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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.
Based on conservation shallow water two-dimensional equation, WENO interpolation was used to interpolate the conservation variables on both sides of the interface and the Roe method was used to calculate the numerical flux at the interface. A mathematical model of planar two-dimensional dam-break flow was established. In order to reduce the overall accuracy of the model, the source term is processed by the third-order Runge-Kutta method and the adaptive step-length method is adopted for the time step.The result of the verification shows that the mathematical model is basically consistent with the exact solution, The solution has no obvious oscillation with high resolution and high precision.The mathematical model is applied to the movement of the water flow on the dry river bed after the dam collapses and the water flow in the part of the dike after the collapse of the river course at the same time in the evolution of the river course and floodplain as well as the natural complex terrain Comparison and selection of actual project embankment and other projections and calculations.