Numerical Modeling Of Shallow Water Flows Over Irregular Topography

China is one of the most seriously flooded countries in the world! The flood disasters not only induce severe damages to infrastructure, but also pose a major threat to people’s lives, and have become a major constraint for sustainable development. Therefore, it is of great significance to effectively manage the flood disaster for public security and social economic development. The generation and propagation of floods over irregular topography remains great challenge to contemporary numerical models and induces great computational difficulty for the practice application of numerical model, which constitutes the key scientific and technical obstacles for flood management. Therefore, the study on numerical modeling of shallow flows over irregular topography is of great importance for scientific research and practical management of flood.A two dimensional full hydrodynamic model over irregular topography is presented in this thesis. A shock-capturing finite volume algorithm is deployed for solving the hyperbolic equations of shallow water flows over irregular topography. The numerical solution is achieved under an operator-splitting framework, a second-order WAF TVD method along with the HLL approximate Riemann solver for the homogeneous equations, and a Runge-Kutta scheme for the ordinary differential equations of source terms. For numerical stability, a self-adaptive time step method is proposed under the Runge-Kutta scheme. Numerical tests for a case of glacier-lake outburst flooding demonstrate that the present model is essentially free from the restriction on time step arising from irregular topography, and therefore computational efficiency is substantially enhanced. The model is benchmarked with an urban flooding event in Glasgow, UK, and the modelling results are in reasonable agreement with those attained by others from the Flood Risk Management Research Consortium, UK. With the proposed algorithm, shallow water hydrodynamic models can be used more extensively in practice, e.g., rainfall-induced flash floods, dam-break floods in mountainous areas and floods in areas with dense urban developments.Incorporating boundary resistance and infiltration loss, the numerical model is proposed for rainfall-triggered flash flooding. On the basis of the full hydrodynamic model, a general methodology is introduced to determine the threshold rainfall for flash flooding, which constitutes the basis for effective operational flash flooding warning. Application of the method to complex terrain with presumed rainfall scenarios is carried out to illustrate the advantage of the proposed method. The present work is a new modeling framework featuring the complete shallow water hydrodynamics of flash flood generation and propagation, current state-of-the-art numerical algorithms and a general methodology facilitating effective application in practical flash flooding warning based on threshold rainfall.A numerical case study is presented of the flooding in urban Jiujiang due to the Yangtze River dike break in August 1998, deploying the 2D full hydrodynamic model. The impacts of mesh resolution, resistance parameterization and turbulent eddy viscosity on the flood propagation are evaluated. The mesh resolution and roughness parameterization have considerable influences on the computed flood inundation area and depth, whilst the effect of the turbulent eddy viscosity is limited to the boundaries of wetting and drying and normally negligible. A coarser mesh could results in a larger inundation area while other parameters remain the same. Likewise, a lumped roughness could produce an appreciably larger inundation area during the course of the flood propagation process, which however could diminish in the long run. The inflow discharge plays a vital role in dictating the flooding in urban Jiujiang, which however bears considerable uncertainty and grants further investigation of the evolutionary process of the dike break. It makes sense to use high resolution meshes for urban flooding in limited region, but the tradeoffs between mesh resolution and computational efficiency should be made on a meaningful scale.