High-order entropy stable discontinuous Galerkin methods for the shallow water equations: Curved triangular meshes and GPU acceleration. (15th January 2021)

• Record Type: Journal Article
• Authors: Wu, Xinhui; Kubatko, Ethan J.; Chan, Jesse
• Is Part Of: Computers & mathematics with applications. Volume 82(2021)
• Page Start: 179
• Page End: 199
• Publication Date: 2021-01-15
• Subjects: High order -- Discontinuous Galerkin -- Entropy stability -- Shallow water equations -- Summation by parts -- GPUs; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2020.11.006
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We present a high-order entropy stable discontinuous Galerkin (ESDG) method for the two dimensional shallow water equations (SWE) on curved triangular meshes. The presented scheme preserves a semi-discrete entropy inequality and remains well-balanced for continuous bathymetry profiles. We provide numerical experiments which confirm the high-order accuracy and theoretical properties of the scheme, and compare the presented scheme to an entropy stable scheme based on simplicial summation-by-parts (SBP) finite difference operators. Finally, we report the computational performance of an implementation on Graphics Processing Units (GPUs) and provide comparisons to existing GPU-accelerated implementations of high-order DG methods on quadrilateral meshes.