institute of Scientific and Technical Information of China (English)

    Fu-le Li; Zi-ku Wu; Kai-mei Huang

    2008-01-01

    In this article, a Timoehenko beam with tip body and boundary damping is considered. A linearized three-level difference scheme of the Timoshenko beam equations on uniform meshes is derived by the method of reduction of order. The unique solvability, unconditional stability and convergence of the difference scheme are proved. The convergence order in maximum norm is of order two in both space and time. A numerical example is presented to demonstrate the theoretical results.

  2. Intercomparison of Martian Lower Atmosphere Simulated Using Different Planetary Boundary Layer Parameterization Schemes

    Science.gov (United States)

    Natarajan, Murali; Fairlie, T. Duncan; Dwyer Cianciolo, Alicia; Smith, Michael D.

    2015-01-01

    We use the mesoscale modeling capability of Mars Weather Research and Forecasting (MarsWRF) model to study the sensitivity of the simulated Martian lower atmosphere to differences in the parameterization of the planetary boundary layer (PBL). Characterization of the Martian atmosphere and realistic representation of processes such as mixing of tracers like dust depend on how well the model reproduces the evolution of the PBL structure. MarsWRF is based on the NCAR WRF model and it retains some of the PBL schemes available in the earth version. Published studies have examined the performance of different PBL schemes in NCAR WRF with the help of observations. Currently such assessments are not feasible for Martian atmospheric models due to lack of observations. It is of interest though to study the sensitivity of the model to PBL parameterization. Typically, for standard Martian atmospheric simulations, we have used the Medium Range Forecast (MRF) PBL scheme, which considers a correction term to the vertical gradients to incorporate nonlocal effects. For this study, we have also used two other parameterizations, a non-local closure scheme called Yonsei University (YSU) PBL scheme and a turbulent kinetic energy closure scheme called Mellor- Yamada-Janjic (MYJ) PBL scheme. We will present intercomparisons of the near surface temperature profiles, boundary layer heights, and wind obtained from the different simulations. We plan to use available temperature observations from Mini TES instrument onboard the rovers Spirit and Opportunity in evaluating the model results.

  3. A Hybrid Solver of Size Modified Poisson-Boltzmann Equation by Domain Decomposition, Finite Element, and Finite Difference

    CERN Document Server

    Ying, Jinyong

    2016-01-01

    The size-modified Poisson-Boltzmann equation (SMPBE) is one important variant of the popular dielectric model, the Poisson-Boltzmann equation (PBE), to reflect ionic size effects in the prediction of electrostatics for a biomolecule in an ionic solvent. In this paper, a new SMPBE hybrid solver is developed using a solution decomposition, the Schwartz's overlapped domain decomposition, finite element, and finite difference. It is then programmed as a software package in C, Fortran, and Python based on the state-of-the-art finite element library DOLFIN from the FEniCS project. This software package is well validated on a Born ball model with analytical solution and a dipole model with a known physical properties. Numerical results on six proteins with different net charges demonstrate its high performance. Finally, this new SMPBE hybrid solver is shown to be numerically stable and convergent in the calculation of electrostatic solvation free energy for 216 biomolecules and binding free energy for a DNA-drug com...

  4. Numerical modeling of wave equation by a truncated high-order finite-difference method

    Institute of Scientific and Technical Information of China (English)

    Yang Liu; Mrinal K. Sen

    2009-01-01

    Finite-difference methods with high-order accuracy have been utilized to improve the precision of numerical solution for partial differential equations. However, the computation cost generally increases linearly with increased order of accuracy. Upon examination of the finite-difference formulas for the first-order and second-order derivatives, and the staggered finite-difference formulas for the first-order derivative, we examine the variation of finite-difference coefficients with accuracy order and note that there exist some very small coefficients. With the order increasing, the number of these small coefficients increases, however, the values decrease sharply. An error analysis demonstrates that omitting these small coefficients not only maintain approximately the same level of accuracy of finite difference but also reduce computational cost significantly. Moreover, it is easier to truncate for the high-order finite-difference formulas than for the pseudospectral formulas. Thus this study proposes a truncated high-order finite-difference method, and then demonstrates the efficiency and applicability of the method with some numerical examples.

  5. Coupling of Dirichlet-to-Neumann boundary condition and finite difference methods in curvilinear coordinates for multiple scattering

    Science.gov (United States)

    Acosta, Sebastian; Villamizar, Vianey

    2010-08-01

    The applicability of the Dirichlet-to-Neumann technique coupled with finite difference methods is enhanced by extending it to multiple scattering from obstacles of arbitrary shape. The original boundary value problem (BVP) for the multiple scattering problem is reformulated as an interface BVP. A heterogenous medium with variable physical properties in the vicinity of the obstacles is considered. A rigorous proof of the equivalence between these two problems for smooth interfaces in two and three dimensions for any finite number of obstacles is given. The problem is written in terms of generalized curvilinear coordinates inside the computational region. Then, novel elliptic grids conforming to complex geometrical configurations of several two-dimensional obstacles are constructed and approximations of the scattered field supported by them are obtained. The numerical method developed is validated by comparing the approximate and exact far-field patterns for the scattering from two circular obstacles. In this case, for a second order finite difference scheme, a second order convergence of the numerical solution to the exact solution is easily verified.

