Vortex Particle Velocity Diffusion Method Using Dynamic Turbulence Control Based on Enstrophy

The Vortex Particle Method (VPM) represents continuous, incompressible, unsteady, viscous flows by using singular, independent particles represented by small concentrations of vorticity. The VPM is particularly convenient for representing viscous flow fields, which is useful for simulating vortex reconnection in an unbounded domain and flow mixing. This study aims to evaluate the accuracy of the VPM predictions using, among others, the diffusion velocity method to represent the molecular diffusion of vortex structures. The VPM can also represent the viscous diffusion of turbulent flow fields using a turbulent viscosity model. However, such models are defined up to a given constant. The dynamic computation of this constant is required for the turbulence model to encompass the diffusion of all the flow scales. A new fast dynamic technique based on the local loss of enstrophy in the flow is proposed. The coupling of the Diffusion Velocity Method with this dynamic procedure is presented. Finally, the method is validated on several known analytical flow solutions, such as the Lamb–Oseen vortex and isolated and leapfrogging vortex rings.