A discontinuous Galerkin method for the shallow water equations in spherical triangular coordinates
Giraldo. Francis X.
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A global model of the atmosphere is presented governed by the shallow water equations and discretized by a Runge–Kutta discontinuous Galerkin method on an unstructured tri- angular grid. The shallow water equations on the sphere, a two-dimensional surface in R3, are locally represented in terms of spherical triangular coordinates, the appropriate local coordinate mappings on triangles. On every triangular grid element, this leads to a two- dimensional representation of tangential momentum and therefore only two discrete momentum equations.
The Discontinuous Galerkin Coastal Ocean Model (DGCOM) is a two-dimensional shallow water model for simulating coastal ocean processes.The article of record may be found at http://www.doi.org/10.1016/j.jcp.2008.08.019
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Hamrick, Thomas A. (Monterey, California. Naval Postgraduate School, 1997-09);This thesis is concerned with the analysis of various methods for the numerical solution of the shallow water equations along with the stability of these methods. Most of the thesis is concerned with the background and ...
Giraldo, F.X. (2001);The spectral element method for the two-dimensional shallow water equations on the sphere is presented. The equations are written in conservation form and the domains are discretized using quadrilateral elements obtained ...
Giraldo, F.X.; Hesthaven, J. S.; Warburton, T. (2002);We present a high-order discontinuous Galerkin method for the solution of the shallow water equations on the sphere. To overcome well-known problems with polar singularities, we consider the shallow water equations in ...