A Parallel Two-Dimensional Discontinuous Galerkin Method for Shallow-Water Flows Using High-Resolution Unstructured Meshes

Abstract

Flood modeling and forecasting using hydraulic models are computationally expensive for high-resolution, large-scale problems. With the advent of high-performance computing, numerical models can obtain promising speedup using parallel computing resources. In this paper, an message passing interface (MPI)-based parallel shallow-water flow solver using the discontinuous Galerkin method is presented. Parallelization is implemented with static domain decomposition using the single program–multiple data design. Data transfer between subdomains are achieved using the MPI implementation. The parallel solver is tested using idealized dam-break tests and field tests, for both fully wet and partially wet domains. The performance of parallel speedup and efficiency are compared for different mesh resolution and cluster architecture. A statistical index (maximum ratio of halo cells to total number of elements) is introduced to evaluate the parallel efficiency and performance, and this index can be used as a guide to choose the number of cores in applications.