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

the front and avoid introducing numerical diffusion which smooths out the front. In the case of irrotational flow, one A level set formulation is derived for incompressible, immiscible Navier–Stokes equations separated by a free surface. The interface can reformulate the problem in the boundary integral form is identified as the zero level set of a smooth function. Eulerian so that it involves the motion of the free surface alone. In finite difference methods based on this level set formulation are this case, it is possible to design high order accurate methproposed. These methods are robust and efficient and are capable ods as long as the fluid interface is smooth. This is essential of computing interface singularities such as merging and reconnecin studying singularity formation in fluid interfaces [18, 23, tion. Numerical experiments are presented to demonstrate the effectiveness of the methods. Q 1996 Academic Press, Inc. 30]. However, when the interface forms a singularity or changes its topology, the tracking methods are difficult to continue beyond the singularity time. Local surgery for the moving grid points is required. This complicates the