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 Equations of Fluid Dynamics,s book. Instead, we give a fairly self—contained summary of the equations and the Thermodynamics in a manner that is immediately useful to the main purpose of this book, namely the detailed treatment of Riemann solvers and numerical methods.

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Notions on Numerical Methods,hose of Smith [315], Anderson et. al. [5], Mitchell and Griffiths [241], Roache [279], Richtmyer and Morton [276], Hoffmann [172] and Fletcher [125]. Very relevant textbooks to the main themes of this book are Sod [319], Holt [173], Hirsch Volumes I [170] and II [171], LeVeque [207], Godlewski and Raviart [144], Kröner [196] and Thomas [344].

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Methods for Multi-Dimensional PDEs,ime—dependent three dimensional Euler equations studied in Sect. 3.2 of Chap. 3. Other examples are the time—dependent two dimensional shallow water equations and the artificial compressibility equations. See Sect. 1.6.3 of Chap. 1.

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tion upwind and centered methods are today a mature generation of computational techniques applicable to a wide range of engineering and scientific disciplines, Computational Fluid Dynamics (CFD) being the most prominent up to now. This textbook gives a comprehensive, coherent and practical presenta

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The Riemann Problem for the Euler Equations,pter is to provide a detailed presentation of the complete, exact solution to the Riemann problem for the one-dimensional, time-dependent Euler equations for ideal and covolume gases, including vacuum conditions. The methodology can then be applied to other hyperbolic systems.

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Notions on Hyperbolic Partial Differential Equations,ons are those thought to be essential for the analysis of the equations of fluid flow and the implementation of numerical methods. For general background on PDEs we recommend the book by John [185] and particularly the one by Zachmanoglou and Thoe [425]. The discretisation techniques studied in this

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Some Properties of the Euler Equations, seen in Chap. 1, the Euler equations result from neglecting the effects of viscosity, heat conduction and body forces on a compressible medium. Here we show that these equations are a system of . conservations laws and study some of their mathematical properties. In particular, we study those prope