Titlebook: Riemann Solvers and Numerical Methods for Fluid Dynamics; A Practical Introduc Eleuterio F. Toro Book 19992nd edition Springer-Verlag Berli

PRE

Approximate-State Riemann Solvers,nov—type methods: one approach is to find an . employed in the numerical method, directly, see Chaps. 10, 11 and 12; the other approach is to find an . and then evaluate the physical flux function at this state. It is the latter route the one we follow in this chapter.

可以任性

The HLL and HLLC Riemann Solvers,ent and robust approximate Godunov—type methods. One difficulty with these schemes, however, is the assumption of a two—wave configuration. This is correct only for hyperbolic systems of two equations, such as the one—dimensional shallow water equations. For larger systems, such as the Euler equatio

Outspoken

The Riemann Solver of Roe,nsiderable period of time has led to various improvements of the scheme. As originally presented the Roe scheme computes rarefaction shocks, thus violating the entropy condition. Harten and Hyman [163], Roe and Pike [290], Roe [288], Dubois and Mehlman [113] and others, have produced appropriate mod

DOSE

The Riemann Solver of Osher,lowly—moving shock waves; see Roberts [280], Billett and Toro [40] and Arora and Roe [13]. The scheme is closely related to the Flux Vector Splitting approach described in Chap. 8 and, as Godunov’s method of Chap. 6, it is a generalisation of the CIR scheme described in Chap. 5 for linear hyperbolic

Introduction

High-Order and TVD Schemes for Non-Linear Systems,Chap. 3. Applications to other systems may be easily accomplished. Techniques for extending the methods to systems with source terms, as for reactive flows for instance, are given in Chap. 15 and to multidimensional systems in Chap. 16.

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Riemann Solvers and Numerical Methods for Fluid Dynamics978-3-662-03915-1

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ALERT

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