Free-surface Flow Simulations Using Parallel Finite Element Method

Abstract

In this paper, we present recent results in numeri cal simulation of free-surface flows using the paral lel finite element method. In our approach, the gov erning equations are the Navier-Stokes equations written for two incompressible fluids. We solve these equations over a non-moving mesh. An inter face function with two distinct values serves as a marker identifying the location of the free-surface. This function is transported throughout the com putational domain with a time-dependent advec tion equation. The stabilized finite element method is used to discretize the governing equations. The finite element formulations are implemented in parallel using Message Passing Interface libraries. High performance computing tools and optimized techniques are utilized to solve applications on un structured meshes with more than one billion tetra hedral elements. Numerical examples include the simulation of sloshing in tanker trucks and ships hydrodynamics.