基于流体速度势的非线性晃动问题的ALE有限元分析

摘要

Based on fluid velocity potential, an ALE finite element formulation for the analysis of nonlinear sloshing problems has been developed. The ALE kinematical description is introduced to move the computational mesh independently of fluid motion, and the container-fixed noninertial coordinate system is employed to establish the governing equations so that the mesh is needed to be updated in this coordinate system only. This leads to a very simple mesh moving algorithm which makes it easy to trace the motion of the moving boundaries and the free surface without producing undesirable distortion of the computational mesh. The finite element method and finite difference method are used spacewise and timewise, respectively. A numerical example involving either forced horizontal oscillation or forced pitching oscillation of the fluid-filled container is presented to illustrate the effectiveness and the robustness of the method. In addition, this work can be extended for the fluid-structure interaction problems.%基于流体速度势,本文导出了非线性晃动问题的ALE有限元格式.通过引入ALE运动学描述,使网格的运动独立于流体的运动,通过采用与贮箱固连的非惯性参考系建立控制方程,使网格只须相对贮箱更新,因此运动边界和自由液面的跟踪算法不仅非常简单,而且不会引起网格畸变.本文分别采用有限元法和有限差分法进行空间和时间离散,文中的算例分别模拟了贮箱受横向激励和俯仰激励时流体的非线性晃动问题,所得结果证实了本文方法的有效性与可靠性.文中的方法还可进一步推广用于流体-结构耦合问题.