Preprint 2001-002

A Class of Approximate Riemann Solvers and Their Relation to Relaxation Schemes

Randall J. LeVeque and Marica Pelanti

Abstract: We show that a simple relaxation scheme of the type proposed by Jin and Xin can be reinterpreted as defining a particular approximate Riemann solver for the original system of $m$ conservation laws. Based on this observation, a more general class of approximate Riemann solvers is proposed which allows as many as $2m$ waves in the resulting solution. These solvers are related to more general relaxation systems and connections with several other standard solvers are explored. The added flexibility of $2m$ waves may be advantageous in deriving new methods. Some potential applications are explored for problems with discontinuous flux functions or source terms.

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Randall J. LeVeque, <>
Marica Pelanti, <>
Publishing information:
J. Comput . Phys. 172 (2001), 573-591.
Revised version received September 24
Submitted by:
<> January 15 2001.

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