Implicit discontinuous Galerkin scheme for shallow water equations

Abstract

The numerical solutions of shallow water equations are presented with implicit discontinuous Galerkin (IDG) method. The motivations for the development of an implicit scheme is stated. Details of the developed model is described including the spatial and temporal discretization, the approximate Riemann solver, and the slope limiter. For the validation of the model, the channel transition flow of contraction and expansion are carried out. As the last case study, the classical dam-break flow is simulated. In all cases, linear triangular meshes are employed and the implicit backward Euler time integration scheme is used. As an approximate Riemann solver, the Roe numerical flux is employed and a van Albada type gradient-reconstruction type slope limiter was applied. Good agreement was observed with experimental observations and exact solutions in all case studies.