Free Surface Navier-Stokes Solver

Dr Steve Roberts

Description of Project

The equations of motion for incompressible two-phase flow can be written in the form

ut + u·∇u+ ∇p ρ(c) = 1 ρ(c) ∇·(μ(c)[∇u+∇uT]) − 1 ρ(c) γκ(c) ∇c− geg (0.1) ∇·u = 0 (0.2)

together with a volume-of-fluid equation

ct + ∇(uc) = 0

(0.3)

where u = (u,v) is fluid velocity, c is the volume-of-fluid or the void fraction function (1 if liquid, 0 if gas) and κ(c) is the mean curvature of the interface between the liquid and gas, as defined by c. We will investigate the methods for solving the Navier Stokes equation. Consider implementation issues. Look at general computational Fluid Dynamical methods and apply this to the solution of the Navier Stokes equation with free boundaries