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: The new method, unlike the older approaches, yields optimal estimates for the primal variable in both the element size h and polynomial degree p, and outperforms the standard upwind DG method.
226 citations
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TL;DR: A semi-implicit numerical model for the 3D Navier-Stokes equations on unstructured grids is derived and discussed in this article, where the governing differential equations are discretized by means of a finite difference-finite volume algorithm which is robust, very efficient, and applies to barotropic and baroclinic, hydrostatic and nonhydrostatic, and one-, two-, and three-dimensional flow problems.
226 citations
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TL;DR: In this article, the two-dimensional hydrodynamics program Nasa•Vof2D is modified to study the generation, propagation, and run-up on the shore of water waves created by landslides.
Abstract: The two‐dimensional hydrodynamics program Nasa‐Vof2D is modified to study the generation, propagation, and run‐up on the shore of water waves created by landslides. Nasa‐Vof2D, developed by the Los Alamos National Laboratory in Los Alamos, New Mexico, is a nonlinear Eulerian code, which solves the complete incompressible Navier‐Stokes equations by a finite difference method. The modification includes making the fluid domain boundaries (i.e., the bathymetry) time‐dependent. It allows a complex geometry box to slide down any incline, provided that the body kinetic is known and that the phenomenon is two‐dimensional or axisymmetric. To verify this numerical Nasa‐Vof2D extension, an experimental study on nonlinear waves generated by a two‐dimensional triangular body sliding a 45° inclined plane is conducted. The computed wave profiles show very close agreement with the experimental ones, except when free‐surface turbulence occurs, which the present numerical method cannot simulate.
226 citations
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TL;DR: The finite difference approximation of Caputo derivative on non-uniform meshes is investigated and a semi-discrete scheme is obtained and the unconditional stability and H^1 norm convergence are proved.
226 citations
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17 Nov 1993
TL;DR: In this article, the basic concepts of finite difference methods and their applications are discussed. But the authors focus on phase change dynamics and do not discuss the application of finite-difference methods in phase-change dynamics.
Abstract: Part 1 Basic concepts of finite difference methods: introduction to finite difference methods parabolic equations elliptic equations hyperbolic equations. Part 2 Pressure-based algorithms and their applications: pressure-based algorithms practical applications. Part 3 Interfacial transport: basic concepts of thermodynamics thermofluid phenomena involving capillarity and gravity physical and computational issues in phase-change dynamics.
223 citations