Dynamic One-Equation Nonviscosity Large-Eddy Simulation Model

Abstract

Anew approach for a nonviscosity large-eddy simulation (LES)subgrid stress model is presented.Theapproach uses a scaling that is provided by the subgrid kinetic energy and a tensor coefe cient that is obtained from the dynamic modeling approach, hence, a dynamic structure model. Mathematical and conceptual issues motivating the development of this new model are explored. Attention is focused on dynamic modeling approaches. The basic equations that originate in dynamic modeling approaches are Fredholm integral equations of the second kind. These equations have solvability requirements that have not been previously addressed in the context of LES models. These conditionsare examined for traditional dynamic Smagorinksy modeling, that is, zero-equation approaches, and one-equation subgrid models. It is shown that standard approaches do not always satisfy the integral equation solvability condition. It is also shown that traditional LES models that use the resolved scale strain rate to estimatethesubgrid stressesscalepoorly with e lterlevel, leading to signie cant errorsin themodeling of the subgrid scale stress. The poor scaling in traditional LES approaches can result in not only weak models, but can also cause nonrealizability of the subgrid stresses. A better scaling based on the subgrid kinetic energy is proposed that leads to a new one-equation nonviscosity model that does satisfy the solvability conditions and appears to maintain realizability. Both integral and algebraic formulations of the new one-equation nonviscosity model are presented. The resolved and subgrid kinetic energies are shown to compare well to a direct numerical simulation of decaying isotropic turbulence.