Numerical simulation of 3D vorticity dynamics with the Diffused Vortex Hydrodynamics method

In this paper the three-dimensional extension of the Diffused Vortex Hydrodynamics (DVH) is discussed along with free vorticity dynamics simulations. DVH is a vortex particle method developed in -house and widely validated in a 2D framework. The DVH approach has been embedded in a new frontend to the open -source code PEPC, the Pretty Efficient Parallel Coulomb solver. Within this parallel Barnes-Hut tree code, a superposition of elementary heat equation solutions in a cubic support is performed during the diffusion step. This redistribution avoids excessive clustering or rarefaction of the vortex particles, providing robustness and high accuracy of the method. An ascending vortex dipole at various resolutions is selected as a test -case and heuristic convergence measurements are performed, taking into account the conservation of prime integrals and the energy-enstrophy balance.