Runge-Kutta Discontinuous Galerkin Method Applied to Shallow Water Equations with Flooding and Drying Treatment

Abstract

This work is devoted to the numerical simulation of Shallow Water Equations involving dry areas and a moving shoreline. The space and time discretization using the Runge-Kutta Discontinuous Galerkin approach is applied to nonlinear hyperbolic Shallow Water Equations. Problems with dry areas are challenging problems for such methods. To counter this issue, special treatment is applied around the shoreline. This work compares two treatments, one based on slope modification and one based on p-adaptation.