An adaptive level set approach for incompressible two-phase flows

We present a numerical method using the level set approach for serving incompressible two-phase flow with surface tension. In the level set approach, the free surface is represented as the zero level set of a smooth function; this has the effect of replacing the advection of density, which has steep gradients at the free surface, with the advection of the level set function, which is smooth. In addition, the free surface can merge or break up with no special treatment. We maintain the level set function as the signed distance from the free surface in order to accurately compute flows with high density ratios and stiff surface tension effects. In this work, we couple the level set scheme to an adaptive projection method for the incompressible Navier-Stokes equations, in order to achieve higher resolution of the free surface with a minimum of additional expense. We present two-dimensional axisymmetric and fully three-dimensional results of air bubble and water drop computations. (C) 1999 Academic Press.