  6. Evolution operator equation: Integration with algebraic and finite difference methods. Applications to physical problems in classical and quantum mechanics and quantum field theory

    Energy Technology Data Exchange (ETDEWEB)

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

    1997-10-01

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

  7. Optimized low-order explicit Runge-Kutta schemes for high- order spectral difference method

    KAUST Repository

    Parsani, Matteo

    2012-01-01

    Optimal explicit Runge-Kutta (ERK) schemes with large stable step sizes are developed for method-of-lines discretizations based on the spectral difference (SD) spatial discretization on quadrilateral grids. These methods involve many stages and provide the optimal linearly stable time step for a prescribed SD spectrum and the minimum leading truncation error coefficient, while admitting a low-storage implementation. Using a large number of stages, the new ERK schemes lead to efficiency improvements larger than 60% over standard ERK schemes for 4th- and 5th-order spatial discretization.

  8. a Finite Difference Numerical Model for the Propagation of Finite Amplitude Acoustical Blast Waves Outdoors Over Hard and Porous Surfaces

    Science.gov (United States)

    Sparrow, Victor Ward

    1990-01-01

    This study has concerned the propagation of finite amplitude, i.e. weakly non-linear, acoustical blast waves from explosions over hard and porous media models of outdoor ground surfaces. The nonlinear acoustic propagation effects require a numerical solution in the time domain. To model a porous ground surface, which in the frequency domain exhibits a finite impedance, the linear phenomenological porous model of Morse and Ingard was used. The phenomenological equations are solved in the time domain for coupling with the time domain propagation solution in the air. The numerical solution is found through the method of finite differences. The second-order in time and fourth -order in space MacCormack method was used in the air, and the second-order in time and space MacCormack method was used in the porous medium modeling the ground. Two kinds of numerical absorbing boundary conditions were developed for the air propagation equations to truncate the physical domain for solution on a computer. Radiation conditions first were used on those sides of the domain where there were outgoing waves. Characteristic boundary conditions secondly are employed near the acoustic source. The numerical model agreed well with the Pestorius algorithm for the propagation of electric spark pulses in the free field, and with a result of Pfriem for normal plane reflection off a hard surface. In addition, curves of pressure amplification versus incident angle for waves obliquely incident on the hard and porous surfaces were produced which are similar to those in the literature. The model predicted that near grazing finite amplitude acoustic blast waves decay with distance over hard surfaces as r to the power -1.2. This result is consistent with the work of Reed. For propagation over the porous ground surface, the model predicted that this surface decreased the decay rate with distance for the larger blasts compared to the rate expected in the linear acoustics limit.

  9. Vibration analysis of rotating turbomachinery blades by an improved finite difference method

    Science.gov (United States)

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

    1985-01-01

    The problem of calculating the natural frequencies and mode shapes of rotating blades is solved by an improved finite difference procedure based on second-order central differences. Lead-lag, flapping and coupled bending-torsional vibration cases of untwisted blades are considered. Results obtained by using the present improved theory have been observed to be close lower bound solutions. The convergence has been found to be rapid in comparison with the classical first-order finite difference method. While the computational space and time required by the present approach is observed to be almost the same as that required by the first-order theory for a given mesh size, accuracies of practical interest can be obtained by using the improved finite difference procedure with a relatively smaller matrix size, in contrast to the classical finite difference procedure which requires either a larger matrix or an extrapolation procedure for improvement in accuracy.

  10. Finite-number-of-periods holographic gratings with finite-width incident beams: analysis using the finite-difference frequency-domain method

    Science.gov (United States)

    Wu, Shun-Der; Glytsis, Elias N.

    2002-10-01

    The effects of finite number of periods (FNP) and finite incident beams on the diffraction efficiencies of holographic gratings are investigated by the finite-difference frequency-domain (FDFD) method. Gratings comprising 20, 15, 10, 5, and 3 periods illuminated by TE and TM incident light with various beam sizes are analyzed with the FDFD method and compared with the rigorous coupled-wave analysis (RCWA). Both unslanted and slanted gratings are treated in transmission as well as in reflection configurations. In general, the effect of the FNP is a decrease in the diffraction efficiency with a decrease in the number of periods of the grating. Similarly, a decrease in incident-beam width causes a decrease in the diffraction efficiency. Exceptions appear in off-Bragg incidence in which a smaller beam width could result in higher diffraction efficiency. For beam widths greater than 10 grating periods and for gratings with more than 20 periods in width, the diffraction efficiencies slowly converge to the values predicted by the RCWA (infinite incident beam and infinite-number-of-periods grating) for both TE and TM polarizations. Furthermore, the effects of FNP holographic gratings on their diffraction performance are found to be comparable to their counterparts of FNP surface-relief gratings. 2002 Optical Society of America

