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

Geophysic al flows over comp lex domains often encompass both coarse and highly resolved regions. Approxim ating these flows using shock-capturing methods with explicit timestep ping 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 timestep ping (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 shallo w 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, add itional 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. 2013 Elsevier B.V. All rights reserved.