High-order Discontinuous Galerkin Methods for Nonhydrostatic Ocean Processes with a Free Surface

Accurate numerical simulation and modeling of ocean dynamics is playing an increasingly large role in scientific ocean applications. However, resolving these dynamics with traditional computational techniques can often be prohibitively expensive, necessitating the creation of next-generation high-order ocean models. In this work, we apply the local discontinuous Galerkin (LDG) and hybridizable discontinuous Galerkin (HDG) finite element methodology to discretize the ocean equations with a free-surface. We provide comparison of the strengths and weaknesses of the two formulations in terms of accuracy, efficiency, and scalability, and provide detailed discussion of numerical choices and their consequences as they relate to ocean modeling. We verify our methodology with numerical experiments and results from nonhydrostatic gravity wave theory.