  11. Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: An accurate correction scheme for electrostatic finite-size effects

    Energy Technology Data Exchange (ETDEWEB)

    Rocklin, Gabriel J. [Department of Pharmaceutical Chemistry, University of California San Francisco, 1700 4th St., San Francisco, California 94143-2550, USA and Biophysics Graduate Program, University of California San Francisco, 1700 4th St., San Francisco, California 94143-2550 (United States); Mobley, David L. [Departments of Pharmaceutical Sciences and Chemistry, University of California Irvine, 147 Bison Modular, Building 515, Irvine, California 92697-0001, USA and Department of Chemistry, University of New Orleans, 2000 Lakeshore Drive, New Orleans, Louisiana 70148 (United States); Dill, Ken A. [Laufer Center for Physical and Quantitative Biology, 5252 Stony Brook University, Stony Brook, New York 11794-0001 (United States); Hünenberger, Philippe H., E-mail: phil@igc.phys.chem.ethz.ch [Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH, 8093 Zürich (Switzerland)

    2013-11-14

    The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges −5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol{sup −1}) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non

  12. A mixed pseudospectral/finite difference method for the axisymmetric flow in a heated, rotating spherical shell. [for experimental atmospheric simulation

    Science.gov (United States)

    Macaraeg, M. G.

    1986-01-01

    For a Spacelab flight, a model experiment of the earth's atmospheric circulation has been proposed. This experiment is known as the Atmospheric General Circulation Experiment (AGCE). In the experiment concentric spheres will rotate as a solid body, while a dielectric fluid is confined in a portion of the gap between the spheres. A zero gravity environment will be required in the context of the simulation of the gravitational body force on the atmosphere. The present study is concerned with the development of pseudospectral/finite difference (PS/FD) model and its subsequent application to physical cases relevant to the AGCE. The model is based on a hybrid scheme involving a pseudospectral latitudinal formulation, and finite difference radial and time discretization. The advantages of the use of the hybrid PS/FD method compared to a pure second-order accurate finite difference (FD) method are discussed, taking into account the higher accuracy and efficiency of the PS/FD method.

  13. Extending geometric conservation law to cell-centered finite difference methods on moving and deforming grids

    Science.gov (United States)

    Liao, Fei; Ye, Zhengyin

    2015-12-01

    Despite significant progress in recent computational techniques, the accurate numerical simulations, such as direct-numerical simulation and large-eddy simulation, are still challenging. For accurate calculations, the high-order finite difference method (FDM) is usually adopted with coordinate transformation from body-fitted grid to Cartesian grid. But this transformation might lead to failure in freestream preservation with the geometric conservation law (GCL) violated, particularly in high-order computations. GCL identities, including surface conservation law (SCL) and volume conservation law (VCL), are very important in discretization of high-order FDM. To satisfy GCL, various efforts have been made. An early and successful approach was developed by Thomas and Lombard [6] who used the conservative form of metrics to cancel out metric terms to further satisfy SCL. Visbal and Gaitonde [7] adopted this conservative form of metrics for SCL identities and satisfied VCL identity through invoking VCL equation to acquire the derivative of Jacobian in computation on moving and deforming grids with central compact schemes derived by Lele [5]. Later, using the metric technique from Visbal and Gaitonde [7], Nonomura et al. [8] investigated the freestream and vortex preservation properties of high-order WENO and WCNS on stationary curvilinear grids. A conservative metric method (CMM) was further developed by Deng et al. [9] with stationary grids, and detailed discussion about the innermost difference operator of CMM was shown with proof and corresponding numerical test cases. Noticing that metrics of CMM is asymmetrical without coordinate-invariant property, Deng et al. proposed a symmetrical CMM (SCMM) [12] by using the symmetric forms of metrics derived by Vinokur and Yee [10] to further eliminate asymmetric metric errors with stationary grids considered only. The research from Abe et al. [11] presented new asymmetric and symmetric conservative forms of time metrics and

  14. 2-D Finite Difference Modeling of the D'' Structure Beneath the Eastern Cocos Plate: Part I

    Science.gov (United States)

    Helmberger, D. V.; Song, T. A.; Sun, D.

