Titlebook: Riemann Solvers and Numerical Methods for Fluid Dynamics; A Practical Introduc Eleuterio F. Toro Book 2009Latest edition Springer-Verlag Be

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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 [110] 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 ran

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The Riemann Solver of Osher, Osher in 1981 [185] and Osher and Solomon the following year [372]. Applications to the Euler equations were published later in a paper by Osher and Chakravarthy [370]. Since then the scheme has gained increasing popularity, particularly within the CFD community concerned with Steady Aerodynamics;

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,High–Order and TVD Methods for Scalar Equations,ysical) oscillations in the vicinity of large gradients. It is well–known that high–order linear (constant coefficients) schemes produce unphysical oscillations in the vicinity of large gradients. This was illustrated by some numerical results shown in Chap. 5. On the other hand, the class of ., def

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,High–Order and TVD Schemes for Non–Linear Systems,ne space dimension .. The upwind schemes are extensions of the Godunov first order upwind method of Chap. 6 and can be applied with any of the Riemann solvers presented in Chap. 4 (exact) and Chaps. 9 to 12 (approximate); they can also be used with the Flux Vector Splitting flux of Chap. 8. The cent