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A well-balanced and non-negative numerical scheme for solving the integrated shallow water and solute transport equations

Lookup NU author(s): Professor Qiuhua Liang


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Based on the recent development in shallow flow modelling, this paper presents a finite volume Godunov-type model for solving a 4×4 hyperbolic matrix system of conservation laws that comprise the shallow water and depth-averaged solute transport equations. The adopted governing equations are derived to preserve exactly the solution of lake at rest so that no special numerical technique is necessary in order to construct a well-balanced scheme. The HLLC approximate Riemann solver is used to evaluate the interface fluxes. Second-order accuracy is achieved using the MUSCL slope limited linear reconstruction together with a Runge-Kutta time integration method. The model is validated against several benchmark tests and the results are in excellent agreement with analytical solutions or other published numerical predictions. © 2010 Global-Science Press.

Publication metadata

Author(s): Liang Q

Publication type: Article

Publication status: Published

Journal: Communications in Computational Physics

Year: 2010

Volume: 7

Issue: 5

Pages: 1049-1075

Print publication date: 06/01/2010

ISSN (print): 1815-2406

ISSN (electronic): 1991-7120

Publisher: Global Science Press


DOI: 10.4208/cicp.2009.09.156


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