Abstract
We describe the application of a local discontinuous Galerkin method to the numerical solution of the three-dimensional shallow water equations. The shallow water equations are used to model surface water flows where the hydrostatic pressure assumption is valid. The authors recently developed a DG\linebreak method for the depth-integrated shallow water equations. The method described here is an extension of these ideas to non-depth-integrated models. The method and its implementation are discussed, followed by numerical examples on several test problems.
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Dawson, C., Aizinger, V. A Discontinuous Galerkin Method for Three-Dimensional Shallow Water Equations. J Sci Comput 22, 245–267 (2005). https://doi.org/10.1007/s10915-004-4139-3
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DOI: https://doi.org/10.1007/s10915-004-4139-3