Monte Carlo Vortical Smoothed Particle Hydrodynamics for Simulating Turbulent Flows

Xingyu Ye, Xiaokun Wang*, Yanrui Xu, Jiří Kosinka, Alexandru C. Telea, Lihua You, Jian Jun Zhang, Jian Chang*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


For vortex particle methods relying on SPH-based simulations, the direct approach of iterating all fluid particles to capture velocity from vorticity can lead to a significant computational overhead during the Biot-Savart summation process. To address this challenge, we present a Monte Carlo vortical smoothed particle hydrodynamics (MCVSPH) method for efficiently simulating turbulent flows within an SPH framework. Our approach harnesses a Monte Carlo estimator and operates exclusively within a pre-sampled particle subset, thus eliminating the need for costly global iterations over all fluid particles. Our algorithm is decoupled from various projection loops which enforce incompressibility, independently handles the recovery of turbulent details, and seamlessly integrates with state-of-the-art SPH-based incompressibility solvers. Our approach rectifies the velocity of all fluid particles based on vorticity loss to respect the evolution of vorticity, effectively enforcing vortex motions. We demonstrate, by several experiments, that our MCVSPH method effectively preserves vorticity and creates visually prominent vortical motions.

Original languageEnglish
Article numbere15024
JournalComputer Graphics Forum
Issue number2
Early online date30 Apr 2024
Publication statusPublished - May 2024


  • CCS Concepts
  • • Computing methodologies → Physical simulation


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