APPROXIMATION OF SHALLOW-WATER EQUATIONS BY ROE RIEMANN SOLVER

The inviscid shallow water equations provide a genuinely hyperbolic sy stem and ail the numerical tools that have been developed for a system of conservation laws can be applied to them. However, this system of equations presents some peculiarities that can be exploited when devel oping a numerical method based on Roe's Riemann solver and enhanced by a slope limiting of MUSCL type. In the present paper a TVD version of the Lax-Wendroff scheme is used and its performance is shown in 1D an d 2D computations. Then two specific difficulties that arise in this c ontext are investigated. The former is the capability of this class of schemes to handle geometric source terms that arise to model the bott om variation. The latter analysis pertains to situations in which stri ct hyperbolicity is lost, i.e. when two eigenvalues collapse into one.