FLOODING AND DRYING IN DISCONTINUOUS GALERKIN DISCRETIZATIONS OF SHALLOW WATER EQUATIONS

Abstract. Accurate modeling of flooding and drying is important in forecasting river floods and near-shore hydrodynamics. We consider the space-time discontinuous Galerkin finite element discretization for shallow water equations with linear approximations of flow field. In which, the means (zeroth order approximation) is used to conserve the mass and momentum, and the slopes (first order approximation) are used to capture the front movement accurately in contrast to the finite volume schemes, where the slopes have to be reconstructed. As a preliminary step, we specify the front movement from some available exact solutions and show that the numerical results are second order accurate for linear polynomials. To resolve the front movement accurately in the context of discontinuous Galerkin discretizations, the front tracking and the front capturing methods are currently under investigation.