    2005-12-01

    The discovery of phase transition from Perovskite (Pv) to Post-Perovskite (PPv) at depth nears the lowermost mantle has revealed a new view of the earth's D'' layer (Oganov et al. 2004; Murakami et al. 2004). Hernlund et al. (2004) recently pusposed that, depending on the geotherm at the core-mantle boundary (CMB), a double-crossing of the phase boundary by the geotherm at two different depths may also occur. To explore these new findings, we adopt 2-D finite difference scheme (Helmberger and Vidale, 1988) to model wave propagation in rapidly varying structure. We collect broadband waveform data recorded by several Passcal experiments, such as La Ristra transect and CDROM transect in the southwest US to constrain the lateral variations in D'' structure. These data provide fairly dense sampling (~ 20 km) in the lowermost mantle beneath the eastern Cocos plate. Since the source-receiver paths are mostly in the same azimuth, we make 2-D cross-sections from global tomography model (Grand, 2002) and compute finite difference synthetics. We modify the lowermost mantle below 2500 km with constraints from transverse-component waveform data at epicentral distances of 70-82 degrees in the time window between S and ScS, essentially foward modeling waveforms. Assuming a velocity jump of 3 % at D'', our preferred model shows that the D'' topography deepens from the north to the south by about 120 km over a lateral distance of 300 km. Such large topography jumps have been proposed by Thomas et al. (2004) using data recorded by TriNet. In addition, there is a negative velocity jump (-3 %) 100 km above the CMB in the south. This simple model compare favorably with results from a study by Sun, Song and Helmberger (2005), who follow Sidorin et al. (1999) approach and produce a thermodynamically consistent velocity model with Pv-PPv phase boundary. It appears that much of this complexity exists in Grand's tomographic maps with rapid variation in velocities just above the D''. We also

  15. Computer difference scheme for a singularly perturbed convection-diffusion equation

    Science.gov (United States)

    Shishkin, G. I.

    2014-08-01

    The Dirichlet problem for a singularly perturbed ordinary differential convection-diffusion equation with a perturbation parameter ɛ (that takes arbitrary values from the half-open interval (0, 1]) is considered. For this problem, an approach to the construction of a numerical method based on a standard difference scheme on uniform meshes is developed in the case when the data of the grid problem include perturbations and additional perturbations are introduced in the course of the computations on a computer. In the absence of perturbations, the standard difference scheme converges at an (δ st ) rate, where δ st = (ɛ + N -1)-1 N -1 and N + 1 is the number of grid nodes; the scheme is not ɛ-uniformly well conditioned or stable to perturbations of the data. Even if the convergence of the standard scheme is theoretically proved, the actual accuracy of the computed solution in the presence of perturbations degrades with decreasing ɛ down to its complete loss for small ɛ (namely, for ɛ = (δ-2max i, j |δ a {/i j }| + δ-1 max i, j |δ b {/i j }|), where δ = δ st and δ a {/i j }, δ b {/i j } are the perturbations in the coefficients multiplying the second and first derivatives). For the boundary value problem, we construct a computer difference scheme, i.e., a computing system that consists of a standard scheme on a uniform mesh in the presence of controlled perturbations in the grid problem data and a hypothetical computer with controlled computer perturbations. The conditions on admissible perturbations in the grid problem data and on admissible computer perturbations are obtained under which the computer difference scheme converges in the maximum norm for ɛ ∈ (0, 1] at the same rate as the standard scheme in the absence of perturbations.

  16. Application of a novel finite difference method to dynamic crack problems

    Science.gov (United States)

    Chen, Y. M.; Wilkins, M. L.

    1976-01-01

    A versatile finite difference method (HEMP and HEMP 3D computer programs) was developed originally for solving dynamic problems in continuum mechanics. It was extended to analyze the stress field around cracks in a solid with finite geometry subjected to dynamic loads and to simulate numerically the dynamic fracture phenomena with success. This method is an explicit finite difference method applied to the Lagrangian formulation of the equations of continuum mechanics in two and three space dimensions and time. The calculational grid moves with the material and in this way it gives a more detailed description of the physics of the problem than the Eulerian formulation.

  17. AN ACCURATE SOLUTION OF THE POISSON EQUATION BY THE FINITE DIFFERENCE-CHEBYSHEV-TAU METHOD

    Institute of Scientific and Technical Information of China (English)

    Hani I. Siyyam

    2001-01-01

    A new finite difference-Chebyshev-Tau method for the solution of the twodimensional Poisson equation is presented. Some of the numerical results are also presented which indicate that the method is satisfactory and compatible to other methods.

  18. Finite difference methods for option pricing under Lévy processes: Wiener-Hopf factorization approach

    National Research Council Canada - National Science Library

    Kudryavtsev, Oleg

    2013-01-01

    In the paper, we consider the problem of pricing options in wide classes of Lévy processes. We propose a general approach to the numerical methods based on a finite difference approximation for the generalized Black-Scholes equation...

