Numerical resolution of well-balanced shallow water equations with complex source terms |
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| Authors: | Qiuhua Liang Fabien Marche |
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| Institution: | 1. School of Civil Engineering and Geosciences, Newcastle University, Newcastle upon Tyne NE1 7RU, UK;2. Université Montpellier 2, I3M Place Eugène Bataillon, CC 051, 34090 Montpellier, France |
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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. |
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| Keywords: | Shallow water equations Well-balanced scheme Wetting and drying Source terms Riemann solver Bed friction |
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