Regularized Vortex Sheet Evolution in Three Dimensions

Abstract

A computational method is presented to track the evolution of regularized three-dimensional vortex sheets through an otherwise irrotational, inviscid, constant-density fluid. The sheet surface is represented by a triangulated mesh with interpolating functions locally defined inside each triangle.C1continuity is maintained between triangles via combinations of cubic Bézier triangular interpolants. The self-induced sheet motion generally results in a highly deformed surface which is adaptively refined as needed to capture regions of increasing curvature and to avoid severe Lagrangian deformation. Automatic mesh refinement is implemented with an advancing front technique. Sheet motion is regularized by adding a length scale cutoff to the Biot–Savart kernel. Toroidal and periodic-cylinder vortex sheets are simulated, modeling vortex rings and vortex/jet combinations, respectively. Comparisons with previous 2D results are favorable and 3D results are presented.