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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
Full Text:
##### References:
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