Abstract
In his classical paper of 1959, Godunov [130] presented a conservative extension of the first-order upwind scheme of Courant, Isaacson and Rees [89] to 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 equations for ideal and covolume gases, including vacuum conditions. The methodology can then be applied to other hyperbolic systems.
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© 1997 Springer-Verlag Berlin Heidelberg
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Toro, E.F. (1997). The Riemann Problem for the Euler Equations. In: Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03490-3_4
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DOI: https://doi.org/10.1007/978-3-662-03490-3_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-03492-7
Online ISBN: 978-3-662-03490-3
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