LAUSR

In this paper, we propose a phase field method for the numerical simulations of a moving solid object in two-phase flows. A three-phase Cahn-Hilliard and Navier-Stokes model is employed for this problem. The solid region is represented by a single phase in the three-phase system. The rigidity constraint of the solid phase and the no-slip boundary condition on the solid-fluid interface is imposed by attributing a high viscosity to the solid phase. The solid velocity is then averaged over the solid phase region by the momentum conservation of solid phase. In the aspect of numerics, we design an efficient adaptive finite element method to solve the problem. Several numerical simulation results are given to show the capacity and efficiency of our model and numerical method.