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The discontinuous Galerkin finite element method for the 2D shallow water equations. (English) Zbl 0987.76054
Summary: A high-order finite element, total variational diminishing Runge-Kutta discontinuous Galerkin method is proposed to solve free-surface problems in hydraulic dynamics. Some cases of circular dam and rapidly varying two-dimensional flows are presented to show the efficiency and stability of this method. The numerical simulations are performed on structured rectangular mesh for regular domain, and on an unstructured triangular mesh for irregular domain, respectively.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
86A05 Hydrology, hydrography, oceanography
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