A weak formulation of Roe's approximate Riemann solver applied to the St. Venant equations (Q1346520)

Recently \textit{I. Toumi} [J. Comput. Phys. 102, No. 2, 360-373 (1992; Zbl 0783.65068)] presented a weak formulation of Roe's approximate Riemann solver based on a definition of a nonconservative product. Toumi first identifies the Lipschitz continuous path connecting two states that leads to the Roe-averaged state for an ideal gas and then constructs a generalised Roe-averaged matrix for the Euler equations for real gases by using the same path. The purpose of this paper is to show that employing the ideas presented by Toumi to the shallow water equations leads to an approximate Riemann solver.