Design considerations for numerical filters used in Vortex-in-cell algorithms

Abstract Vortex methods constitute a class of numerical algorithms for the simulation of flow fields characterized by regions of concentrated vorticity. Vortex-in-cell (VIC) algorithms call for some choices in the distribution functions (numerical filters) implicit in the distribution of vorticity or circulation onto a fixed mesh and interpolation of velocities from the mesh back onto the Lagrangian points. This choice is dictated by several considerations, including accuracy, grid independence, Fourier transformability and computational efficiency. In this paper, we examine and compare five numerical filters found in the literature and one developed by one of us (Bartholomew) in terms of local conservation of circulation, subgrid spatial resolution, reduction of undesirable grid effects or aliassing effects and computer work load (i.e. execution time). Based upon these comparisons, an optimum filter with respect to accuracy considerations is established.