Effects of the Similarity Model in Finite-Difference LES of Isotropic Turbulence Using a Lagrangian Dynamic Mixed Model

A Lagrangian dynamic formulation of the mixed similarity subgrid (SGS) model for large-eddy simulation (LES) of turbulence is proposed. In this model, averaging is performed over fluid trajectories, which makes the model applicable to complex flows without directions of statistical homogeneity. An alternative version based on a Taylor series expansion (nonlinear mixed model) is also examined. The Lagrangian models are implemented in a finite difference code and tested in forced and decaying isotropic turbulence. As comparison, the dynamic Smagorinsky model and volume-averaged formulations of the mixed models are also tested. Good results are obtained, except in the case of low-resolution LES (32³) of decaying turbulence, where the similarity coefficient becomes negative due to the fact that the test-filter scale exceeds the integral scale of turbulence. At a higher resolution (64³), the dynamic similarity coefficient is positive and good agreement is found between predicted and measured kinetic energy evolution. Compared to the eddy viscosity term, the similarity or the nonlinear terms contribute significantly to both SGS dissipation of kinetic energy and SGS force. In order to dynamically test the accuracy of the modeling, the error incurred in satisfying the Germano identity is evaluated. It is found that the dynamic Smagorinksy model generates a very large error, only 3% lower than the worst-case scenario without model. Addition of the similarity or nonlinear term decreases the error by up to about 50%, confirming that it represents a more realistic parameterization than the Smagorinsky model alone.