计算二维浅水方程中静水压力项与底坡项的积分平衡法

Integral balance method for computing stationary hydraulic pressure term and bed slope term in two-dimensional shallow water equations

考虑静水压力项随水深的非线性变化,推导出计算二维浅水方程中静水压力项和底坡项的积分平衡法,以消除静水条件下的虚假流动。采用三角形网格的有限体积法模拟浅水流动,在以斜底模型逼近实际地形和控制体内变量线性分布的条件下,准确积分得出沿控制体界面的静水压力项和控制体上底坡项的表达式,从理论上证明了在静水条件下两者能够达到平衡。过丘恒定流算例计算结果表明,该算法能够使水流保持静水状态,不产生虚假流动。

The integral balancing method has been developed in to compute the hydraulic pressure terms and bed slope terms in two-dimensional shallow water equations, with consideration of the fact that the hydraulic pressure term changes non-linearly with water depth, so as to eliminate artificial flow under hydrostatic conditions. As the finite volume method （FVM） based on a triangle mesh is applied to simulate shallow flowing water, with a slope model being used to simulate natural topography and with the assumption that the variance is linearly distributed in the control volume, expressions of the two terms are integrated. The balance between the two terms under hydrostatic conditions is theoretically proven. An example of steady flow over the hump demonstrates that the velocity error computed under hydrostatic conditiom is within the scope of acceptance and no artificial flow occurs.