  19. Combination of the discontinuous Galerkin method with finite differences for simulation of seismic wave propagation

    Energy Technology Data Exchange (ETDEWEB)

    Lisitsa, Vadim, E-mail: lisitsavv@ipgg.sbras.ru [Institute of Petroleum Geology and Geophysics SB RAS, Novosibirsk (Russian Federation); Novosibirsk State University, Novosibirsk (Russian Federation); Tcheverda, Vladimir [Institute of Petroleum Geology and Geophysics SB RAS, Novosibirsk (Russian Federation); Kazakh–British Technical University, Alma-Ata (Kazakhstan); Botter, Charlotte [University of Stavanger (Norway)

    2016-04-15

    We present an algorithm for the numerical simulation of seismic wave propagation in models with a complex near surface part and free surface topography. The approach is based on the combination of finite differences with the discontinuous Galerkin method. The discontinuous Galerkin method can be used on polyhedral meshes; thus, it is easy to handle the complex surfaces in the models. However, this approach is computationally intense in comparison with finite differences. Finite differences are computationally efficient, but in general, they require rectangular grids, leading to the stair-step approximation of the interfaces, which causes strong diffraction of the wavefield. In this research we present a hybrid algorithm where the discontinuous Galerkin method is used in a relatively small upper part of the model and finite differences are applied to the main part of the model.

  20. Study on the influence of finite element formulation and equation of motion solution scheme on FEM analysis results based on the asymmetrically loaded plate problem

    Directory of Open Access Journals (Sweden)

    Marcin Krzeszowiec

    2015-03-01

    Full Text Available Computer simulations of physical phenomena are at the moment common both in science and industry. The possibility of finding approximate solutions for complicated systems of differential equations, mathematically describing issues in the fields of mechanics, physics or chemistry, allows for shorten design and research time, often significantly reducing the need for expensive experimental studies or costly production of prototypes. However, the mentioned prevalence of these methods, particularly the Finite Element Method, resulted in analysis outcomes to be often in advance regarded as accurate ones. The purpose of the article is to showcase, on a simple stress analysis problem, how parameters such as the density of the finite element mesh, finite element formulation or integration scheme significantly influence on the simulation results and how easy it is to end up with the results that do not hold any physical sense, despite the fact that all the basic assumptions of correct analysis (suitable boundary conditions, total system energy stored etc. have been met. The results of this study can serve as a warning against premature conclusion drawing from calculations carried out by means of FEM simulation.[b]Keywords[/b]: computational mechanics, finite element method, shell elements, numerical integration

  1. Finite difference method of first boundary problem for quasilinear parabolic systems (III)——Stability

    Institute of Scientific and Technical Information of China (English)

    周毓麟; 沈隆钧; 袁光伟

    1996-01-01

    The explicit, weak and strong implicit difference solution for the first boundary problem ofquasilinear parabolic system is considered:where u,, and f are m-dimensional vector valued functions, A is an m x m positively definite matrix, andFor this problem, the absolute and relative stability for the general difference schemes is justifiedin the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete data of the original problems.

  2. Difference schemes with intrinsic parallelism for quasi-linear parabolic systems

    Institute of Scientific and Technical Information of China (English)

    周毓麟

    1997-01-01

    The boundary value problem for quasi-linear parabolic system is solved by the finite difference method with intrinsic parallelism The existence and uniqueness and convergence theorems of the discrete vector solu tions of the nonlinear difference system with intrinsic parallelism are proved The limiting vector function is just the unique generalized solution of the original problem for the parabolic system

  3. Novel UEP LT Coding Scheme with Feedback Based on Different Degree Distributions

    Directory of Open Access Journals (Sweden)

    Li Ya-Fang

    2016-01-01

    Full Text Available Traditional unequal error protection (UEP schemes have some limitations and problems, such as the poor UEP performance of high priority data and the seriously sacrifice of low priority data in decoding property. Based on the reasonable applications of different degree distributions in LT codes, this paper puts forward a novel UEP LT coding scheme with a simple feedback to compile these data packets separately. Simulation results show that the proposed scheme can effectively protect high priority data, and improve the transmission efficiency of low priority data from 2.9% to 22.3%. Furthermore, it is fairly suitable to apply this novel scheme to multicast and broadcast environments since only a simple feedback introduced.

  4. Efficiency of High-Order Accurate Difference Schemes for the Korteweg-de Vries Equation

    Directory of Open Access Journals (Sweden)

    Kanyuta Poochinapan

    2014-01-01

    Full Text Available Two numerical models to obtain the solution of the KdV equation are proposed. Numerical tools, compact fourth-order and standard fourth-order finite difference techniques, are applied to the KdV equation. The fundamental conservative properties of the equation are preserved by the finite difference methods. Linear stability analysis of two methods is presented by the Von Neumann analysis. The new methods give second- and fourth-order accuracy in time and space, respectively. The numerical experiments show that the proposed methods improve the accuracy of the solution significantly.

  5. Analysis and improvement of Brinkman lattice Boltzmann schemes: bulk, boundary, interface. Similarity and distinctness with finite elements in heterogeneous porous media.

