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本文首先在势流假定的基础上，通过迭代自由面残压分布的分析，提出了一种简单、易行的求解带自由面势流问题的方法──残压反馈方法（ＲＰＦ）。进而，本文对带自由面高雷诺数流动的阶梯溢流坝提出了一种数值模拟方法，即自由面先由ＲＰＦ方法确定，由Ｔｈｏｍｐｓｏｎ变换方程将不规则域换成规则域，然后用由作者提出的平均化差分格式［１］在变换平面上离散求解涡量──流函数方程，其中涉及到的壁面涡量的计算采用由作者导出的不规则形状壁面涡量一阶公式［２］进行计算。取ＮｅｗＭｏｎｋｓｖｉｌｌｅ坝的前三个阶梯作为计算例子，在条件：ｑ＝９．３ｍ２／ｓ．ｍ，网格尺寸５４×２１和Ｒｅ＝１０４下，进行了流场模拟，将其计算结果与我们进行的实验结果相比，符合良好，证明了本文方法的可行性。所得结果对了解阶梯溢流坝水力特性及此类坝型的优化设计提供了一定的依据，同时，这一方法亦可用于求解任意边界带自由面高雷诺数的问题。
In this paper, based on the assumption of potential flow, a simple and easy solution to the problem of free surface potential flow-residual pressure feedback (RPF) is proposed by iterative analysis of residual voltage distribution in free surface. In addition, a numerical simulation method is proposed for a stepped overflow dam with high Reynolds number flow over the free surface. The free surface is first determined by the RPF method and the irregular domain is replaced by the Thompson transformation equation. Then, The proposed averaging difference scheme [1] discretely solves the vorticity-flow equation on the transformation plane, and the calculation of the wall vorticity involved is carried out by the first order formula [2] of the irregular shape wall vorticity derived by the author Calculate. Taking the first three steps of the NewMonksville dam as an example, under the conditions: q = 9.3m2 / s. m, grid size of 54 × 21 and Re = 104, the flow field simulation was carried out. The calculated results are in good agreement with our experimental results, which proves the feasibility of this method. The results obtained provide some references for understanding the hydraulic characteristics of stepped spillway dam and the optimal design of such dam types. Meanwhile, this method can also be used to solve the problem of high Reynolds number of free surface in arbitrary boundary zone.