An immersed interface method for the vortex - in - cell algorithm †

The paper presents a two-dimensional immersed interface technique for the vortex-in-cell (VIC) method for the simulation of flows past complex geometries. The particle–mesh VIC algorithm is augmented by a local particle– particle (PP) correction term in a particle–particle particle–mesh (PPPM) context to resolve sub-grid scales incurred by the presence of the immersed interface. The PP correction furthermore allows mesh and particle resolution to be disjoined by explicitly resolving sub-grid scales on the particles. This PPPM algorithm uses an influence matrix technique to annihilate the anisotropic sub-grid scales and an exact PP correction term. Free-space boundary conditions are satisfied through the use of modified Green's functions in the solution of the Poisson equation for the stream function. The random walk technique is employed for the diffusion in order to relax the need for a remeshing of the computational elements close to solid boundaries. The immersed interface technique is applied to the flow past a circular cylinder at a Reynolds number of 3000 and the convergence of the method is demonstrated by a systematic refinement of the spatial and temporal parameters. Finally, the flow past a cactus-like geometry is considered, demonstrating the efficient handling of complex bluff body flows.