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Numerical resolution of well-balanced shallow water equations with complex source terms

Lookup NU author(s): Professor Qiuhua Liang

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Abstract

This paper presents a well-balanced numerical scheme for simulating frictional shallow flows over complex domains involving wetting and drying. The proposed scheme solves, in a finite volume Godunov-type framework, a set of pre-balanced shallow water equations derived by considering pressure balancing. Non-negative reconstruction of Riemann states and compatible discretization of slope source term produce stable and well-balanced solutions to shallow flow hydrodynamics over complex topography. The friction source term is discretized using a splitting implicit scheme. Limiting value of the friction force is derived to ensure stability. This new numerical scheme is validated against four theoretical benchmark tests and then applied to reproduce a laboratory dam break over a domain with irregular bed profile.

Publication metadata

Author(s): Liang Q, Marche F

Publication type: Article

Publication status: Published

Journal: Advances in Water Resources

Year: 2009

Volume: 32

Issue: 6

Pages: 873-884

ISSN (print): 0309-1708

ISSN (electronic): 1872-9657

Publisher: Pergamon

URL: http://dx.doi.org/10.1016/j.advwatres.2009.02.010

DOI: 10.1016/j.advwatres.2009.02.010

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