High Order Numerical Methods for Geophysical Fluid Flows on HPC Architectures

New HPC architectures such as GPUs and/or hybrid GPU/CPU machines require rethinking the algorithms used to numerically solve partial differential equations, such as those arising in geophysical fluid flows in the atmosphere and oceans. Traditionally, large-scale solvers for these problems have been based on low order finite difference or finite volume methods; however, these methods may not scale well on current and future HPC machines. In the past few years, new high order methods have been investigated which can outperform traditional methods with respect to both accuracy and HPC efficiency. In this talk, we will report on the application of one method in particular, the discontinuous Galerkin (DG) finite element method, and its applications to geophysical flows in coastal oceans. We will demonstrate how the DG method can be implemented to take advantage of fine grain parallelism and improve cache performance. We will also compare the DG method to a well established model, the Advanced Circulation (ADCIRC) model, for coastal science applications.