Homogenisation by Multiple Scales Expansion of the Navier Stokes Equations.Scientific Report

摘要

In this study simulation models for turbulent incompressible viscous flow,governed by the Navier Stokes Equations (NSE), will be analyzed using homogenization by multiple scales expansion. Simulation models for turbulent incompressible viscous flow are generally derived by filtering the NSE over a finite interval of time, homogeneous directions or across an ensemble of equivalent flows providing the class of Reynolds Average Simulation (RAS) models, or by low-pass filtering in space, providing the class of Large Eddy Simulation (LES) or Very Large Eddy Simulation (VLES) models, depending on spatial resolution. Semi-empirical closure models must therewith be formulated to close the resulting RAS or LES equations. The motivation for the present work comes from the need to improve the simulation models for complex turbulent flows. More specifically, to extend the usefulness of LES-type models into the coarse grid/infinite Re number regime, and to let the model extend from a direct numerical simulation model, via LES and VLES, to a state-of-the-are Reynolds Simulation model. The use of the homogenization method emphasises aspects of the filtered NSE and its relation to the closure modelling that has not been known before, which may aid in developing improved subgrid turbulence models and increasing our present understanding of turbulence.