A NEW NUMERICAL METHOD FOR A 2-D NON-LINEAR SHALLOW WATER EQUATION SATISFAYING BOUNDARY CONDITIONS ON ARBITRARY TOPOGRAPHY AND WATER SURFACE

Abstract

A new scheme of numerical simulation for a flow with a free water surface is proposed. First, a technique of weight residual method using “reversed weight function” is presented, with which physical condition such as “pressure is constant at a surface” can be set inside the computational domain. As a result, flow with a free water surface on a complicated topography can be simulated on a coarse grid system, which contains the surface and the bottom of water inside. Then, the theory is formulated for FEM with rectangular regular grid system, and a demonstration is made for 2-D waves in a tank with a bottom undulation. The simulation result shows a good agreement with that from CCUP method though the grid of the former is far coarser than the latter's.