A Two-Phase Flow Solver for Incompressible Viscous Fluids, Using a Pure Streamfunction Formulation and the Volume of Fluid Technique

Accurate multi-phase flow solvers at low Reynolds number are of particular interest for the simulation of interface instabilities in the co-processing of multilayered material. We present a two-phase flow solver for incompressible viscous fluids which uses the streamfunction as the primary variable of the flow. Contrary to fractional step methods, the streamfunction formulation eliminates the pressure unknowns, and automatically fulfills the incompressibility constraint by construction. As a result, the method circumvents the loss of temporal accuracy at low Reynolds numbers. The interface is tracked by the Volume-of-Fluid technique and the interaction with the streamfunction formulation is investigated by examining the Rayleigh-Taylor instability and broken dam problem. The results of the solver are in good agreement with previously published theoretical and experimental results of the first and latter mentioned problem, respectively.