AN EULERIAN APPROACH FOR VORTEX MOTION USING A LEVEL SET REGULARIZATION PROCEDURE

We present an Eulerian, fixed grid, approach to solve the motion of an incompressible fluid, in two and three dimensions, in which the vorti city is concentrated on a lower dimensional set. Our approach uses a d ecomposition of the vorticity of the form xi = P(phi) eta, in which bo th phi (the level set function) and eta (the vorticity strength vector ) are smooth. We derive coupled equations for phi and eta which give a regularization of the problem. The regularization is topological and is automatically accomplished through the use of numerical schemes who se viscosity shrinks to zero with grid size. There is no need for expl icit filtering, even when singularities appear in the front, The metho d also has the advantage of automatically allowing topological changes such as merging of surfaces. Numerical examples, including two and th ree dimensional vortex sheets, two-dimensional vortex dipole sheets, a nd point vortices, are given. To our knowledge, this is the first thre e-dimensional vortex sheet calculation in which the sheet evolution fe eds back to the calculation of the fluid velocity. Vortex in cell calc ulations for three-dimensional vortex sheets were done earlier by Tryg vasson et al. (C) 1996 Academic Press, Inc.