A discontinuous Galerkin finite element shallow water model in simulating tidal flows

The tidal flows are simulated by a discontinuous Galerkin (DG) finite element method (FEM), which can capture shock waves near the discontinuities and conserve the system fluxes during a long term calculation. A nonconforming linear triangular element is used to simplify the discretization of the boundary integration of horizontal diffusion terms, though there is no difference in treating convective terms for any other linear element. The nature of the diagonal mass matrix couples with the special element makes the time integral explicit so that no mass lumping is needed, whereas it does in the usual continuous FEM. The numerical flux between the discontinuous element interfaces is obtained by the HLL approximate Riemann solver, together with an efficient multi-dimensional limiter on a triangular mesh. Numerical results show the robustness of the present model.