An Adaptive Level Set Approach for Incompressible Two-Phase Flows

Mark Sussman

Ann S. Almgren

John B. Bell

Phillip Colella

Louis H. Howell

Michael L. Welcome


In Sussman et al. (1994), a level set method was formulated for solving incompressible two-phase flow with surface tension. In the level set approach, the interface 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 interface, with the advection of the level set function, which is smooth. In addition, the interface can merge or break up with no special treatment. We maintain the level set function as the signed distance from the interface in order to robustly compute flows with high density ratios (1000:1) 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 interface with a minimum of additional expense.