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

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The Riemann Problem for the Euler Equations,o non-linear systems of hyperbolic conservation laws. The key ingredient of the scheme is the solution of the Riemann problem. The purpose of this chapter is to provide a detailed presentation of the complete, exact solution to the Riemann problem for the one-dimensional, time-dependent Euler equati

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Notions on Numerical Methods,ll assume the concepts of truncation error, order of accuracy, consistency, modified equation, stability and convergence. For background on these concepts the reader may consult virtually any standard book on numerical methods for differential equations. As general references, useful textbooks are t

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Random Choice and Related Methods,ems of hyperbolic conservation laws. In 1976, Chorin [73] successfully implemented a modified version of the method, as a computational technique, to solve the Euler equations of Gas Dynamics. In essence, to implement the RCM one requires (i) exact solutions of local Riemann problems and (ii) a rand

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Approximate-State Riemann Solvers,ons of times, making the Riemann problem solution process the single most demanding task in the numerical method. In Chap. 4 we provided exact Riemann solvers for the Euler equations for ideal and covolume gases. An iterative procedure is always involved and the associated computational effort may n

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The HLL and HLLC Riemann Solvers,The resulting Riemann solvers have become known as HLL Riemann solvers. In this approach an ., unlike the Riemann solvers presented previously in Chaps. 4 and 9. The central idea is to assume a wave configuration for the solution that consists of two waves separating three constant states. Assuming

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The Riemann Solver of Roe, [281]. Since then, the method has not only been refined, but it has also been applied to a very large variety of physical problems. Refinements to the Roe approach were introduced by Roe and Pike [290], whereby the computation of the necessary items of information does not explicitly require the Ro

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The Riemann Solver of Osher, Osher in 1981 [120] and Osher and Solomon the following year [255]. Applications to the Euler equations were published later in a paper by Osher and Chakravarthy. [253]. Since then the scheme has gained increasing popularity, particularly within the CFD community concerned with Steady Aerodynamics;

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