A dynamic global-coefficient subgrid-scale model for large-eddy simulation of turbulent scalar transport in complex geometries

The " local-equilibrium " hypothesis that assumes a local balance between the viscous dissipation and the subgrid-scale dissipation at the same physical location in turbulent flow has been commonly used for turbulence modeling. For example, based on the local equilibrium hypothesis, Germano et al. (1991) and Moin et al. (1991) developed dynamic procedures for determining the model coefficients of the Smagorinsky-model-based subgrid-scale eddy viscosity as a function of space and time. The local equilibrium assumption results in both favorable and unfavorable consequences to large-eddy simulation. The dynamic modeling procedure allows vanishing eddy viscosity by the model coefficient vanishing in regions where the flow is laminar or the eddy viscosity should be zero. However, the dynamic model coefficient can cause numerical instability since its value often becomes negative and/or highly fluctuates in space and time. The unfavorable feature of the dynamic model coefficient is closely related to the fact that the chance of local equilibrium between the subgrid-scale dissipation and the viscous dissipation is low as observed by da Silva & Metais (2002) and Borue & Orszag (1998). Therefore, the numerical instability has been remedied by additional numerical procedures such as an averaging of the model coefficient over statistically homogeneous directions or an ad hoc clipping procedure (e.g., Meneveau et al. 1996). However, the numerical stabilization procedure becomes complicated when the dynamic model is applied to a complex flow configuration in which there are no homogeneous directions. The shortcoming of the dynamic Smagorinsky models based on the local-equilibrium hypothesis was overcome by Park et al. (2006). They proposed a dynamic procedure for determining the model coefficient of an eddy-viscosity model developed by Vreman (2004) utilizing a " global equilibrium " hypothesis that assumes a global balance between the subgrid-scale dissipation and the viscous dissipation. However, the dynamic procedure of Park et al. (2006) requires two-level test filters of which utilization is difficult and impractical, especially with unstructured grid topology where defining the second-level test filter is not straightforward. More recently, an improved dynamic procedure for a closure of Vreman's model (2004) has been proposed by You & Moin (2007). The model by You & Moin (2007) also assumes global equilibrium between the subgrid-scale dissipation and the viscous dissipation, and requires only a single-level test filter, which improves the applicability of the model for complex flow configurations. In the global-equilibrium approaches (You & Moin 2007; Park et al. 2006), the model coefficient …