HIGH-RESOLUTION FINITE VOLUME METHODS FOR THE SHALLOW WATER EQUATIONS WITH BATHYMETRY AND DRY STATES

We give a brief review of the wave-propagation algorithm, a high-resolution finite volume method for solving hyperbolic systems of conservation laws. These methods require a Riemann solver to resolve the jump in variables at; each cell interface into waves. We present a Riemann solver for the shallow water equations that works robustly with bathymetry and dry states. This method is implemented in CLAWPACK and applied to benchmark problems from the Third International Workshop on Long-Wave Runup Models, including a two-dimensional simulation of runup during the 1993 tsunami event on Okushiri Island. Comparison is made with wave tank experimental data provided for the workshop. Some preliminary results using adaptive mesh refinement on the 26 December 2004 Sumatra event are also presented.