Topic
Finite difference
About: Finite difference is a research topic. Over the lifetime, 19693 publications have been published within this topic receiving 408603 citations.
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TL;DR: It is shown how stable fully discrete high order accurate approximations of the Maxwells' equations, the elastic wave equations and the linearized Euler and Navier-Stokes equations can obtained.
91 citations
TL;DR: In this article, the numerical solution of the time-domain Maxwell's equations in dispersive propagation media by a discontinuous Galerkin time domain method is presented, where the Debye model is used to describe the dispersive behaviour of the media.
Abstract: This work is about the numerical solution of the time-domain Maxwell's equations in dispersive propagation media by a discontinuous Galerkin time-domain method. The Debye model is used to describe the dispersive behaviour of the media. The resulting system of differential equations is solved using a centred-flux discontinuous Galerkin formulation for the discretization in space and a second-order leapfrog scheme for the integration in time. The numerical treatment of the dispersive model relies on an auxiliary differential equation approach similar to that which is adopted in the finite difference time-domain method. Stability estimates are derived through energy considerations and convergence is proved for both the semidiscrete and the fully discrete schemes.
91 citations
Book•
01 Aug 1988
TL;DR: This book discusses ocean acoustic wave propagation problems, Applicable solution methods other than the implicit finite difference scheme, and some of the methods used in this scheme.
Abstract: Foreword. Preface. Introduction. Ocean acoustic wave propagation problems. Finite difference schemes. Initial and boundary conditions. Range step size analysis. Wide-angle capability. Applicable solution methods other than the implicit finite difference scheme. Representative test examples. Listing of computer codes. Reference citation index. Subject index.
91 citations
TL;DR: A Symmetrical Conservative Metric Method (SCMM) is newly proposed based on the discussions of the metrics and Jacobian in FDM from geometry viewpoint by following the concept of vectorized surface and cell volume in Finite Volume Methods (FVMs).
91 citations
TL;DR: In this paper, two approaches to finite difference approximation of turbulent flows of electrically conducting incompressible fluids in the presence of a steady magnetic field are analyzed, one based on high-order approximations and up-biased discretization of the nonlinear term, and another consistent of the second order and nearly fully conservative in regard of mass, momentum, kinetic energy, and electric charge conservation principles.
91 citations