Journal ArticleDOI
Dissipative mechanism in Godunov-type schemes
TLDR
In this article, the dissipative mechanism in the shock capturing schemes, where exact or approximate Riemann solvers are used in the flux evaluation, is analyzed, from which some pathological phenomena from the FVS scheme and the Godunov method will be explained.Abstract:
This paper concerns the dissipative mechanism in the shock capturing schemes, where exact or approximate Riemann solvers are used in the flux evaluation. More specifically, we are going to analyze the dissipation in the flux vector splitting (FVS) scheme and the Godunov method, from which some pathological phenomena from the FVS scheme and the Godunov method will be explained, such as the artificial dissipation and the shock instability. Copyright © 2001 John Wiley & Sons, Ltd.read more
Citations
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Journal ArticleDOI
A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method
TL;DR: In this article, an improved gas-kinetic scheme based on the Bhatnagar-Gross-Krook (BGK) model for the compressible Navier-Stokes equations is presented.
Journal ArticleDOI
A unified gas-kinetic scheme for continuum and rarefied flows IV
TL;DR: The UGKS as discussed by the authors is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path.
Journal ArticleDOI
On Validating an Astrophysical Simulation Code
Alan C. Calder,B. Fryxell,Tomasz Plewa,Tomasz Plewa,Robert Rosner,L. J. Dursi,V. G. Weirs,Todd F. Dupont,Harry Robey,J. Kane,Bruce Remington,R. P. Drake,Guy Dimonte,Michael Zingale,Michael Zingale,Francis Timmes,K. Olson,K. Olson,Paul M. Ricker,Peter MacNeice,Henry M. Tufo +20 more
TL;DR: In this paper, a case study of validating an astrophysical simulation code is presented, focusing on validating FLASH, a parallel adaptive-mesh hydrodynamics code for studying the compressible, reactive flows found in many astrophysical environments.
Journal ArticleDOI
Towards shock-stable and accurate hypersonic heating computations: A new pressure flux for AUSM-family schemes
Keiichi Kitamura,Eiji Shima +1 more
TL;DR: Three schemes are developed that have Mach-proportional dissipation inside the numerical shock wave structure, in contrast to Mach independent dissipation provided by conventional AUSM fluxes, and their desired performances are demonstrated for a wide spectrum of Mach numbers.
Journal ArticleDOI
Very simple, carbuncle-free, boundary-layer-resolving, rotated-hybrid Riemann solvers
TL;DR: New Euler flux functions for use in a finite-volume Euler/Navier-Stokes code are proposed, which are very simple, carbuncle-free, yet have an excellent boundary-layer-resolving capability, by combining two different Riemann solvers into one based on a rotated Riem Mann solver approach.
References
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Journal ArticleDOI
Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes
TL;DR: In this article, it is shown that these features can be obtained by constructing a matrix with a certain property U, i.e., property U is a property of the solution of the Riemann problem.
Book
Riemann Solvers and Numerical Methods for Fluid Dynamics
TL;DR: In this article, the authors present references and index Reference Record created on 2004-09-07, modified on 2016-08-08 and a reference record created on 2003-09 -07.
Journal Article
Finite difference methods for numerical computation of discontinous solutions of the equations of fluid dynamics
Journal ArticleDOI
A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
Gary A. Sod,Gary A. Sod +1 more
TL;DR: In this paper, the finite difference methods of Godunov, Hyman, Lax and Wendroff (two-step), MacCormack, Rusanov, the upwind scheme, the hybrid scheme of Harten and Zwas, the antidiffusion method of Boris and Book, and Glimm's method, a random choice method, are discussed.
Journal ArticleDOI
Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection
TL;DR: In this paper, an approach to numerical convection is presented that exclusively yields upstream-centered schemes, which start from a meshwise approximation of the initial-value distribution by simple basic functions, e.g., Legendre polynomials.
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