Non-Boussinesq subgrid-scale model with dynamic tensorial coefficients

Abstract

A major drawback of Boussinesq-type subgrid-scale stress models used in large-eddy simulations is the inherent assumption of alignment between large-scale strain rates and filtered subgrid-stresses. A priori analyses using direct numerical simulation (DNS) data has shown that this assumption is invalid locally as subgrid-scale stresses are poorly correlated with the large-scale strain rates [Bardina et al., AIAA 1980; Meneveau and Liu, Ann. Rev. Fluid Mech. 2002]. In the present work, a new, non-Boussinesq subgrid-scale model is presented where the model coefficients are computed dynamically. Some previous non-Boussinesq models have observed issues in providing adequate dissipation of turbulent kinetic energy [e.g.: Bardina et al., AIAA 1980; Clark et al. J. Fluid Mech., 1979; Stolz and Adams, Phys. of Fluids, 1999]; however, the present model is shown to provide sufficient dissipation using dynamic coefficients. Modeled subgrid-scale Reynolds stresses satisfy the consistency requirements of the governing equations for LES, vanish in laminar flow and at solid boundaries, and have the correct asymptotic behavior in the near-wall region of a turbulent boundary layer. The new model, referred to as the dynamic tensor-coefficient Smagorinsky model (DTCSM), has been tested in simulations of canonical flows: decaying and forced homogeneous isotropic turbulence (HIT), and wall-modeled turbulent channel flow at high Reynolds numbers; the results show favorable agreement with DNS data. In order to assess the performance of DTCSM in more complex flows, wall-modeled simulations of high Reynolds number flow over a Gaussian bump exhibiting smooth-body flow separation are performed. Predictions of surface pressure and skin friction, compared against DNS and experimental data, show improved accuracy from DTCSM in comparison to the existing static coefficient (Vreman) and dynamic Smagorinsky model.