A parallel local timestepping Runge–Kutta discontinuous Galerkin method with applications to coastal ocean modeling

Abstract

Geophysical flows over complex domains often encompass both coarse and highly resolved regions. Approximating these flows using shock-capturing methods with explicit timestepping gives rise to a Courant–Friedrichs–Lewy (CFL) timestep constraint. This approach can result in small global timesteps often dictated by flows in small regions, vastly increasing computational effort over the whole domain. One approach for coping with this problem is to use locally varying timesteps. In previous work, we formulated a local timestepping (LTS) method within a Runge–Kutta discontinuous Galerkin framework and demonstrated the accuracy and efficiency of this method on serial machines for relatively small-scale shallow water applications. For more realistic models involving large domains and highly complex physics, the LTS method must be parallelized for multi-core parallel computers. Furthermore, additional physics such as strong wind forcing can effect the choice of local timesteps. In this paper, we describe a parallel LTS method, parallelized using domain decomposition and MPI. We demonstrate the method on tidal flows and hurricane storm surge applications in the coastal regions of the Western North Atlantic Ocean.