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建立了基于非结构三角网格系统的非恒定浅水二维水流数学模型。基本控制方程采用浅水二维水流方程;采用能够有效捕捉激波的HLLC近似黎曼算子求解界面通量,并对界面变量进行数据重构,模型具有二阶精度;将地形高程定义在三角单元节点上,使得单元间地形连续变化,结合处理底坡的DFB(divergence form for bed slope source term)方法,保证了模型的和谐性,使其能够有效地模拟不规则地形条件上干湿边界变化过程中的水流过程;采用了隐式方法处理阻力项,从而保证了模型的稳定性。最后,通过四个经典算例对模型进行了系统地检验。结果表明:此模型具有很好的和谐性和稳定性,能够有效、准确地模拟复杂地形情况下水流运动,显示了广阔的应用前景。
A mathematical model of unsteady shallow water two-dimensional flow based on unstructured triangular grid system was established. The basic governing equation adopts the shallow water two-dimensional flow equation. The HLLC approximate Riemann operator, which can effectively capture the shock wave, is used to solve the interface flux and the interface variables are reconstructed. The model has the second-order accuracy. The terrain elevation is defined in the triangular unit Node, making the terrain continuously change between units, combined with the DFB (divergence form for bed slope source term) approach to ensure the harmony of the model, so that it can effectively simulate the variation process of wet and dry boundary conditions on irregular topography In the water flow process; using an implicit method to deal with resistance items, thus ensuring the stability of the model. Finally, the model is systematically tested by four classical examples. The results show that this model has good harmony and stability, and can effectively and accurately simulate water flow under complex terrain, showing a broad application prospect.