A CARTESIAN CUT CELL METHOD FOR SHALLOW WATER FLOWS WITH MOVING BOUNDARIES

Abstract

A new computational method for the calculation of shallow water flows with moving physical boundaries is presented. The procedure can cope with shallow water problems having arbitrarily complex geometries and moving boundary elements. Although the method provides a fully boundary-fitted capability, no mesh generation is required in the conventional sense. Solid regions are simply cut out of a background Cartesian mesh with their boundaries represented by different types of cut cell. Moving boundaries are accommodated by up-dating the local cut cell information on a stationary background mesh as the boundaries move. No large-scale re-meshing is required. For the flow calculations, a multi-dimensional high resolution upwind finite volume scheme is used in conjunction with an efficient approximate Riemann solver at flow interfaces, and an exact Riemann solution for a moving piston at moving boundary elements. The method is validated for test problems that include a ship's hull moving at supercritical velocity and two hypothetical landslide events where material plunges laterally into a quiescent shallow lake and a fiord.