Extension of the volume-of-fluid method for analysis of free surface viscous flow in an ideal gas

The volume-of-fluid (VOF) method is a simple and robust technique for simulating free surface flows with large deformations and intersecting free surfaces. Earlier implementations used Laplace's formula for the normal stress boundary condition at the interface between the liquid and vapour phases. We have expanded the interfacial boundary conditions to include the viscous component of the normal stress in the liquid phase and in a limited manner, to allow the pressure in the vapour phase to vary. Included are sample computations that show the accuracy of added third-order-accurate differencing schemes for the convective terms in the Navier-Stokes equation (NSE), the viscous terms in the normal stress at the interface and the solution of potential flow in the vapour phase coupled with the solution of the NSE in the liquid phase. With these modifications we show that the VOF method can accurately predict the instability of a thin viscous sheet flowing through a stagnant vapour phase.