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@INPROCEEDINGS{Durante:1048570,
      author       = {Durante, Danilo and Marrone, Salvatore and Brömmel, Dirk
                      and Speck, Robert},
      title        = {{N}umerical simulations of colliding rings using
                      {PEPC}-{DVH}, the 3{D} extension of {D}iffused {V}ortex
                      {H}ydrodynamics},
      reportid     = {FZJ-2025-04710},
      year         = {2025},
      abstract     = {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.},
      month         = {Oct},
      date          = {2025-10-20},
      organization  = {IX International Conference on
                       Particle-based Methods, Barcelona
                       (Spain), 20 Oct 2025 - 22 Oct 2025},
      subtyp        = {After Call},
      cin          = {JSC},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs)
                      and Research Groups (POF4-511) / RGRSE - RG Research
                      Software Engineering for HPC (RG RSE) (RG-RSE)},
      pid          = {G:(DE-HGF)POF4-5112 / G:(DE-Juel-1)RG-RSE},
      typ          = {PUB:(DE-HGF)6},
      url          = {https://juser.fz-juelich.de/record/1048570},
}