Method of fundamental solutions on simulating sloshing liquids in a 2D tank

Abstract

A two dimensional numerical model for sloshing response of the partially filled container is developed by a meshless method in this study. Laplace equation is considered as the governing equation for potential flow, and fully non-linear free surface boundary conditions are implemented on the free surface. The numerical model is established in the moving coordinate system attached to the container. The present meshless method, method of fundamental solutions, only need to distribute nodes on the physical boundaries and the virtual boundaries outside the computational domain. Comparing with the traditional mesh-based numerical method, this method has the advantage of being easy to construct and flexible in dealing with the moving boundary problem. The program is written in Python. A simple method for tracking fully non-linear free surface is implemented, and the physical boundaries are updated with time. The numerical results agree very well with existing results in both resonance and off-resonance cases. The present numerical model is further applied to the sloshing response under coupled motions (horizontal and vertical). In order to study the stability of sloshing response (Benjamin and Ursell, 1954) under vertical motion, 25 cases are conducted in various sloshing parameters. In addition, the present numerical model has been successfully applied to investigating sloshing response under coupled motions.