A self-adjusting flow dependent formulation for the classical Smagorinsky model coefficient

Abstract

In this paper, we propose an efficient formula for estimating the model coefficient of a Smagorinsky model based subgrid scale eddy viscosity. The method allows vanishing eddy viscosity through a vanishing model coefficient in regions where the eddy viscosity should be zero. The advantage of this method is that the coefficient of the subgrid scale model is a function of the flow solution, including the translational and the rotational velocity field contributions. Furthermore, the value of model coefficient is optimized without using the dynamic procedure thereby saving significantly on computational cost. In addition, the method guarantees the model coefficient to be always positive with low fluctuation in space and time. For validation purposes, three test cases are chosen: (i) a fully developed channel flow at ${\mathop{\rm Re}\nolimits} _\tau = 180,\,395$ Re τ=180,395, (ii) a fully developed flow through a rectangular duct of square cross section at ${\mathop{\rm Re}\nolimits} _\tau = 300$ Re τ=300, and (iii) a smooth subcritical flow past a stationary circular cylinder, at a Reynolds number of ${\mathop{\rm Re}\nolimits} = 3900$ Re =3900, where the wake is fully turbulent but the cylinder boundary layers remain laminar. A main outcome is the good behavior of the proposed model as compared to reference data. We have also applied the proposed method to a CT-based simplified human upper airway model, where the flow is transient.