MOVING BOUNDARY TREATMENT FOR RUNGE-KUTTA DISCONTINUOUS GALERKIN SHALLOW WATER MODEL

A wet-dry scheme for moving boundary treatment is implemented in the framework of discontinuous Galerkin shallow water equations. As a formulation of approximate Riemann solver, the HLL (Harten-Lax-van Leer) numerical fluxes are employed and the TVB (Total Variation Bounded) slope limiter is used for the removal of unnecessary oscillations. As benchmark test problems, the dam-break problems and the classical problem of periodic oscillation in the parabolic bowl are solved with linear triangular elements and second-order Runge-Kutta scheme. The results are compared with exact solutions and the numerical solutions of previous study. For a more practical application, the implicit Runge-Kutta scheme is employed for the bottom friction terms and the moving shoreline in a rectangular basin of varying slopes is simulated. In all case studies, good agreement is observed with exact solutions or other well-known numerical solutions.