Roe-type Riemann solvers for general hyperbolic systems

We present a Roe-type weak formulation Riemann solver where the average coefficient matrix is computed numerically. The novelty of this approach is that it is general enough that can be applied to any hyperbolic system while retaining the accuracy of the original Roe solver. We show applications to the compressible Euler equations with general equation of state. An alternative version of the method uses directly the eigenvectors in the averaging process, simplifying the algorithm. These new solvers are applied in conservative and path-conservative schemes with high-order accuracy and on unstructured meshes. © 2014 John Wiley & Sons, Ltd.