Application of the vorticity redistribution method to LES of incompressible flow

Abstract

The vorticity redistribution method (VRM) for constant-viscosity diffusion was recently extended to the case with variable viscosity, and its accuracy and convergence rate demonstrated. Herein, a method for the grid-free LES of turbulent incompressible unbounded flow is presented, utilizing the Lagrangian vortex element method and VRM to account for the dynamics of the resolved vorticity field and turbulent diffusion, respectively. Turbulence is modelled using the standard Smagorinsky subgrid-scale model; a dynamic version will be developed next. In this paper, the algorithm for VRM-based LES is formulated briefly, followed by a demonstration of the robustness of the proposed strategy using the prototypical problem of a fat vortex ring initially perturbed by its most unstable wavenumber. Results indicate that VRM helps maintain the stability and accuracy of the predictions for relatively long times, without the necessity to apply frequent remeshing as is customary with other methods.