平面二维溃坝水沙输移动床数学模型研究

2D movable-bed mathematical model for dam-break flow and sediment transport

为数值模拟溃坝洪水作用下泥沙输移及河床变形,建立了无结构三角形网格的平面二维水沙耦合数学模型。水动力学模型采用浑水流动方程,考虑了泥沙输移及床面冲淤变化对水流动量的影响;泥沙输移采用不平衡泥沙输移模式。模型数值计算格式采用守恒性较好的有限体积法,单元界面的对流通量采用基于近似黎曼解的Roe格式计算,扩散通量采用中心格式,不平衡泥沙输移方程采用坡度限制的二阶空间精度格式离散。模型经经典算例和小尺度瞬间全溃的动床实验资料检验,水面、床面及流速等计算结果与实验资料或解析解等比较吻合,分析了动床与定床水面及洪水传播速度的差异。在上述检验的基础上,采用动床模型对某河道型水库溃坝诱发的水沙运动进行了数值模拟,结果表明溃坝洪水下水流、泥沙及河床变形发生强烈的相互作用,采用水沙及河床变形耦合的数学模型是必要的。

A two-dimensional movable-bed mathematical model with unstructured grid has been established to simulate sediment transport and riverbed deformation under dam-break flow over movable beds. The hy- drodynamic model adopts water-sediment mixture flow equations, which consider the effects of sediment transport and bed deformation on the flow. The sediment model adopts the nonequilibrium transport of sus- pended load. The governing equations are solved by an explicit finite-volume method with the second-order Roe＇ scheme based approximate Riemann for intercell advection fluxes, and centre difference scheme with unstructured grid is adopted to compute diffusive fluxes. The model was tested by two examples with exact solution or experimental data on dam-break flow, with fairly good agreement between simulations and mea- surements or exact solution. Based on the verifications, the flow and sediment transport due to a dam fail- ure were simulated respectively by means of this model. The result shows that dam-break flows over mobile beds can provoke very active sediment exchange between the water column and the bed, and it is quite necessary to simulate the flow and sediment transport process by means of coupled mathematical model.