Vortex Methods for High-Resolution Simulations of Viscous Flow Past Bluff Bodies of General Geometry

Recent contributions to the 2-D vortex method are presented. A technique to accurately redistribute particles in the presence of bodies of general geometry is developed. The particle strength exchange (PSE) scheme for diffusion is modified for particles in the vicinity of the solid boundaries to avoid a spurious vorticity flux during the convection/PSE step. The scheme used to enforce the no-slip condition through the vorticity flux at the boundary is modified in a way that is more accurate than in the previous method. Finally, to perform simulations with nonuniform resolution, a mapping of the redistribution lattice is also used. In that case, the PSE is still done in the physical domain, using a symmetrized, conservative scheme. The quadratic convergence of this scheme is proved mathematically, and numerical tests are shown to support the proof. These elements are all validated on the benchmark problem of the flow past an impulsively started cylinder. High-resolution, long-time simulations of the flow past other bluff bodies are also presented: the case of a square and of a capsule at angle of attack.