Variable density shallow flow model for flood simulation
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Flood inundation is a major natural hazard that can have very severe socio-economic consequences. This thesis presents an enhanced numerical model for flood simulation. After setting the context by examining recent large-scale flood events, a literature review is provided on shallow flow numerical models. A new version of the hyperbolic horizontal variable density shallow water equations with source terms in balanced form is used, designed for flows over complicated terrains, suitable for wetting and drying fronts and erodible bed problems. Bed morphodynamics are included in the model by solving a conservation of bed mass equation in conjunction with the variable density shallow water equations. The resulting numerical scheme is based on a Godunov-type finite volume HLLC approximate Riemann solver combined with MUSCL-Hancock time integration and a non-linear slope limiter and is shock-capturing. The model can simulate trans-critical, steep-fronted flows, connecting bodies of water at different elevations. The model is validated for constant density shallow flows using idealised benchmark tests, such as unidirectional and circular dam breaks, damped sloshing in a parabolic tank, dam break flow over a triangular obstacle, and dam break flow over three islands. The simulation results are in excellent agreement with available analytical solutions, alternative numerical predictions, and experimental data. The model is also validated for variable density shallow flows, and a parameter study is undertaken to examine the effects of different density ratios of two adjacent liquids and different hydraulic thrust ratios of species and liquid in mixed flows. The results confirm the ability of the model to simulate shallow water-sediment flows that are of horizontally variable density, while being intensely mixed in the vertical direction. Further validation is undertaken for certain erodible bed cases, including deposition and entrainment of dilute suspended sediment in a flat-bottomed tank with intense mixing, and the results compared against semi-analytical solutions derived by the author. To demonstrate the effectiveness of the model in simulating a complicated variable density shallow flow, the validated numerical model is used to simulate a partial dam-breach flow in an erodible channel. The calibrated model predictions are very similar to experimental data from tests carried out at Tsinghua University. It is believed that the present numerical solver could be useful at describing local horizontal density gradients in sediment laden and debris flows that characterise certain extreme flood events, where sediment deposition is important.