A consistent dynamic localization model for large eddy simulation of turbulent flows based on a variational formulation

In this study, a new approach for the dynamic localization model, which was originally proposed in Ghosal et al. [S. Ghosal, T.S. Lund, P. Moin, K. Akselvoll, A dynamic localization model for large-eddy simulation of turbulent flows, J. Fluid Mech. 286 (1995) 229–255], is described. This approach is integrated in a consistent manner into large eddy simulation based on a variational formulation. As a result, the variationally formulated condition for the model parameter is considered as an additional equation in a resulting system of two variational equations. This variational system may then be implemented using either a finite element or a finite volume method. The new version of the dynamic localization model proposed in this work has three advantages compared to the original dynamic localization model in Ghosal et al.: it relies on a simpler formulation overall, it obviates any iterative solution procedure, and it requires the solution of a number of small independent local equations instead of one large global equation. These three advantages make its solution theoretically easier and computationally more efficient. The new consistent dynamic localization model is tested for two different numerical flow examples, turbulent flow in a channel and turbulent flow in a planar asymmetric diffuser.