Space-time discontinuous Galerkin finite element method for shallow water flows

Authors:
V. R. Ambati;O. Bokhove
Affiliations:
Numerical Analysis and Computational Mechanics Group, Department of Applied Mathematics, University of Twente, Enschede, P.O. Box 217, The Netherlands;Numerical Analysis and Computational Mechanics Group, Department of Applied Mathematics, University of Twente, Enschede, P.O. Box 217, The Netherlands
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 3
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Abstract

A space-time discontinuous Galerkin (DG) finite element method is presented for the shallow water equations over varying bottom topography. The method results in nonlinear equations per element, which are solved locally by establishing the element communication with a numerical HLLC flux. To deal with spurious oscillations around discontinuities, we employ a dissipation operator only around discontinuities using Krivodonova's discontinuity detector. The numerical scheme is verified by comparing numerical and exact solutions, and validated against a laboratory experiment involving flow through a contraction. We conclude that the method is second order accurate in both space and time for linear polynomials.