ABSTRACT

The vortex method has been extensively used to simulate external flows around bluff and streamlined bodies. It relies on the discretization of the vorticity field into a cloud of vortex blobs to simulate the convective−diffusive transport of vorticity. Vortex blobs are generated in the neighborhood of the solid wall in order to satisfy the no-slip and the no-penetration boundary conditions, and they move in a Lagrangian manner to solve the vorticity transport equation. Despite the tremendous development that this powerful mesh-free technique has recently achieved, the numerical implementation of the wall boundary conditions is currently under intense investigation, since it is intimately connected to the vorticity generation process in the vicinity of the body surface. In this paper we describe an efficient two-dimensional vortex method algorithm, with emphasis on a new model for the vortex creation near the surface that increases the accuracy of the simultaneous implementation of the wall boundary conditions. We employ the adaptive fast multipole method to calculate the induced velocities and the corrected core-spreading method to simulate the vorticity diffusion in the boundary layer and wake. The method is second-order accurate in space when Gaussian vortex blobs are used and second-order accurate in time when the Adams-Bashforth scheme is used to march the integration process in time. The algorithm is tested against the well-known two-dimensional, incompressible boundary-layer flow over a flat plate. The agreement between the numerical results and the exact Blasius solution indicates that the algorithm provides an excellent representation of the vorticity field.