A Level Set Formulation of Eulerian Interface Capturing Methods for Incompressible Fluid Flows

A level set formulation is derived for incompressible, immiscible Navier–Stokes equations separated by a free surface. The interface is identified as the zero level set of a smooth function. Eulerian finite difference methods based on this level set formulation are proposed. These methods are robust and efficient and are capable of computing interface singularities such as merging and reconnection. Numerical experiments are presented to demonstrate the effectiveness of the methods.