Modified interpolation kernels for treating diffusion and remeshing in vortex methods

A scheme treating diffusion and remeshing, simultaneously, in Lagrangian vortex methods is proposed. The vorticity redistribution method is adopted to derive appropriate interpolation kernels similar to those used for remeshing in inviscid methods. These new interpolation kernels incorporate diffusion as well as remeshing. During implementation, viscous splitting is employed. The flow field is updated in two fractional steps, where the vortex elements are first convected according to the local velocity, and then their vorticity is diffused and redistributed over a predefined mesh using the extended interpolation kernels. The error characteristics and stability properties of the interpolation kernels are investigated using Fourier analysis. Numerical examples are provided to demonstrate that the scheme can be successfully applied in complex problems, including cases of nonlinear diffusion.