A dynamic global-coefficient subgrid-scale eddy-viscosity model for large-eddy simulation in complex geometries

Abstract

An improvement of the dynamic procedure of Park et al. [Phys. Fluids 18, 125109 (2006)] for closure of the subgrid-scale eddy-viscosity model developed by Vreman [Phys. Fluids 16, 3670 (2004)] is proposed. The model coefficient which is globally constant in space but varies in time is dynamically determined assuming the “global equilibrium” between the subgrid-scale dissipation and the viscous dissipation of which utilization was proposed by Park et al. Like the Vreman model with a fixed coefficient and the dynamic-coefficient model of Park et al., the present model predicts zero eddy-viscosity in regions where the vanishing eddy viscosity is theoretically expected. The present dynamic model is especially suitable for large-eddy simulation in complex geometries since it does not require any ad hoc spatial and temporal averaging or clipping of the model coefficient for numerical stabilization and more importantly, requires only a single-level test filter in contrast to the dynamic model of Park et al., which employs two-level test filters.

Large-eddy simulation of circular cylinder flow at subcritical Reynolds number: Turbulent wake and sound radiation

“…The filtered strain rate tensor isS i j . The eddy-viscosity coefficient ν t is calculated from the global coefficient dynamic Vremen's SGS model [14], which will be introduced below.…”

“…Incorrectly large dissipation of a SGS model can enlarge the separation zone artificially in the mean velocity profiles, whereas improper small dissipation may erroneously shorten it. In the work by You and Moin [14], a dynamic procedure was proposed to determine the global coefficient in Vreman's model [13]. In the Vreman SGS model, the eddy-viscosity coefficient ν t is calculated by using…”

“…This leads to it having a low SGS dissipation in the laminar regions of the present case. The coefficient in Vremann's model is determined using a dynamic procedure proposed by You et al [14]. This SGS model also prevents a negative eddy-viscosity.…”

Building proper invariants for eddy-viscosity subgrid-scale models

“…For the sake of clarity, sometimes the invariant Q Ω is also used. Notice that it can always be written in terms of Q S , Q G via identity (7). Starting from the classical Smagorinsky model, they are presented in chronological order.…”

“…More recently, Park et al 6 introduced two global dynamic approaches: a dynamic global model based on the Germano identity and a dynamic global model with two test filters based on the global equilibrium between the viscous dissipation and the SGS dissipation. Instead of using two test filters, You and Moin 7 presented a dynamic global approach using only one test filter. However, Lee et al 8 showed that the assumption of the global equilibrium is not valid for freely decaying isotropic turbulence.…”