    Science.gov (United States)

    Ginzburg, Irina; Silva, Goncalo; Talon, Laurent

    2015-02-01

    This work focuses on the numerical solution of the Stokes-Brinkman equation for a voxel-type porous-media grid, resolved by one to eight spacings per permeability contrast of 1 to 10 orders in magnitude. It is first analytically demonstrated that the lattice Boltzmann method (LBM) and the linear-finite-element method (FEM) both suffer from the viscosity correction induced by the linear variation of the resistance with the velocity. This numerical artefact may lead to an apparent negative viscosity in low-permeable blocks, inducing spurious velocity oscillations. The two-relaxation-times (TRT) LBM may control this effect thanks to free-tunable two-rates combination Λ. Moreover, the Brinkman-force-based BF-TRT schemes may maintain the nondimensional Darcy group and produce viscosity-independent permeability provided that the spatial distribution of Λ is fixed independently of the kinematic viscosity. Such a property is lost not only in the BF-BGK scheme but also by "partial bounce-back" TRT gray models, as shown in this work. Further, we propose a consistent and improved IBF-TRT model which vanishes viscosity correction via simple specific adjusting of the viscous-mode relaxation rate to local permeability value. This prevents the model from velocity fluctuations and, in parallel, improves for effective permeability measurements, from porous channel to multidimensions. The framework of our exact analysis employs a symbolic approach developed for both LBM and FEM in single and stratified, unconfined, and bounded channels. It shows that even with similar bulk discretization, BF, IBF, and FEM may manifest quite different velocity profiles on the coarse grids due to their intrinsic contrasts in the setting of interface continuity and no-slip conditions. While FEM enforces them on the grid vertexes, the LBM prescribes them implicitly. We derive effective LBM continuity conditions and show that the heterogeneous viscosity correction impacts them, a property also shared

  6. On the validity of the modified equation approach to the stability analysis of finite-difference methods

    Science.gov (United States)

    Chang, Sin-Chung

    1987-01-01

    The validity of the modified equation stability analysis introduced by Warming and Hyett was investigated. It is shown that the procedure used in the derivation of the modified equation is flawed and generally leads to invalid results. Moreover, the interpretation of the modified equation as the exact partial differential equation solved by a finite-difference method generally cannot be justified even if spatial periodicity is assumed. For a two-level scheme, due to a series of mathematical quirks, the connection between the modified equation approach and the von Neuman method established by Warming and Hyett turns out to be correct despite its questionable original derivation. However, this connection is only partially valid for a scheme involving more than two time levels. In the von Neumann analysis, the complex error multiplication factor associated with a wave number generally has (L-1) roots for an L-level scheme. It is shown that the modified equation provides information about only one of these roots.

  7. Minimum divergence viscous flow simulation through finite difference and regularization techniques

    Science.gov (United States)

    Victor, Rodolfo A.; Mirabolghasemi, Maryam; Bryant, Steven L.; Prodanović, Maša

    2016-09-01

    We develop a new algorithm to simulate single- and two-phase viscous flow through a three-dimensional Cartesian representation of the porous space, such as those available through X-ray microtomography. We use the finite difference method to discretize the governing equations and also propose a new method to enforce the incompressible flow constraint under zero Neumann boundary conditions for the velocity components. Finite difference formulation leads to fast parallel implementation through linear solvers for sparse matrices, allowing relatively fast simulations, while regularization techniques used on solving inverse problems lead to the desired incompressible fluid flow. Tests performed using benchmark samples show good agreement with experimental/theoretical values. Additional tests are run on Bentheimer and Buff Berea sandstone samples with available laboratory measurements. We compare the results from our new method, based on finite differences, with an open source finite volume implementation as well as experimental results, specifically to evaluate the benefits and drawbacks of each method. Finally, we calculate relative permeability by using this modified finite difference technique together with a level set based algorithm for multi-phase fluid distribution in the pore space. To our knowledge this is the first time regularization techniques are used in combination with finite difference fluid flow simulations.

  8. Performance of Two Cloud-Radiation Parameterization Schemes in the Finite Volume General Circulation Model for Anomalously Wet May and June 2003 Over the Continental United States and Amazonia

    Science.gov (United States)

    Sud, Y. C.; Mocko, David M.; Lin, S. J.

