A sharp interface method for incompressible two-phase flows

We present a sharp interface method for computing incompressible immiscible two-phase flows. It couples the level-set and volume-of-fluid techniques and retains their advantages while overcoming their weaknesses. It is stable and robust even for large density and viscosity ratios on the order of 1000 to 1. The numerical method is an extension of the second-order method presented by Sussman [M. Sussman, A second order coupled levelset and volume of fluid method for computing growth and collapse of vapor bubbles, Journal of Computational Physics 187 (2003) 110–136] in which the previous method treated the gas pressure as spatially constant and the present method treats the gas as a second incompressible fluid. The new method yields solutions in the zero gas density limit which are comparable in accuracy to the method in which the gas pressure was treated as spatially constant. This improvement in accuracy allows one to compute accurate solutions on relatively coarse grids, thereby providing a speed-up over continuum or “ghost-fluid” methods.