High-order entropy stable discontinuous Galerkin methods for the shallow water equations: curved triangular meshes and GPU acceleration

2020/05/05 by Wu, Xinhui, Chan, Jesse, Kubatko, Ethan
#Computational Engineering #FOS: Computer and information sciences #FOS: Mathematics #Finance #Numerical Analysis (math.NA) #and Science (cs.CE)

paper · doi:10.48550/arxiv.2005.02516

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.

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