An immersed interface method for the Vortex-In-Cell algorithm

The paper presents a two-dimensional immersed interface for the Vortex-In-Cell (VIC) method for simulation of flows past bodies of complex geometry. The particle-mesh VIC algorithm is augmented by a local particle correction term in a Particle-Particle Particle-Mesh (P3M) context to resolve sub-grid scales incurred by the presence of the immersed interface. The particle-particle correction furthermore allows to disjoin mesh and particle resolution by explicitly resolving sub-grid scales on the paticle. This P3M algorithm uses an influence matrix technique to annihilate the anisotropic sub-grid scales and ads an exact particle-particle correction term. Free-space boundary conditions are satisfied through the use of modified Green's functions in the solution of the Poisson quation for the streamfunction. The concept is extended such as to provide exact velocity predictions on the mesh with free-space boundary conditions. The random walk thechnique is employed for the diffusion in order to relax the need for a remeshing of the computational elements close to solid boundaries. A novel partial remeshing thchnique is introduced which only performs remeshing of the vortex elements which are located sufficiently distant from the emmersed interfaces, thus maintaining a sufficient spatial representation of the vorticity field. Convergence of the present P3M algorithm is demonstrated for a circulat patch of vorticity. The immersed interface tchnique 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 parameters. Finally, the flow past a cactus-like geometry considered to demenstrate the efficient handling of complex bluff body geometries. The simulations offer an insight into physically interesting flow behavior involving a temporarily negative total drag force on the section.