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A robust, finite element model for hydrostatic surface water flows. (English) Zbl 0915.76056
Summary: We introduce a finite element scheme for the two-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level, such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. We examine the convergence rates and relative computational efficiency with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.

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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