Stability-enhanced viscous vortex particle method in high Reynolds number flow and shear turbulence

The Vortex Particle Method (VPM) is a meshless Lagrangian vortex method. Its low numerical dissipation is exceptionally suitable for wake simulation. Nevertheless, the inadequate numerical stability of VPM prevents its widespread application in high Reynolds number flow and shear turbulence. To better simulate these flows, this paper proposes the stability-enhanced VPM based on a Reformulated VPM (RVPM) constrained by conservation of angular momentum, integrating a relaxation scheme to suppress the divergence of the vorticity field, and further coupling the Sub-Grid Scale (SGS) model to account for the turbulence dissipation caused by vortex advection and vortex stretching. The validity of the RVPM is confirmed by simulating an isolated vortex ring's evolution. The results also demonstrate that the relaxation scheme of vorticity enhances the numerical stability of the VPM by mitigating the divergence of the vorticity field. The leapfrogging vortex rings simulation demonstrates that the RVPM with the present SGS model can more precisely feature the leapfrog and fusion of vortex rings and has improved numerical stability in high Reynolds number flows. The round turbulent jet simulation confirms that the stability-enhanced VPM can stably simulate shear turbulence and accurately resolve fluctuating components and Reynolds stresses in the turbulence.