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In this paper we present a new family of approximate Riemann solvers for thenumerical approximation of solutions of hyperbolic conservation laws. They areapproximate, also referred to as incomplete, in the sense that the solversavoid computing the characteristic decomposition of the flux Jacobian. Instead,they require only an estimate of the globally fastest wave speeds in bothdirections. Thus, this family of solvers is particularly efficient for largesystems of conservation laws, i.e. with many different propagation speeds, andwhen no explicit expression for the eigensystem is available. Even though onlyfastest wave speeds are needed as input values, the new family of Riemannsolvers reproduces all waves with less dissipation than HLL, which has the sameprerequisites, requiring only one additional flux evaluation.

Hybrid Riemann Solvers for Large Systems of Conservation Laws