A high-order triangular discontinuous Galerkin oceanic shallow water model
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Authors
Giraldo, F.X.
Warburton, T.
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2008
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Abstract
A high-order triangular discontinuous Galerkin (DG) method is applied to the two-dimensional oceanic shallow water equations. The DG method can be characterized as the fusion of finite elements with finite volumes. This DG formulation uses high-order Lagrange polynomials on the triangle using nodal sets up to 15th order. Both the area and boundary integrals are evaluated using order 2N Gauss cubature rules. The use of exact integration for the area integrals leads naturally to a full mass matrix; however, by using straight-edged triangles we eliminate the mass matrix completely from the discrete equations. Besides obviating the need for a mass matrix, triangular elements offer other obvious advantages in the construction of oceanic shallow water models, specifically the ability to use unstructured grids in order to better represent the continental coastlines for use in tsunami modeling. In this paper, we focus primarily on testing the discrete spatial operators by using six test cases-three of which have analytic solutions. The three tests having analytic solutions show that the high-order triangular DG method exhibits exponential convergence. Furthermore, comparisons with a spectral element model show that the DG model is superior for all polynomial orders and test cases considered. Copyright (C) 2007 John Wiley & Sons, Ltd.
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The article of record as published may be located at http://dx.doi.org/10.1002/fld.1562
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Applied Mathematics
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International Journal for Numerical Methods in Fluids / Volume 56, Issue 7, 899-925
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.