期刊
COMPUTERS & FLUIDS
卷 39, 期 10, 页码 2040-2050出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.compfluid.2010.07.008
关键词
Godunov-type method; Discontinuous Galerkin; Well-balanced scheme; Friction effects; Wetting and drying; Shallow water equations
资金
- UK Engineering and Physical Sciences Research Council (EPSRC) [EP/F030177/1]
- Engineering and Physical Sciences Research Council [EP/F030177/1] Funding Source: researchfish
- EPSRC [EP/F030177/1] Funding Source: UKRI
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. (C) 2010 Elsevier Ltd. All rights reserved.
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