Development of the Subgrid-Scale Models in Large Eddy Simulation for the Finite Difference Schemes

Abstract

This chapter discusses development of the subgrid-scale (SGS) models in large eddy simulation (LES) for the finite difference (FD) schemes. A novel method is applied to SGS stress in this chapter and heat flux modeling and eddy viscosity/ diffusivity-type models are derived, which are specially designed for the dynamic procedure using the FD scheme. The models are validated in turbulent channel flows at various grid resolutions, and show better agreement with direct numerical simulation (DNS) results than the classical Smagorinsky's model. The most notable feature of these new models is their insensitivity to the discretized test filtering operation, contrary to the Smagorinsky's model which shows strong dependence on the adopted filter parameter. Effects of the FD errors on the accuracy of SGS models are intensively studied in a turbulent pipe flow. The mixed high and second-order FD scheme is adopted and dependence of the results on the order of accuracy is investigated. At the second-order accuracy, the numerical error seriously affects the obtained results, and the mean velocity profile predicted by LES without SGS model (coarse DNS) shows good agreement with DNS results. At the higher order accuracy, the coarse DNS underestimates the mean velocity, while the proposed eddy-viscosity model highlights good agreement with the empirical law at the logarithmic layer and mitigates the serious overestimation of Smagorinsky's model.