A WELL-BALANCED SCHEME FOR SHALLOW WATER EUQATIONS OVER IRREGULAR BED TOPOGRAPHY INCLUDING FLOODED AND PARTIAL FLOODED CELLS

摘要

This study develops a new well-balanced scheme for the one dimensional shallow water flow over irregular bed topography with wet/dry fronts, in a finite volume of Godunov-type framework. A new reconstruction technique is proposed including flooded cells and partial flooded cells which preserves non-negative of water depth values. For the wet cell, a modified RSGM (Revised Surface Gradient Method) is presented assuming that the bed topography is irregular in the cell. If the cell is partial flooded, this paper gives a special reconstruction technique of flow variables which has an assumption that the bottom function is linear in it. The HLL approximate Riemann solver is applied to evaluate the flux at cell faces. The numerical results show better agreements with analytical solutions of a set of test cases and experiment results.