Topic
Finite difference method
About: Finite difference method is a research topic. Over the lifetime, 21603 publications have been published within this topic receiving 468852 citations. The topic is also known as: Finite-difference methods & FDM.
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TL;DR: This paper investigates the accurate numerical solution of the equations governing bed-load sediment transport and two approaches: a steady and an unsteady approach are discussed and five different formulations within these frameworks are derived.
Abstract: This paper investigates the accurate numerical solution of the equations governing bed-load sediment transport. Two approaches: a steady and an unsteady approach are discussed and five different formulations within these frameworks are derived. A flux-limited version of Roe's scheme is used with the different formulations on a channel test problem and the results compared.
123 citations
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TL;DR: This work describes a finite difference solution technique for the full-vector waveguide equation based upon the alternating-direction-implicit (ADI) iterative method that accurately treats dielectric boundaries, requires minimal computer resources, and executes faster than other iterative approaches.
Abstract: We describe a finite difference solution technique for the full-vector waveguide equation based upon the alternating-direction-implicit (ADI) iterative method. Our technique accurately treats dielectric boundaries (including corners), requires minimal computer resources, and executes faster (by factors of 3-10) than other iterative approaches. In addition, we employ a transparent boundary condition that effectively removes the sensitivity of the calculated results to the size of the computational domain. This feature greatly facilitates the examination of modes near cutoff. >
123 citations
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TL;DR: The ADE-CPML method provides a more flexible representation that can be extended to higher-order methods and is applied to the discontinuous Galerkin finite element time-domain method.
Abstract: An efficient auxiliary-differential equation (ADE) form of the complex frequency shifted perfectly matched layer (CPML) absorbing media derived from a stretched coordinate PML formulation is presented. It is shown that a unit step response of the ADE-CPML equations leads to a discrete form that is identical to Roden's convolutional PML method for FDTD implementations. The derivation of discrete difference operators for the ADE-CPML equations for FDTD is also presented. The ADE-CPML method is also extended in a compact form to a multiple-pole PML formulation. The advantage of the ADE-CPML method is that it provides a more flexible representation that can be extended to higher-order methods. In this paper, it is applied to the discontinuous Galerkin finite element time-domain (DGFETD) method. It is demonstrated that the ADE-CPML maintains the exponential convergence of the DGFETD method.
123 citations
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TL;DR: A block-centered finite difference scheme is introduced to solve the nonlinear Darcy--Forchheimer equation, in which the velocity and pressure can be approximated simultaneously.
Abstract: A block-centered finite difference scheme is introduced to solve the nonlinear Darcy--Forchheimer equation, in which the velocity and pressure can be approximated simultaneously. The second-order error estimates for both pressure and velocity are established on a nonuniform rectangular grid. Numerical experiments using the scheme show the consistency of the convergence rates of our method with the theoretical analysis.
123 citations
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TL;DR: This work reformulates CPR methods using summation-by-parts (SBP) operators with simultaneous approximation terms (SATs), a framework popular for finite difference methods, and proves entropy stability for Burgers' equation is proved for general SBP CPR methods not including boundary nodes.
123 citations