Godunov Methods

  • Peter K. Sweby

Abstract

This paper reviews the class of numerical schemes, known as Godunov Methods, used for the solution of hyperbolic conservation laws. Such numerical schemes can be characterised by the solution (exact or approximate) of a Riemann Problem (classical or generalised) within computational cells in order to obtain the numerical fluxes.

Since the original first order scheme, proposed by Godunov in 1959, there has been much development of the idea; for example, the MUSCL scheme of van Leer in 1979, the PPM scheme of Woodward and Colella in 1984 and the Higher Order Godunov schemes of Bell, Colella and Trangenstein (1989).

As well as considering the original scheme and its later variants, we place these developments in historical context, making links with other work in the area.

Keywords

Entropy Convection Petroleum Advection Stein 

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Peter K. Sweby
    • 1
  1. 1.Department of MathematicsThe University of ReadingReadingEngland

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