Space-time discontinuous Galerkin nite element method for shallow water ows

A space-time discontinuous Galerkin (DG) nite element method is presented for the shallow water equations over varying bottom topography. The method results in non-linear equations per element, which are solved locally by establishing the ele-ment communication with a numerical HLLC ux. To deal with spurious oscillations around discontinuities, we employ a dissipation operator only around discontinu-ities using Krivodonova's discontinuity detector. The numerical scheme is veried by comparing numerical and exact solutions, and validated against a laboratory experiment involving ow through a contraction. We conclude that the method is second order accurate in both space and time for linear polynomials