Krylov-Riemann Solver for Large Hyperbolic Systems of Conservation Laws

This paper presents a Riemann solver for nonlinear hyperbolic systems of conservation laws based on a Krylov subspace approximation of the upwinding dissipation vector. In the general case, the solver does not require any detailed information of the eigensystem, except an estimate of the global maximal propagation speed. It uses successive flux function evaluations to obtain a numerical flux which is almost equivalent to that of a Godunov scheme with complete upwinding. The new Krylov–Riemann solver is particularly efficient when used for large systems with many nonlinear equations such that typically no explicit expression for the eigensystem is available. Also, no numerical procedures are necessary to compute the eigensystem. Numerical examples demonstrate the excellent performance of the solver with respect to other solvers.