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讨论了贮腔类三维自由液面动力学问题的数值研究,将任意的拉格朗日-欧拉运动学描述关系引入到系统的控制方程中,采用任意的拉格朗日-欧拉描述跟踪自由液面,推导了自由面上结点的法向矢量计算公式。采用Galerkin余量法推导了Navier-Stokes方程的空间离散有限元方程,采用三维自由液面上微分几何理论推导了表面张力计算公式。数值研究中考虑了接触角效应,最后进行了三维数值算例分析。
In this paper, we discuss the numerical study of the three-dimensional free surface dynamics problem of storage cavity. Introduce any Lagrange-Euler kinematic description into the control equation of the system, and use any Lagrangian-Euler description tracking Free surface, the normal vector formula of node on free surface is deduced. The spatial discrete finite element equation of Navier-Stokes equation is deduced by the Galerkin method. The surface tension calculation formula is deduced by using the three-dimensional free surface upper-differential geometry theory. In the numerical study, the contact angle effect was considered. Finally, a three-dimensional numerical example analysis was carried out.