Balancing the source terms in a SPH model for solving the shallow water equations |
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Institution: | 1. Dept. of Bioenvironmental Systems Engineering, National Taiwan University, Taipei 106, Taiwan;2. Center for Weather Climate and Disaster Research, National Taiwan University, Taipei 106, Taiwan;3. Taiwan Typhoon and Flood Research Institute, National Applied Research Laboratories, Taipei 100, Taiwan |
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Abstract: | A shallow flow generally features complex hydrodynamics induced by complicated domain topography and geometry. A numerical scheme with well-balanced flux and source term gradients is therefore essential before a shallow flow model can be applied to simulate real-world problems. The issue of source term balancing has been exhaustively investigated in grid-based numerical approaches, e.g. discontinuous Galerkin finite element methods and finite volume Godunov-type methods. In recent years, a relatively new computational method, smooth particle hydrodynamics (SPH), has started to gain popularity in solving the shallow water equations (SWEs). However, the well-balanced problem has not been fully investigated and resolved in the context of SPH. This work aims to discuss the well-balanced problem caused by a standard SPH discretization to the SWEs with slope source terms and derive a corrected SPH algorithm that is able to preserve the solution of lake at rest. In order to enhance the shock capturing capability of the resulting SPH model, the Monotone Upwind-centered Scheme for Conservation Laws (MUSCL) is also explored and applied to enable Riemann solver based artificial viscosity. The new SPH model is validated against several idealized benchmark tests and a real-world dam-break case and promising results are obtained. |
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Keywords: | Smooth particle hydrodynamics (SPH) Shallow water equations Well-balanced solution Irregular topography MUSCL scheme Wetting and drying |
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