Level Set Methods for Fluid Interfaces

We provide an overview of level set methods, introduced by Osher and Sethian, for computing the solution to fluid interface problems. These are computational techniques which rely on an implicit formulation of the interface, represented through a time-dependent initial value partial differential equation. We discuss the essential ideas behind the techniques, the coupling of these techniques to finite difference methods for incompressible and compressible flow, and a collection of applications including two phase flow, ship hydrodynamics, and inkjet printhead design.