Multidimensional approximate Riemann solvers for hyperbolic nonconservative systems. Applications to shallow water systems

This paper deals with the development of efficient incomplete multidimensional Riemann solvers for hyperbolic systems. Departing from a four-waves model for the speeds of propagation arising at each vertex of the computational structured mesh, we present a general strategy for constructing genuinely multidimensional Riemann solvers, that can be applied for solving systems including source and coupling terms.