Applying the Kolmogorov equation to the problem of subgrid modeling for Large-Eddy Simulation of turbulence
Résumé
The aim of the current work is to investigate a series of new subgrid models by employing the Kolmogorov equation of ltered quantities (KEF), which is an exact relation of turbulence in physical space. Different formulations of KEF are derived, including the forms in velocity eld (homogeneous isotropic turbulence, inhomogeneous anisotropic turbulence, homogeneous shear turbulence, homogeneous rotating turbulence), in scalar turbulence and in magnetohydrodynamic turbulence. The corresponding subgrid models are then formulated, for example: - The multi-scale improvement of CZZS model. - A new anisotropic eddy-viscosity model in homogeneous shear turbulence. - The improved velocity increment model (IVI). - The rapid-slow analysis and model application in inhomogeneous anisotropic scalar turbulence. - The attempt in magnetohydrodynamic (MHD) turbulence. Besides, there are also other important conclusions in this thesis: - The anisotropic effect of mean shear in physical space is analyzed. - Analytical corrections to the scaling of the second-order structure function in isotropic turbulence in introduced. - It is shown that the two-point distance of velocity increment must be much larger than the lter size, in order to satisfy the classical scaling law. Otherwise, the classical scaling law can not be directly applied in subgrid modeling. - A thought-experiment is described to analyse the time-reversibility problem of subgrid models. - A rapid algorithm for Tophat lter operator in discrete eld is introduced.