Parallel Scalability of Adaptive Mesh Refinement in a Finite Difference Solution to the Shallow Water Equations

Abstract

The Shallow Water Equations model the fluid dynamics of deep ocean flow, and are used to simulate tides, tsunamis, and storm surges. Numerical solutions using finite difference methods are computationally expensive enough to mandate the use of large computing clusters, and the cost grows not only with the amount of fluid, but also the duration of the simulated event, and the resolution of the approximation. The benefits of increased resolution are mostly connected to regions where complex fluid interactions occur, and are not required globally for the entire simulation. In this paper, we nvestigate the potential for conserving computational resources by applying Adaptive Mesh Refinement to dynamically determined areas of the fluid urface. We implement adaptive mesh refinement in a MacCormack finite difference solver, develop a performance model to predict its behavior on large-scale parallel platforms, and validate its predictions experimentally on two computing clusters. We find that the solver itself has highly favorable parallel scalability, and that the addition of refined areas introduces a performance penalty due to load imbalance that is at most proportional to the refinement degree raised to the third power.