On the extension of the integral length-scale approximation model to complex geometries

Abstract

A new model for the unresolved stresses in large-eddy simulations was recently proposed by Piomelli et al. [J Fluid Mech 2015; 766:499–527] and Rouhi et al., [Phys Rev Fluids 2016; 1(4):0444011], in which the length scale is not related to the grid size, but determined based on turbulence properties. This model, the Integral Length-Scale Approximation (ILSA), has a single parameter, sτ, which represents the contribution of the unresolved scales to the momentum transport, and is assigned by the user. We test ILSA in complex geometries using a low-dissipation finite-element method, and propose a rational method to determine sτ on the basis of a grid-convergence study. The interaction of the model with the numerical method and grid topology is studied first; then, two cases are considered: the subcritical flow around a sphere, and the flow over the Ahmed body, a simplified car model. In each case calculations are performed using three grids and varying sτ. With a consistent combination of grid size and sτ the statistical results are in very good agreement with DNS data and experimental measurements. The eddy viscosity is insensitive to sudden variation of the mesh size, and the model adjusts to the different dissipation and diffusion characteristics associated with different grid topologies and numerical techniques.