Research On Mathematical Model And Hydrodynamic Characteristics Of Dam-break Floods

There are about 87,000 reservoirs currently in China. Reservoirs have played an important role in flood control, water supply, hydropower generation, irrigation, etc. Howervr, there are many dangerous reservoirs in China, and the dam-break is a critical problem of national disaster prevention and mitigation. According to the present status of frequent dam failure and severe flood control situation, it is vital to carry out research into mathatical model of dam-break floods, and to develop the theory and method system on dam-break disaster prediction. High-performance numerical model for dam-break floods simulation with complex geometry and topography is always a frontier research field in academic and engineering circles. However, there is an overall lack of systemic and deep research on the dam-break floods simulation in China. To provide a theoretical and technical foundation for constructing the system of dam-break risk analysis and disaster evaluation, as well as to provide scientific basis for government to make an appropriate dicision in disaster prevention and mitigation, it is necessary to develop a high-performance mathematical model of dam-break floods, and to analyse the hydrodynamic characteristics of dam-break floods.In this thesis, a high-performance two-dimensional mathematical model for dam-break floods over complex topography and irregular domain is developed, and the hydrodynamic characteristics of dam-break floods is analysed by some ideal dam-break problems. Besides, the proposed model is used in Zhang River reservoir and Jingjiang flood diversion area for flood risk analysis. The main work and innovation includes:(1) A new formulation of the SWEs is presented as the basis of a well-balanced Godunov-type finite volume scheme. In the framework of sloping bottom model, the need for momentum flux corrections to preserve C-property is revealed theoretically when the bed slope terms are approximated directly. At the same time, the potential problem result from the corrections is mathematically analysed.(2) A high-performance, two-dimensional mathematical model for dam-break floods simulation with complex domain and topography is developed. The proposed model has some advantages including modeling terrain with second-order accuracy, preserving the well-balanced property without any momentum flux corrections, accurately predicting all flow regimes (subcritical, supercritical, transcritical, discontinuities, etc.), and effectively reproducing the wetting and drying processes over irregular terrain on fixed meshed.(3) The potential stiff problem of two step explicit Runge-Kutta method for friction term treatment is theoretically analysed, and a semi-implicit scheme is used to deal with the stiff problem. The semi-implicit scheme not only preserves the direction of velocity component, but also greatly reduces a large velocity to a reasonable value when the water depth is very small, which is beneficial to model stability.(4) The proposed model is validated by a set of benchmarks, including ideal test cases with theoretical solutions, laboratory experiments with measured datas, and so on. Results show that the porposed model is accurate, well-balanced and mass conservative, and has the ability to simulate complex flow and to capture shocks with high-resolution.(5) The influence of bed slope, friction, initial states, inflow and width of dam-breach on peak discharge, elapsed time until arrival of flood, maximum water depth is analysed.(6) The enhancement effect due to cascade reservoirs failure is simulated. Numerical results show that dam-break floods results from upstream reservoir would make an additive effect at the downstream dam site, increase the peak value of water level, and further influence the flood routine in the downstream river.(7) The proposed dam-break floods model is used for flood analysis in Zhang River reservoir and Jingjiang flood diversion area, and some special flood risk maps based on computational grids are presented, including maximum water depth, maximum velocity, maximum unit discharge per length, elapsed time until arrival of flood, and elapsed time until arrival of maximum water depth.