An adaptive level set approach for incompressible two-phase flows

We present a numerical method using the level set approach for serving inco mpressible 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 functio n, which is smooth. In addition, the free surface can merge or break up wit h no special treatment. We maintain the level set function as the signed di stance 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 incompressibl e Navier-Stokes equations, in order to achieve higher resolution of the fre e surface with a minimum of additional expense. We present two-dimensional axisymmetric and fully three-dimensional results of air bubble and water dr op computations. (C) 1999 Academic Press.