High-order discontinuous Galerkin methods for coastal hydrodynamics applications

This paper applies high-order discontinuous Galerkin finite element solutions of the shallow water equations to realistic coastal hydrodynamics problems. The goal is to obtain results on par with the accuracy of current low-order models, while significantly surpassing their performance. Accomplishing this requires developing mesh discretizations with boundary and parameter field representations that are consistent with the high-order accuracy of the numerical methods. These developments allow coarse-mesh, high-order, solutions to provide comparable accuracy to today’s state-of-the-art high-resolution, low-order coastal models at reduced computational expense.