Development And Application Of A Multifunctional Shallow Water Model

The objective of this study is to provide a multifunctional Sallow Water Model, which is versatile in dealing with dry and wet fronts, coupled with two-dimentional (2D) and three-dimentional (3D) models, and numerically stable and reliable. The model is established through careful consideration on the fitness of complex nature boundaries, the freedom of mesh density control and the efficiency of calculation. Recent advancements in numerical approach on solving convective term, bottom friction and diffusion term are adopted in the present study. A new numerical method is proposed to deal with the dry and wet fronts based on the finite volume method. The new method is capable to accurately capture the complex interface between wet and dry boundaries, to ensure the conservation without modifying the time step and to avoid calculation errors caused by discontinuity in coupling2D and3D models. Numerical simulations on hydrodynamics and related water environmental problems are carried out in complex topographies, such as, estuarine and coastal waters. Numerical results show that the model performs satisfactorily with respect to its effectiveness and robustness and thus has promising application prospects.The main works of this thesis are summarized as follows:(1) A depth-averaged shallow water equations (2D model), based on Godunov-type finite volume method using the technique of hybrid unstructured grid, are developed for unsteady flow over arbitrary topography with moving lateral boundaries caused by flooding or recession. An HLLC approximate Riemann solver is selected to evaluate fluxes. A linear reconstruction procedure with WBAP-L1limiter and modified4stages Runge-Kutta time stepping method are employed to provide a second order accuracy which is free from spurious oscillations. Also, a robust technique is presented to efficiently and accurately simulate the movement of wet/dry fronts. The model predictions are compared satisfactorily with analytical solutions, experimental data and a two-dimensional dam-break event.(2) A new formulation of well-balanced3D shallow water equations is established with the same method as2D model. The σ-coordinate transformation is used in the vertical direction in order to obtain an adaptive capacity in calculation withirregular surface elevation and bottom topography. In order to have second order accuracy, the vertical convection fluxes and diffusion term are calculated with TVD scheme and fully implicit treatment, while the horizontal convection-and diffusion-terms are discretized with same method as in2D hydrodynamic model. The3D model is validated by a set of benchmark calculatons.(3) A fully coupled2D-3D model system has been established based on the interpolation/averaging procedure in order to exchange data between the ID and3D models. The new coupled model is applicable to complex layed and swirling flows. The two models in the coupled model share the same grid and each model receives its boundary condition at the interface from inside the other model’s domain. A comparison has been made between the developed coupled system and trandistional3D models, and the the results show that the proposed coupled system considerably improves the calculation.(4) The proposed multifunctional Shallow Water Model is applied to a wide range of practical engineering problems, including dam break flood, tsunami wave propagation, wave-induced current, wind-driven flow, material transportation and large-scale physical processes of water exchange. The results suggest that the proposed model is accurate and well-balanced, and thus is capable to be applied to many hydrodynamic prolems such as circulation, salinity intrusion, hot water discharge, contaminant and water exchange.