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A discontinuous Galerkin algorithm for the two-dimensional shallow water equations

Lookup NU author(s): Dr Georges Kesserwani, Professor Qiuhua Liang


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A new high-resolution finite element scheme is introduced for solving the two-dimensional (2D) depth-integrated shallow water equations (SWE) via local plane approximations to the unknowns. Bed topography data are locally approximated in the same way as the flow variables to render an instinctive well-balanced scheme. A finite volume (FV) wetting and drying technique that reconstructs the Riemann states by ensuring non-negative water depth and maintaining well-balanced solution is adjusted and implemented in the current finite element framework. Meanwhile, a local slope-limiting process is applied and those troubled-slope-components are restricted by the minmod FV slope limiter. The inter-cell fluxes are upwinded using the HLLC approximate Riemann solver. Friction forces are separately evaluated via stable implicit discretization to the finite element approximating coefficients. Boundary conditions are derived and reported in details. The present model is validated against several test cases including dam-break flows on regular and irregular domains with flooding and drying.

Publication metadata

Author(s): Kesserwani G, Liang Q

Publication type: Article

Publication status: Published

Journal: Computer Methods in Applied Mechanics and Engineering

Year: 2010

Volume: 199

Issue: 49-52

Pages: 3356-3368

Print publication date: 12/08/2010

ISSN (print): 0045-7825

Publisher: Elsevier BV


DOI: 10.1016/j.cma.2010.07.007


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Funder referenceFunder name
EP/F030177/1UK Engineering and Physical Sciences Research Council (EPSRC)