基于精确Riemann求解器的复杂明渠水流运动模拟

Simulation of flow in complex open channel based on exact Riemann solver

断面几何形状复杂条件下一维明渠水流运动高精度模拟面临较大困难。该文以守恒形式圣维南方程作为控制方程,提出基于动量方程的变量空间重构方法,在动量方程中增加因断面宽度变化而产生的侧压力项,适用于混合流及断面几何形状复杂等条件下变量空间的精确重构。数值计算方面,基于Godunov格式,采用精确Riemann求解器对复杂明渠水流运动进行高精度模拟。实例研究表明,数值计算结果与解析解或实测值吻合良好,算法具备和谐、稳健和高精度等特点,特别适用于泄水闸泄流等复杂明渠水流运动数值模拟,具有较高的实用价值。

It is difficult to simulate the flow of one-dimensional open channel with high precision under the condition of complex section geometry. In this paper, the conservation type Saint-Venant equation is used as the governing equation, and the method of variable space reconstruction based on momentum equation is proposed. The lateral pressure term caused by the change of section width is added to the momentum equation, which is suitable for the space precise reconstruction of variable under the conditions of mixed flow and complex section geometry. In the aspect of numerical calculation, based on Godunov scheme, the exact Riemann solver is used to simulate the complex open channel flow with high resolution. The case study shows that the numerical calculation results are in good agreement with the analytical solution or the measured value, and the algorithm has the characteristics of harmony, robustness and high resolution, which is especially suitable for the numerical simulation of the complex open channel flow, such as sluice discharge, and has high practical value.