Numerical modelling of free-surface shallow flows over irregular topography with complex geometry |
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Authors: | Yi Liu Jianzhong Zhou Lixiang Song Qiang Zou Li Liao Yueran Wang |
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Institution: | 1. School of Hydropower and Information Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China;2. School of Electrical and Electronic Engineering, Hubei University of Technology, Wuhan 430068, PR China;3. Hubei Key Laboratory of Digital Valley Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, PR China;4. Laboratory of Numerical Modeling Technique for Water Resources, Department of Water Resources and Environment, Pearl River Water Resources Research Institute, Guangzhou 510623, PR China;5. School of Engineering and Technology, Hubei University of Technology, Wuhan 430068, PR China |
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Abstract: | A well-balanced Godunov-type finite volume algorithm is developed for modelling free-surface shallow flows over irregular topography with complex geometry. The algorithm is based on a new formulation of the classical shallow water equations in hyperbolic conservation form. Unstructured triangular grids are used to achieve the adaptability of the grid to the geometry of the problem and to facilitate localised refinement. The numerical fluxes are calculated using HLLC approximate Riemann solver, and the MUSCL-Hancock predictor–corrector scheme is adopted to achieve the second-order accuracy both in space and in time where the solutions are continuous, and to achieve high-resolution results where the solutions are discontinuous. The novelties of the algorithm include preserving well-balanced property without any additional correction terms and the wet/dry front treatments. The good performance of the algorithm is demonstrated by comparing numerical and theoretical results of several benchmark problems, including the preservation of still water over a two-dimensional hump, the idealised dam-break flow over a frictionless flat rectangular channel, the circular dam-break, and the shock wave from oblique wall. Besides, two laboratory dam-break cases are used for model validation. Furthermore, a practical application related to dam-break flood wave propagation over highly irregular topography with complex geometry is presented. The results show that the algorithm can correctly account for free-surface shallow flows with respect to its effectiveness and robustness thus has bright application prospects. |
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Keywords: | Free-surface shallow flows Unstructured grids Finite volume Well-balanced Wetting and drying Dam break |
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