Application of the least-squares finite element method on the simulations of 3D incompressible free surface flows

Abstract

This paper presents the simulation of 3D free surface flows by the two-phase least-squares finite element method (LSFEM). It is believed that this is the first time the LSFEM be extended from a 2D model to a 3D one and applied to investigate the 3D free surface flow phenomena. The dynamic and kinematic boundary conditions of free surface are described in an Eulerian coordinate system. The governing 3D Navier-Stokes equations in association with the color function are solved by the element-by-element scheme. In this simulation, the volume of fluid (VOF) method and continuous stress force (CSF) models are applied for the determination of the interface between the two phases of liquid and gas. The free surface position at each time step is determined by the distribution of the color function. The formation of the 3D model is carefully examined; and the quantitative comparisons of the 3D numerical simulations with experimental measurements and previous 2D numerical results are verified in good agreement. For the partial dam-break flows, it is shown that the two-phase LSFEM can effectively simulate the 3D flows. The unsteady water surface profiles of dam-break flow moving over an obstacle and the liquid drop are also simulated in this study. A 3D two-phase LSFEM has been established and carefully justified by some benchmark free surface flows. The method will be useful for the actual application to the two-phase flows with two immiscible fluids, such as liquid-gas flow, and metallurgic flow.