A Discontinuous Galerkin Method for Three-Dimensional Shallow Water Equations

We describe the application of a local discontinuous Galerkin method to the numerical solution of the three-dimensional shallow water equations. The shallow water equations are used to model surface water flows where the hydrostatic pressure assumption is valid. The authors recently developed a DGmethod for the depth-integrated shallow water equations. The method described here is an extension of these ideas to non depth-integrated models. The method and its implementation are discussed, followed by numerical examples on several test problems.