The Riemann Problem for the Euler Equations

  • Eleuterio F. Toro

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.

Keywords

Cavitation Dition 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Eleuterio F. Toro
    • 1
  1. 1.Dept. of Computing and MathematicsManchester Metropolitan UniversityManchesterUK

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