Numerical Simulation of Three-Dimensional Free Surface Fluid Sloshing with ALE Finite Element Method

Abstract

This paper presents the methodology for the simulation of free surface fluid sloshing. Particularly the nu- merical solution of the fluid flow i.e., Navier-Stokes equations which is posed in a moving mesh framework is presented. The time-changing nature of the domain is handled by the arbitrary Lagrangian-Eulerian (ALE) framework. The govern- ing equations are discretized with the finite element method. A fixed point iteration technique is used for linearizing the resultant set of non-linear algebraic equations. A fully implicit one-step scheme is used for time stepping. For the mesh movement, a linear elastic model is used which is known to preserve the mesh quality. The stability estimates for the semi-discrete and fully discrete scheme are analyzed. The methodology is assessed through the simulation of fluid sloshing in a rectangular tank with an initial uneven surface. The methodology is shown to result in stable simulations for many time steps. The conservation of mass and other physical parameters along with numerical parameters are presented.