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Well-balanced RKDG2 solutions to the shallow water equations over irregular domains with wetting and drying

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



This paper presents a new one-dimensional (1D) second-order Runge–Kutta discontinuous Galerkin (RKDG2) scheme for shallow flow simulations involving wetting and drying over complex domain topography. The shallow water equations that adopt water level (instead of water depth) as a flow variable are solved by an RKDG2 scheme to give piecewise linear approximate solutions, which are locally defined by an average coefficient and a slope coefficient. A wetting and drying technique proposed originally for a finite volume MUSCL scheme is revised and implemented in the RKDG2 solver. Extra numerical enhancements are proposed to amend the local coefficients associated with water level and bed elevation in order to maintain the well-balanced property of the RKDG2 scheme for applications with wetting and drying. Friction source terms are included and evaluated using splitting implicit discretization, implemented with a physical stopping condition to ensure stability. Several steady and unsteady benchmark tests with/without friction effects are considered to demonstrate the performance of the present model.

Publication metadata

Author(s): Kesserwani G, Liang Q

Publication type: Article

Publication status: Published

Journal: Computers & Fluids

Year: 2010

Volume: 39

Issue: 10

Pages: 2040-2050

Print publication date: 01/01/2010

Date deposited: 07/12/2010

ISSN (print): 0045-7930

ISSN (electronic): 1879-0747

Publisher: Elsevier


DOI: 10.1016/j.compfluid.2010.07.008


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