A novel multi-resolution technique for solving complex vorticity patterns in planar viscous flows past bodies through the DVH method

The Diffused Vortex Hydrodynamics (DVH) is a Vortex Particle Method widely validated in the last decade. This numerical approach allows cost-effective simulations of viscous flows past bodies at moderate and high Reynolds numbers, by taking into account only the rotational part of the flow field. In the present work a novel multi-resolution technique is presented in order to limit the number of particles in the computational domain, further improving the solver efficiency. The proposed technique preserves the total circulation and uses the (Benson et al., 1989) deterministic algorithm to regularize the particle spatial distribution during the diffusion step. Simulations of the planar flow past five cylindrical sections at Re=10,000 are discussed: flat plate, triangle, square, circular cylinder and a symmetrical airfoil. Although the simulations are carried out in a two-dimensional framework, complex vorticity patterns develop because of the flow separation and the Reynolds number considered. Comparisons with a Finite Volume solver are carried out and discussed, such highlighting the advantages of the present numerical approach.