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GPU Accelerated Discontinuous Galerkin Methods for Shallow Water Equations

Part of: Hyperbolic equations and systems Equations of mathematical physics and other areas of application Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  03 July 2015

Rajesh Gandham ,
David Medina  and
Timothy Warburton
Rajesh Gandham*
Affiliation:
Department of Computational and Applied Mathematics, Rice University, 6100 Main Street, MS-134, Houston, TX-77005, USA
David Medina
Affiliation:
Department of Computational and Applied Mathematics, Rice University, 6100 Main Street, MS-134, Houston, TX-77005, USA
Timothy Warburton
Affiliation:
Department of Computational and Applied Mathematics, Rice University, 6100 Main Street, MS-134, Houston, TX-77005, USA
*
*Corresponding author. Email addresses: Rajesh.Gandham@rice.edu (R. Gandham), David.S.Medina@rice.edu (D. Medina), timwar@rice.edu (T. Warburton)
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Abstract

We discuss the development, verification, and performance of a GPU accelerated discontinuous Galerkin method for the solutions of two dimensional nonlinear shallow water equations. The shallow water equations are hyperbolic partial differential equations and are widely used in the simulation of tsunami wave propagations. Our algorithms are tailored to take advantage of the single instruction multiple data (SIMD) architecture of graphic processing units. The time integration is accelerated by local time stepping based on a multi-rate Adams-Bashforthscheme. A total variational bounded limiter is adopted for nonlinear stability of the numerical scheme. This limiter is coupled with a mass and momentum conserving positivity preserving limiter for the special treatment of a dry or partially wet element in the triangulation. Accuracy, robustness and performance are demonstrated with the aid of test cases. Furthermore, we developed a unified multi-threading model OCCA. The kernels expressed in OCCA model can be cross-compiled with multi-threading models OpenCL, CUDA, and OpenMP. We compare the performance of the OCCA kernels when cross-compiled with these models.

Keywords

Shallow water equationsdiscontinuous Galerkinpositivity preservingslope limitingGPUsacceleratorsmulti-threading

MSC classification

Secondary: 35Q35: PDEs in connection with fluid mechanics 35L60: Nonlinear first-order hyperbolic equations 35L65: Conservation laws 65Z05: Applications to physics 65M99: None of the above, but in this section
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 1 , July 2015 , pp. 37 - 64
Copyright
Copyright © Global-Science Press 2015 

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