    2006-01-01

    An objective assessment of the impact of a new cloud scheme, called Microphysics of Clouds with Relaxed Arakawa-Schubert Scheme (McRAS) (together with its radiation modules), on the finite volume general circulation model (fvGCM) was made with a set of ensemble forecasts that invoke performance evaluation over both weather and climate timescales. The performance of McRAS (and its radiation modules) was compared with that of the National Center for Atmospheric Research Community Climate Model (NCAR CCM3) cloud scheme (with its NCAR physics radiation). We specifically chose the boreal summer months of May and June 2003, which were characterized by an anomalously wet eastern half of the continental United States as well as northern regions of Amazonia. The evaluation employed an ensemble of 70 daily 10-day forecasts covering the 61 days of the study period. Each forecast was started from the analyzed initial state of the atmosphere and spun-up soil moisture from the first-day forecasts with the model. Monthly statistics of these forecasts with up to 10-day lead time provided a robust estimate of the behavior of the simulated monthly rainfall anomalies. Patterns of simulated versus observed rainfall, 500-hPa heights, and top-of-the-atmosphere net radiation were recast into regional anomaly correlations. The correlations were compared among the simulations with each of the schemes. The results show that fvGCM with McRAS and its radiation package performed discernibly better than the original fvGCM with CCM3 cloud physics plus its radiation package. The McRAS cloud scheme also showed a reasonably positive response to the observed sea surface temperature on mean monthly rainfall fields at different time leads. This analysis represents a method for helpful systematic evaluation prior to selection of a new scheme in a global model.

  9. Finite-time stochastic outer synchronization between two complex dynamical networks with different topologies.

    Science.gov (United States)

    Sun, Yongzheng; Li, Wang; Zhao, Donghua

    2012-06-01

    In this paper, the finite-time stochastic outer synchronization between two different complex dynamical networks with noise perturbation is investigated. By using suitable controllers, sufficient conditions for finite-time stochastic outer synchronization are derived based on the finite-time stability theory of stochastic differential equations. It is noticed that the coupling configuration matrix is not necessary to be symmetric or irreducible, and the inner coupling matrix need not be symmetric. Finally, numerical examples are examined to illustrate the effectiveness of the analytical results. The effect of control parameters on the settling time is also numerically demonstrated.

  10. Effect of different lateral occlusion schemes on peri-implant strain: A laboratory study

    Science.gov (United States)

    Lo, Jennifer; Palamara, Joseph

    2017-01-01

    PURPOSE This study aims to investigate the effects of four different lateral occlusion schemes and different excursions on peri-implant strains of a maxillary canine implant. MATERIALS AND METHODS Four metal crowns with different occlusion schemes were attached to an implant in the maxillary canine region of a resin model. The included schemes were canine-guided (CG) occlusion, group function (GF) occlusion, long centric (LC) occlusion, and implant-protected (IP) occlusion. Each crown was loaded in three sites that correspond to maximal intercuspation (MI), 1 mm excursion, and 2 mm excursion. A load of 140 N was applied on each site and was repeated 10 times. The peri-implant strain was recorded by a rosette strain gauge that was attached on the resin model buccal to the implant. For each loading condition, the maximum shear strain value was calculated. RESULTS The different schemes and excursive positions had impact on the peri-implant strains. At MI and 1 mm positions, the GF had the least strains, followed by IP, CG, and LC. At 2 mm, the least strains were associated with GF, followed by CG, LC, and IP. However, regardless of the occlusion scheme, as the excursion increases, a linear increase of peri-implant strains was detected. CONCLUSION The peri-implant strain is susceptible to occlusal factors. The eccentric location appears to be more influential on peri-implant strains than the occlusion scheme. Therefore, adopting an occlusion scheme that can reduce the occurrence of occlusal contacts laterally may be beneficial in reducing peri-implant strains. PMID:28243391

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

    African Journals Online (AJOL)

    This cavity was restored with three different materials (Group I: Resin composite, Group II: ... Introduction. In restorative dentistry, the preferred method of treatment for cervical ... cold liquids. The cavity environment can be exposed to thermal.

  12. ORIGINAL ARTICLE Fitted-Stable Finite Difference Method for ...

    African Journals Online (AJOL)

    Gemechis

    A fitted-stable central difference method is presented for solving singularly perturbed two point ... with exact solutions. The error bound and convergence of the proposed method has also ... explicit method involving the reduction of order for ...

  13. Numerical Simulation of Chennai Heavy Rainfall Using MM5 Mesoscale Model with Different Cumulus Parameterization Schemes

    Science.gov (United States)

    Litta, A. J.; Chakrapani, B.; Mohankumar, K.

    2007-07-01

    Heavy rainfall events become significant in human affairs when they are combined with hydrological elements. The problem of forecasting heavy precipitation is especially difficult since it involves making a quantitative precipitation forecast, a problem well recognized as challenging. Chennai (13.04°N and 80.17°E) faced incessant and heavy rain about 27 cm in 24 hours up to 8.30 a.m on 27th October 2005 completely threw life out of gear. This torrential rain caused by deep depression which lay 150km east of Chennai city in Bay of Bengal intensified and moved west north-west direction and crossed north Tamil Nadu and south Andhra Pradesh coast on 28th morning. In the present study, we investigate the predictability of the MM5 mesoscale model using different cumulus parameterization schemes for the heavy rainfall event over Chennai. MM5 Version 3.7 (PSU/NCAR) is run with two-way triply nested grids using Lambert Conformal Coordinates (LCC) with a nest ratio of 3:1 and 23 vertical layers. Grid sizes of 45, 15 and 5 km are used for domains 1, 2 and 3 respectively. The cumulus parameterization schemes used in this study are Anthes-Kuo scheme (AK), the Betts-Miller scheme (BM), the Grell scheme (GR) and the Kain-Fritsch scheme (KF). The present study shows that the prediction of heavy rainfall is sensitive to cumulus parameterization schemes. In the time series of rainfall, Grell scheme is in good agreement with observation. The ideal combination of the nesting domains, horizontal resolution and cloud parameterization is able to simulate the heavy rainfall event both qualitatively and quantitatively.

