A three-dimensional extension of the Diffused Vortex Hydrodynamics (DVH), called PEPC-DVH, was a recently developed as a frontend to the open-source code PEPC, the Pretty Efficient Parallel Coulomb solver [1]. DVH is a vortex particle method developed in-house in a 2D framework and widely validated [2], whereas the PEPC engine for multi-body interaction is based on a parallel Barnes–Hut tree code [3]. The time integration is carried out using the Chorin decomposition: an inviscid advection is followed by a steady diffusion. 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 vortex particles, providing robustness and high accuracy to the method. The new PEPC-DVH code was used to simulate free vorticity dynamics. In particular, the collision of two identical viscous vortex rings, starting in a side-by-side configuration, is investigated. The Reynolds number considered, calculated as the ring circulation over the viscosity, spans from 577 to 1153, in agreement with the numerical simulations of Kida et al. [4]. Differently from the literature, where a spectral method was adopted for simulations with about 250,000 grid points, the exploitation of vortex method abilities allow us to follow the rings interaction at high resolution and to preserve the whole vortex wake. A final amount of about 150 Millions of vortices was used for achieving the same final time considered in literature. Bridging and second reconnection are correctly captured and comparisons are offered in terms of vorticity fields and global quantities, like the time evolution of the circulation around the vortex core. Heuristic convergence measurements were also performed, by considering the conservation of prime integrals and the energy–enstrophy balance. Finally, a new algorithm for a multi-resolution strategy, embedded in PEPC-DVH, is introduced. The multi-resolution is obtained by means of a multi-layered distribution of vorticity, which guarantees higher resolution where particles at higher vorticity are found. Low vorticity particles are interpolated on a sparser grid-level, maintaining the same global circulation and ensuring compliance with Kelvin's circulation theorem. This strategy functions similarly to an Automatic Mesh Refinement (AMR) algorithm but eliminates the complexity of constructing a hash table as required in that approach.