Session Ci - Vortex Dynamics.
ORAL session, Sunday, November 23
309, Moscone Center
A computational method is presented to track the evolution of three dimensional vortex sheets through an inviscid, constant-density fluid. The sheet surface is represented by a triangulated mesh with interpolating functions locally defined inside each triangle. C^1 continuity is provided 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. Mesh refinement is performed automatically by an advancing front technique. Sheet motion is regularized by adding a length scale cut-off to the Biot-Savart kernel, a 3D extension of the Rosenhead--Krasny desingularization. At this point, 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.