The Numerical Solution Of The Diffusion Wave Equation And Application In Flood Routing

It is known that the diffusion-wave flood routing method is a good one with accuracy and simplicity. In this thesis, this method is systematically studied, especially the numerical difference solution to the equations.Based on principle that numerical dispersion of the linear kinematic-wave can simulate physical dispersion of the diffusion wave on certain condition, Muskingum-Cunge method and a flood routing method with forecasting period are discussed; the compatibility, stability and convergence of the two methods are analyzed, and the conditions to handle the compatibility, stability and convergence at the boundary in different methods; accurate principles of the approximation of that simulation are introduced, and optimal conditions necessary to obtain second-, third-and fourth-order accurate solutions are also given. By making use of the diversity of the finite difference scheme, two explicit direct difference, one implicit direct difference and three mixed direct difference schemes are given, and the above six kinds of difference equations together with their compatibility, stability and convergence conditions at the boundary are discussed.In the case of Xiangyang-Huangzhuang channel (part of Hanjiang river of Changjiang) and Wuzhou-Gaoyao channel (part of Xijiang river of Zhujiang), methods of the diffusion wave analysis and Muskingum-Cunge, flood routing method with forecasting period, and six finite difference solutions are applied to the calculation of the diffusion wave; according to certain rules, real coding based accelerating genetic algorithm is used to optimize the model parameters of studied samples, from which the model parameters of the verified samples are obtained by the way of information diffusive technique; in addition, the forecasting outcome the model parameters of the verified samples through different methods are given.After comparing the results of different methods, the outcome shows that all methods have satisfactory precision, and model parameters of samples gained by optimization and information diffusive technique are better than those by physical means.