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

    Science.gov (United States)

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

    1995-01-01

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

  15. Recovery schemes for different distributed connection management in generalized multi-protocol label switching networks

    Institute of Scientific and Technical Information of China (English)

    Can Wang; Yuefeng Ji

    2007-01-01

    As the wavelength division multiplexing (WDM) technology matures and the demands for bandwidth increase, survivability becomes more and more important in generalized multi-protocol label switching (GMPLS) controlled intelligent optical networks (IONs). There are great interests to study the performance of restorability under one certain connection management strategy. And studies in the problem of providing recovery from link failures under two different resource reservation schemes, forward reservation protocols (FRPs) and backward reservation protocols (BRPs), are presented. They are examined from the point of view of connection blocking probability, restorability and average recovery time. The two different connection management schemes and the survey of different recovery schemes are first presented. The performance of these recovery strategies is analyzed and compared both through theoretical analysis and simulation results. The main stressed idea is that using BRPs gives the best performance in terms of restorability and blocking probability in restorable GMPLS networks.

  16. Exploring the Effectiveness of Different Approaches to Teaching Finite Mathematics

    Science.gov (United States)

    Smeal, Mary; Walker, Sandra; Carter, Jamye; Simmons-Johnson, Carolyn; Balam, Esenc

    2013-01-01

    Traditionally, mathematics has been taught using a very direct approach which the teacher explains the procedure to solve a problem and the students use pencil and paper to solve the problem. However, a variety of alternative approaches to mathematics have surfaced from a number of different directions. The purpose of this study was to examine the…

  17. M2Di: Concise and efficient MATLAB 2-D Stokes solvers using the Finite Difference Method

    Science.gov (United States)

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

    2017-02-01

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

  18. A generalized finite difference method for modeling cardiac electrical activation on arbitrary, irregular computational meshes.

    Science.gov (United States)

    Trew, Mark L; Smaill, Bruce H; Bullivant, David P; Hunter, Peter J; Pullan, Andrew J

    2005-12-01

    A generalized finite difference (GFD) method is presented that can be used to solve the bi-domain equations modeling cardiac electrical activity. Classical finite difference methods have been applied by many researchers to the bi-domain equations. However, these methods suffer from the limitation of requiring computational meshes that are structured and orthogonal. Finite element or finite volume methods enable the bi-domain equations to be solved on unstructured meshes, although implementations of such methods do not always cater for meshes with varying element topology. The GFD method solves the bi-domain equations on arbitrary and irregular computational meshes without any need to specify element basis functions. The method is useful as it can be easily applied to activation problems using existing meshes that have originally been created for use by finite element or finite difference methods. In addition, the GFD method employs an innovative approach to enforcing nodal and non-nodal boundary conditions. The GFD method performs effectively for a range of two and three-dimensional test problems and when computing bi-domain electrical activation moving through a fully anisotropic three-dimensional model of canine ventricles.

  19. Leveraging performance of 3D finite difference schemes in large scientific computing simulations

    OpenAIRE

    De la Cruz, Raúl

    2015-01-01

    Gone are the days when engineers and scientists conducted most of their experiments empirically. During these decades, actual tests were carried out in order to assess the robustness and reliability of forthcoming product designs and prove theoretical models. With the advent of the computational era, scientific computing has definetely become a feasible solution compared with empirical methods, in terms of effort, cost and reliability. Large and massively parallel computational resources have...

  20. A Stable Finite-Difference Scheme for Population Growth and Diffusion on a Map

    Science.gov (United States)

    Callegari, S.; Lake, G. R.; Tkachenko, N.; Weissmann, J. D.; Zollikofer, Ch. P. E.

    2017-01-01

    We describe a general Godunov-type splitting for numerical simulations of the Fisher–Kolmogorov–Petrovski–Piskunov growth and diffusion equation on a world map with Neumann boundary conditions. The procedure is semi-implicit, hence quite stable. Our principal application for this solver is modeling human population dispersal over geographical maps with changing paleovegetation and paleoclimate in the late Pleistocene. As a proxy for carrying capacity we use Net Primary Productivity (NPP) to predict times for human arrival in the Americas. PMID:28085882