Volume fraction flux approximation in a two-fluid flow

The broken dam problem flow is tested to check accuracy of different procedures for gas-liquid interface resolution based on solution of the additional equation for the volume fraction of liquid phase. The study is focused on the numerical schemes used to approximate advection fluxes of this equation. In particular, the MUSCL scheme with QUICK interpolants and compressive minmod TVD limiters with the slope modification technique for the volume fraction fluxes is applied, as well as the upwind-downwind donor acceptor procedure designed in the VOF method. As the first stage, the quite simple and explicit procedure adopting the artificial compressibility method is used to solve the velocity and pressure equations. Computations are initially performed with a careful grid and time step independence studies. Importance of the wall boundary condition is also discussed. To present free surface motion, results of numerical investigation are shown in terms of contour plots for the volume fraction at successive times, as well as surge front and column height positions versus time.