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 simulation of flows past bodies of complex geometry. The particle–mesh VIC algorithm is augmented by a local particle–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 particles. This P3M algorithm uses an influence matrix technique to annihilate the anisotropic sub-grid scales and adds 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 equation 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 technique 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 technique is introduced which only performs remeshing of the vortex elements which are located sufficiently distant from the immersed interfaces, thus maintaining a sufficient spatial representation of the vorticity field.Convergence of the present P3M algorithm is demonstrated for a circular patch of vorticity. 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 parameters. Finally, the flow past a cactus-like geometry is considered to demonstrate 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.