Implicit iterative particle shifting for meshless numerical schemes using kernel basis functions

P. Rastelli, R. Vacondio, J.C. Marongiu, G. Fourtakas, Benedict D. Rogers

Research output: Contribution to journalArticlepeer-review


A novel particle shifting technique (PST) for meshless numerical methods is presented. The proposed methodology uses an implicit iterative particle shifting (IIPS) technique aiming to reduce the spatial particle’ anisotropy, which is associated with the discretization error in meshless numerical schemes based on kernel basis functions. The algorithm controls the particle spatial distribution through an implicit minimization problem, related to the particle concentration gradient and therefore, to the particles’ anisotropy. This results in accurate particle distributions, to demonstrate the effectiveness of the proposed method, the IIPS algorithm is tested within a smoothed particle hydrodynamics (SPH) framework, with static and kinematic cases, by examining the particle distributions and the corresponding spatial accuracy. Further, the computational cost of the proposed methodology is reported and it is shown that it introduces minimal overhead. Moreover, the simulations of the Taylor–Green vortex (TGV), employing a weakly-compressible SPH Navier–Stokes solver, confirmed the superior accuracy of the IIPS in comparison to existing explicit shifting approaches, in simulating internal flows.

Original languageEnglish
Article number114716
JournalComputer Methods in Applied Mechanics and Engineering
Early online date7 Mar 2022
Publication statusPublished - Apr 2022


  • Convergence rates
  • Error minimization
  • Implicit iterative particle shifting
  • Meshless discretization schemes
  • Particle anisotropy


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