A multiresolution remeshed particle vortex method using patches

We present a novel multi-resolution Vortex-In-Cell (VIC) algorithm using overlapping mesh patches of different resolution. The approach is based on the method of Bergdorf et al. 2005 and the free-space solution obtained using fast Fourier transforms (FFT) by Hockney and Eastwood 1988. The hybrid vortex particle-mesh VIC algorithm interpolates particle vorticity to a mesh, solves a Poisson equation for the stream function using FFTs and calculates velocities as the curl of the stream function.

With both vorticity and velocity available on the mesh, values of the substantial derivative of particle strengths is calculated on the mesh and interpolated back to the particles. This allows particle strengths and positions to be updated without expensive direct particle-particle interaction. The no-slip condition of complex solid bodies is imposed with Brinkman penalization.

In the work presented, a VIC implementation with patches of varying resolution, is applied to the two-dimensional flow past a cylinder. The vorticity field can be divided into two regions, an arbitrary patch of vorticity and the remaining exterior vorticity field. Due to the linearity of the Poisson equation the velocity field corresponding to the total vorticity field is the sum of the free space solutions to the Poisson equation to each region.

Hereby the flow on the patch can be simulated at a higher resolution, while including the influence from the coarser exterior region. Particles are remeshed and interpolated only to the region from which they are formed and each region is extended by a buffer1 to ensure full interpolation support in its interior.

Patches of varying resolutions may be nested and can contain multiple patches.