A fast resurrected core-spreading vortex method with no-slip boundary conditions

To simulate two-dimensional viscous incompressible flows based on a scheme of blob splitting and merging, we developed a vortex method and employed a fast multipole method to speed the computation of velocities. The diffusion of the vortex sheet induced at a solid wall by the no-slip boundary conditions is first modeled according to the analytical solution of Koumoutsakos and then converted into discrete blobs in the vicinity of the wall. To prevent the vorticity from entering the solid body, we introduce a concept residual circulation in a sense that only a partial circulation of the vortex sheet is diffused into the flow field; the rest remains at the wall. Blobs near the wall are thus avoided. Blobs near the wall that might cause large fluctuations in the strength of the vortex sheet are handled similarly. The solver thus developed requires no grid-based remeshing. We applied this solver to simulate the flow induced with an impulsively initiated circular cylinder; the results agree satisfactorily with those of previous experimental and numerical investigations.