Stable Vortex Particle Method Formulation for Meshless Large-Eddy Simulation

A novel formulation of the vortex particle method (VPM) is developed for large-eddy simulation (LES) in a meshless scheme that is numerically stable. A new set of VPM governing equations are derived from the LES-filtered Navier-Stokes equations. The new equations reinforce the conservation of angular momentum by resizing vortex elements subject to vortex stretching. In addition to the VPM reformulation, a new anisotropic dynamic model of subfilter-scale (SFS) vortex stretching is developed. This SFS model is well suited for turbulent flows with coherent vortical structures, where the predominant cascade mechanism is vortex stretching. The mean and fluctuating components of turbulent flow and Reynolds stresses are validated through the simulation of a turbulent round jet. The computational efficiency of the scheme is showcased in the simulation of an aircraft rotor in hover, showing our meshless LES to be 100 times faster than a mesh-based LES with similar fidelity. The implementation of our meshless LES scheme is released as open-source software, called FLOWVPM.