A high order semi-implicit discontinuous Galerkin method for the two dimensional shallow water equations on staggered unstructured meshes

A well-balanced, spatially arbitrary high order accurate semi-implicit discontinuous Galerkin scheme is presented for the numerical solution of the two dimensional shallow water equations on staggered unstructured non-orthogonal grids. The semi-implicit method is derived in such a fashion that all relevant integrals can be precomputed and stored in a preprocessing stage so that the extension to curved isoparametric elements is natural and does not increase the computational effort of the simulation at runtime. For p 0 the resulting scheme becomes a generalization of the classical semi-implicit finite-volume/finite difference scheme of Casulli and Walters (2000) [25], but with less conditions on the grid geometry. The method proposed in this paper allows large time steps with respect to the surface wave speed root gH p and is thus particularly suitable for low Froude number flows. The approach is validated on some typical academic benchmark problems using polynomial degrees up to p 6. (C) 2014 Elsevier Inc. All rights reserved.