Modeling Swash Zone Hydrodynamics Using Discontinuous Galerkin Finite-Element Method

Abstract

A two-dimensional numerical model for the solution of the nonlinear shallow water equations (NSWEs) using the discontinuous Galerkin finite element method (DGFEM) is presented. A new adaptation of the thin-film approach is developed for the wetting/drying treatment. The model is applied to a number of test cases that can be characterized as swash flows, or as cases that are particularly useful for swash flow modeling. The DGFEM model shows robustness and provides accurate predictions of water depth, velocities, and shoreline movement. For the case of bore collapse on a plane beach the model performs well against a state-of-the-art finite volume swash code. The new wetting/drying algorithm is tested against a previous algorithm within the same framework for simulating a solitary wave propagating on a beach with bottom friction, showing a noticeable improvement in the shoreline prediction. The model is also tested against a more subtle test case, including generation of subharmonic edge waves, in order to test the effectiveness of DGFEM in reproducing second-order effects. The model simulates the excitation and development of the subharmonic edge waves when compared with the analytical solutions in the literature. Overall, it is shown here for the first time that the DGFEM technique can be used to simulate accurately a wide range of swash zone flows and therefore swash zone processes.