Solving the Shallow Water Equations Using the High Order Space-Time Discontinuous Galerkin Cell-Vertex Scheme

摘要

This paper attempts to solve the shallow water equations (SWEs) using a new Riemann-solver-free high order space time method named the discontinuous Galerkin cell-vertex scheme (DG-CVS). The detailed DG-CVS formulation for SWEs is provided and the solution updating strategy is based on the alternate solution updating at the cell level and the vertex level within one physical time step. Therefore, DG-CVS is built upon the staggered space-time mesh which leads to a Riemann-solver-free approach. The high order accuracy is obtained by employing space-time discontinuous Galerkin basis functions to approximate the solution. Numerical results demonstrate the accuracy of our method.