Subgrid scale modeling taking the numerical error into consideration

Large eddy simulation (LES) is regarded as one of the most promising numerical methods to predict unsteady turbulent flows at high Reynolds number. In LES the flow field is decomposed into grid and subgrid scales. The grid scale (GS) flow field is computed numerically using discrete filtered Navier-Stokes equation with a model for the subgrid scale (SGS) stress. Therefore, the reliability of the computed flow field is strongly affected by both the reliability of the SGS model and the accuracy of the numerical method (Ghosal 1996), particularly in the approximation of the convective term. This means that even if we use the exact SGS stress, the computed flow field will be contaminated by the numerical error. This connection between SGS modeling and numerical error was mostly overlooked. As a result all of the existing SGS models have been developed independently from the numerical methods. One of the objectives of this study is to develop a dynamic subgrid scale model, for which computational results will not depend on the accuracy of the numerical method. The most commonly used SGS model is based on the Smagorinsky eddy viscosity model (Smagorinsky, 1963) with the model coefficient computed dynamically through the tensor level identity by Germano et al. (1991), hereafter denoted by DSM. However, the tensor level identity does not explicitly include the effect of the numerical error, and thus the computational results strongly depend on the numerical method, especially in simulations with poor resolution. In this report we will present a new dynamic procedure with the vector level identity, which takes the numerical error into consideration. We will test the dynamic Smagorinsky SGS model with the vector level identity, hereafter referred as VDSM model. The second objective of this study is to present a modification to the dynamic two-parameter mixed model. It is well known that the correlation between the Smagorinsky model and the SGS stress is low (for example see Horiuti 1989) while the model based on the scale similarity assumption by Bardina et al. (1983) has considerably higher correlation. However, the scale similarity model has a defect: it is not dissipative enough. Therefore, the model is usually used together with the Smagorinsky model. Model coefficients are commonly computed using the dynamic procedure (Zang et al. 1993; Vreman et al. 1994; Salvetti & Banerjee 1995; Horiuti