Numerical Simulation For Discontinuous Shallow Water Flow And Its Application To The Analysis Of The Tidal Bore At The Qiantang Estuary

Numerical simulation of discontinuous shallow water flows, such as tidal bores, hydraulic jumps, dam-break waves, waves distorted due to shallow water, surge wave formed by suddenly-opened sluice, etc. is of great academic and practical significance, and thus has long been a hotspot and difficult issue in computational hydrodynamics.In this thesis, based on the analyses of basic characteristics of the tidal bores on the Qiantang River and of the related shallow water equations, 1D and 2D mathematical models were developed for simulating discontinuous shallow water flow by using the Godunov scheme and KFVS (Kinetic Flux Vector Splitting) scheme, in which the well-balanced problem of conservative computational schemes was solved by applying the WLTF(Water Level-bottom Topography Formulation) combined with the discretization technique for treating the source term generated by uneven bottom topography, and the wet/dry technique was invoked to improve the Riemann solution for the dry bed. On the basis of the verification of the above models by simulating typical examples, the models were employed to compute the propagation of the tidal bore on the Qiantang River and the sediment transportation under the effect of the tidal bore.The main results in this thesis are as follows.(1) The 1D and 2D mathematical models were established for simulating the discontinuous shallow water flow by using the Godunov scheme. In order to keep the well-balance between the pressure term on the left-hand side and the source term due to bottom topography on the right-hand side of the shallow water equations (SWE), the WLTF was applied in the process of solving the normal numerical flux, and the same discretization method was used for both the pressure term and the source terms. With the triangular grids, two methods were proposed to keep the models well-balanced. Firstly, the source term due to bottom topography was discretize by using hydrostatic pressure law. Secondly, the governing equations were transformed to reach the well-balance. With a technique similar to the MUSCLE, a 2nd-order accuracy scheme in space with triangular grids was developed.(2) Based on the Boltzmann equation for the equilibrium state, the 1D and 2D shallow water equations were derived from the basic relationship between macroscopic and microcosmic variables. The 1D and 2D KFVS schemes for solving the SWE were developed with the 2nd-order accuracy in space by using the finite volume method (FVM) to discretize the SWE and the KFVS method to compute normal numerical flux. In order to keep the scheme well-balanced, in addition to the WLTF, the effect of the source term due to bottom topography was considered in the computation of normal numerical flux.(3) There are extensive shoals at the Qiantang estuary, so the wet/dry technique has great impact on the computed results for the tidal bore. In this thesis, an improved Riemann solution on dry bed was proposed to deal with moving boundary. According to the idea of WLTF, the classical Riemann solution on dry bed only applicable to even bottoms was improved to be applied to uneven bottom. Numerical tests show that the method can be applied to simulate discontinuous flow in the condition of moving boundary.(4) The above two 2D mathematical models with the Godunov scheme and KFVS scheme were validated by some typical tests, and then employed to simulate the formation, evolution and dissipation of the tidal bore at the Qiantang estuary, and to replicate some bore sceneries, such as the crossed tidal bore, thread-shape bore and returned tidal bore. The computed results were verified by field data, showing the sudden and sharp rise of the tidal level, the rapid velocity conversion from ebb to flood and fast reaching to its extremum during the bore arriving. The models have overcome the problems which appeared in common mathematical models, such as unreasonably smaller water-level rise, velocity increase, and the nonconservatve computed discharge.(5) Based on the mathematical model of water flow, a 2D sediment transport mathematical model with the 2nd-order accuracy in space was developed by using the Godunov scheme with triangular grids. The model was used to simulate sediment transport under the tidal bore on the Qiantang River, and to replicate the abrupt variation process of the sediment concentration during the bore arriving. The computed results show that the tidal bore has great impact on sediment transport and fluvial process, and reveals the cause of formation of high sediment concentration region at the Qiantang estuary, the mechanism of erosion by runoff and deposit by tidal current, and the riverbed variation with large amplitude.