Two-dimensional numerical modelling of shallow water flows over multilayer movable beds |
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| Institution: | 1. Department of Civil and Environmental Engineering, Imperial College London, SW7 2AZ, UK;2. Department of Engineering, University of Durham, South Road, Durham DH1 3LE, UK;1. College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 200016, China;2. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China;3. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;1. Department of Astronautic Science and Mechanics, Harbin Institute of Technology, Harbin 150001, China;2. College of Mathematics, Sichuan University, Chengdu 610043, China;1. School of Mechanical and Transportation Engineering, Guangxi University of Science and Technology, Liuzhou 545006, China;2. School of Sciences, Nanjing University of Science and Technology, Nanjing 210094, China;1. Center of Materials Science and Optoelectronics Engineering, College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China;2. Qiushi Honors College, Tianjin University, Tian jin 300350, China;3. McGill Metals Processing Centre, McGill University, Montreal, Quebec H3A 2B2 Canada;1. Institue of Solid Mechanics (IFKM), Technische Universität Dresden, Dresden 01062, Germany;2. Institute of Textile Machinery and High Performance Material Technology (ITM), Technische Universität Dresden, Dresden, Germany |
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| Abstract: | The two-dimensional modelling of shallow water flows over multi-sediment erodible beds is presented. A novel approach is developed for the treatment of multiple sediment types in morphodynamics. The governing equations include the two-dimensional shallow water equations for hydrodynamics, an Exner-type equation for morphodynamics, a two-dimensional transport equation for the suspended sediments, and a set of empirical equations for entrainment and deposition. Multilayer sedimentary beds are formed of different erodible soils with sediment properties and new exchange conditions between the bed layers are developed for the model. The coupled equations yield a hyperbolic system of balance laws with source terms. As a numerical solver for the system, we implement a fast finite volume characteristics method. The numerical fluxes are reconstructed using the method of characteristics which employs projection techniques. The proposed finite volume solver is simple to implement, satisfies the conservation property and can be used for two-dimensional sediment transport problems in non-homogeneous isotropic beds without need of complicated three-dimensional equations. To assess the performance of the proposed models, we present numerical results for a wide variety of shallow water flows over sedimentary layers. Comparisons to experimental data for dam-break problems over movable beds are also included in this study. |
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