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黄河下游冲淤变形剧烈,其平面二维泥沙数学模型的研究与开发是一个极其复杂的难题,在学术与工程实践上都具有重要意义。本文构建起具有通用性的黄河下游平面二维非恒定输沙数学模型。在该模型中:采用修正的河床变形方程;克服了以往数学模型计算中取饱和恢复系数小于1的缺陷;引入了符合黄河下游河道水沙特点的水流挟沙力和河床糙率计算等公式。在数值方法上:采用边界拟合坐标,对水流连续性方程与动量方程采用交错网格上的ADI方法进行离散求解,对泥沙连续性方程则采用控制容积法进行离散。
The scouring and silting in the lower reaches of the Yellow River deforms drastically. The research and development of its mathematical model for two-dimensional sediment transport in the plane is an extremely complicated problem, which is of great significance both in academic and engineering practice. In this paper, a general two-dimensional mathematical model of unsteady sediment transport in the lower Yellow River has been constructed. In this model, a modified river bed deformation equation is adopted, the defect that the saturated recovery coefficient is less than 1 in the calculation of the previous mathematical model is overcome, the formulas for calculating the sediment carrying capacity and the roughness of the river bed which conform to the characteristics of water and sediment in the lower Yellow River are introduced. In the numerical method, the boundary fitting coordinates are used to discretize the water continuity and momentum equations by the ADI method on the staggered grid. The sediment continuity equation is discretized by the control volume method.