An efficient shock capturing algorithm to the extended Boussinesq wave equations |
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| Institution: | 1. The State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China;2. National Marine Environment Monitoring Center, State Oceanic Administration, Dalian 116023, China;3. Division of Civil Engineering, University of Dundee, Dundee City DD1 4HN, UK;1. Division of Civil Engineering, University of Dundee, Dundee DD1 4HN, UK;2. State Key Laboratory of Estuarine and Coastal Research, East China Normal University, Shanghai 200062, China;3. College of Marine Geosciences, Ocean University of China, Qingdao 266100, China |
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| Abstract: | A hybrid finite-volume and finite-difference method is proposed for numerically solving the two-dimensional (2D) extended Boussinesq equations. The governing equations are written in such a way that the convective flux is approximated using finite volume (FV) method while the remaining terms are discretized using finite difference (FD) method. Multi-stage (MUSTA) scheme, instead of commonly used HLL or Roe schemes, is adopted to evaluate the convective flux as it has the simplicity of centred scheme and accuracy of upwind scheme. The third order Runge–Kutta method is used for time marching. Wave breaking and wet–dry interface are also treated in the model. In addition to model validation, the emphasis is given to compare the merits and limitations of using MUSTA scheme and HLL scheme in the model. The analytical and experimental data available in the literature have been used for the assessment. Numerical tests demonstrate that the developed model has the advantages of stability preserving, shock-capturing and numerical efficiency when applied in the complex nearshore region. Compared with that using HLL scheme, the proposed model has comparable numerical accuracy, but requires slightly less computation time and is much simpler to code. |
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