Toward Meshless Turbulent Flow Simulation: LES-Integrated Vortex Particle Method

TL;DR

This paper addresses meshless simulation of turbulent incompressible flows by integrating a dynamic LES model into a vortex particle method (VPM), enabling viscous diffusion via core-spreading and per-particle dynamic eddy viscosity guided by a Germano identity. A high-order algebraic kernel is employed to obtain closed-form velocity and diagnostic quantities, with an energy-matching relation linking particle core size to a conventional LES filter width. Validation on isolated and leapfrogging vortex rings demonstrates accurate reproduction of velocity decay, enstrophy evolution, and instability onset, showing strong agreement with DNS and rVPM while maintaining stability in the turbulent phase. The results highlight a scalable, mesh-free alternative for simulating 3D vortex-dominated turbulence without reliance on background grids, potentially benefiting aeroacoustic, atmospheric, and wind-energy applications.

Abstract

Recent developments in vortex particle methods for simulating three-dimensional incompressible flows are presented. A lightweight, dynamic Large-Eddy Simulation model is tested, featuring a dynamic procedure that relies solely on Lagrangian information and requires minimal auxiliary computation to update the model constant. The method employs a high-order algebraic kernel which enables direct, analytical expressions for conservation laws, the strain-rate tensor, and quadratic velocity diagnostics. Viscous diffusion is modeled using the core-spreading technique. The particle method is assessed with respect to kinematics and the conservation of energy, helicity, and enstrophy in vortex ring and leapfrogging vortex ring scenarios, both unperturbed and perturbed. The results indicate that the kinematics and flow diagnostics are accurately captured using relatively sparse particle distributions, effectively resolving the dynamics of the unstable flow phase. However, after the onset of instabilities, the sub-grid-scale methodology becomes strongly dependent on particle regularization to stabilize the flow solution.

Figures (6)

• Figure 1: Vortex ring with azimuthal perturbations represented by vortex particles, colored by normalized strength magnitude. The self-induced velocity direction, $u_\Gamma$, is highlighted. An unperturbed ring, depicted as a gray surface, is overlaid for reference.
• Figure 2: Translational velocity of the vortex ring from the present LES-VPM model, compared with DNS results, theoretical predictions, and the rVPM method. The white, yellow, and blue regions represent the laminar, transitional, and turbulent flow regimes, respectively.
• Figure 3: Evolution of vortex ring diagnostics for perturbed and unperturbed cases: (top row) circulation and enstrophy; (bottom row) kinetic energy and linear impulse. The white, yellow, and blue regions represent the laminar, transitional, and turbulent flow regimes, respectively.
• Figure 4: Two leapfrogging vortex rings represented by strength-colored vortex particles. The rings are radially perturbed to induce the onset of flow instabilities during the turbulent flow regime. The non-disturbed shape of the vortex rings is overlaid as gray surfaces for reference.
• Figure 5: Translational velocity of the leapfrogging vortex rings from the present LES-VPM model, compared with LBM results by cheng2015leapfrogging and rVPM results by alvarez2022reviving. The white, yellow, and blue regions represent the laminar, transitional, and turbulent flow regimes, respectively.