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A class of approximate Riemann solvers and their relation to relaxation schemes. (English) Zbl 0988.65072
Summary: The authors show that a simple relaxation scheme of the type proposed by S. Jin and Z. Xin [Commun. Pure Appl. Math. 48, No. 3, 235-276 (1995; Zbl 0826.65078)] 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.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35R05 PDEs with low regular coefficients and/or low regular data
35L65 Hyperbolic conservation laws
65H10 Numerical computation of solutions to systems of equations
Software:
CLAWPACK; HE-E1GODF; HLLE
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References:
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