间断洪水波高精度数值模拟与应用

Numerical simulation with high precision for flood shock wave

基于守恒型浅水二维方程,采用三单元模板的加权本质无震荡(WENO)格式插值界面两侧守恒变量,并采用Roe方法计算界面处数值通量,建立了平面二维溃坝水流数学模型.为使模型总体精度不致因为时间离散而降低,源项采用三阶Runge-Kutta方法进行处理,时间步进采用自适应步长法.验证结果表明数学模型计算结果与精确解基本一致,间断处数值解无明显震荡,具有高分辨率和高精度.数学模型应用于坝体溃决后水流在干河床上运动、河道部分堤防溃决后水流同时在河道以及洪泛区的演进过程以及天然复杂地形条件下实际工程溃堤方案的比选等预测计算.

A 2D numerical model for flow with shock is established based on the differential conservation law form of nonlinear shallow water equations,which uses WENO sheme containning three cells to calculate the conserved variables at the interface and Roe method to calculate the flux at the interface.In order to keep the precision of the model,three steps Runge-Kutta method is used for solving source terms; and the adaptive method for time step is applied for time evolvement.The model is verified by compared the numerical result with the analytical results; and it is shown that the two results are indentical.The result of the numerical model shows high accurancy and with essentially non-oscillatory; so it can be used in calculating the flow evolution due to dam-break.Finally,the model is applied to two practical situations,one is predicting the dam-break flow evolvement in dry river bed; the other is to simulate the flow in the river and in the flood storage and detention basins at the same time when dike burst happens,in which the flow field and water level around the burst are presented.