刚性容器内流体非线性大幅晃动的数值模拟

取与容器固结的坐标系,将外激励视为质量力,针对刚性容器内流体非线性大幅晃动问题,提出了在时间和空间上均具有二阶精度的两步Taylor-Galerkin分步有限元方法.该方法首先显式地求解忽略压力梯度项的中间速度场,然后通过压力泊松方程求得压力场,最后根据求得的压力对速度场进行修正.求解中利用Level Set方法隐式地追踪自由面,即在每个时间步求解Level-Set函数随水流的输运方程,并通过迭代方法对其重新进行初始化处理,使其保持为距离的函数,从而达到捕捉自由面的目的.控制方程统一采用简便且具有较高精度的两步Taylor-Galerkin格式进行离散.算例验证结果表明,该数值方法是正确和有效的.

Numerical simulation of nonlinear large-amplitude sloshing of liquid in rigid container

A Taylor-Galerkin fractional step method of two steps with the second order accuracy in time and space was developed to deal with the 3-D nonlinear large-amplitude sloshing problem.The calculation coordinates was fixed in the container,and the external excitation was regarded as the mass force.According to the method,the intermediate velocity field neglecting pressure gradient term was obtained explicitly,and then,the velocity field was corrected based on the pressure field obtained from the pressure Poisson equation.Moreover,the Level Set approach was applied to track the free surface implicitly.During this process,the transport equation of the Level Set function was solved in each time step,and the function was reinitialized through the iteration method so that it was maintained as a distance function and the tracking of free surface was realized.The governing equations of the system were discretized by the two-step Taylor-Galerkin method,which was of high accuracy and easy to be carried out.The validity and reliability of the method were proved by two numerical examples.