A numerical method for the incompressible Navier-Stokes equations with application to two-phase flow

A finite difference numerical method is developed for the simulation of time-dependent incompressible Navier-Stokes equations

As in the original projection method developed by Chorin, we first solve diffusion-convection equations to predict a intermediate velocity field which are then projected onto the space of divergence-free field. We integrate the diffusion-convection by θ implicit scheme and solve the pressure Poisson equation by successive over-relaxation method. The second order centered difference is employed to discretize both the convective and viscous terms

We develop two-dimensional and three-dimensional computer programs in Fortran language Numerical results are presented

We couple our inpressible Navier-Stokes solver with an interacting continuum model for two-phase flows with heat, mass transfer and phase change The Volume of Fluid method is employed in the present study Two example simulations are presented, convective melting of solid particles in a fluid under micro-gravity, and a three dimensional driven cavity problem.