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A conservative high‐order discontinuous Galerkin method for the shallow water equations with arbitrary topography
Author(s) -
Kesserwani Georges,
Liang Qiuhua
Publication year - 2010
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3044
Subject(s) - initialization , discontinuous galerkin method , shallow water equations , mathematics , differentiable function , finite element method , galerkin method , flow (mathematics) , limiting , mathematical analysis , geometry , computer science , engineering , structural engineering , programming language , mechanical engineering
A 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 transient benchmark flow tests with irregular (either differentiable or non‐differentiable) topography. Copyright © 2010 John Wiley & Sons, Ltd.