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A conservative high-order discontinuous Galerkin method for the shallow water equations with arbitrary topography

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


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conservative high-order Godunov-type scheme is presented for solving the balance laws of the 1D shallow water equations (SWE). The scheme adopts a finite element Runge–Kutta (RK) discontinuous Galerkin (DG) framework. Based on an overall third-order accurate formulation, the model is referred to as RKDG3. Treatment of topographic source term is built in the DG approximation. Simplified formulae for initializing bed data at a discrete level are derived by assuming a local linear bed function to ease practical flow simulations. Owing to the adverse effects caused by using an uncontrolled global limiting process in an RKDG3 scheme (RKDG3-GL), a new conservative RKDG3 scheme with user-parameter-free local limiting method (RKDG3-LL) is designed to gain better accuracy and conservativeness. The advantages of the new RKDG3-LL model are demonstrated by applying to several steady and ransient benchmark flow tests with irregular (either differentiable or non-differentiable) topography.

Publication metadata

Author(s): Kesserwani G, Liang Q

Publication type: Article

Publication status: Published

Journal: International Journal for Numerical Methods in Engineering

Year: 2010

Volume: 86

Issue: 1

Pages: 47–69

Print publication date: 28/10/2010

ISSN (print): 0029-5981

ISSN (electronic): 1097-0207

Publisher: John Wiley & Sons Ltd.


DOI: 10.1002/nme.3044


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