On Homogenization-Based Methods for Large-Eddy Simulation

The ability to predict complex engineering flows is limited by the available turbulence models and the present-day computer capacity. In Reynolds averaged numerical simulations (RANS), which is the most prevalent approach today, equations for the mean flow are solved in conjunction with a model for the statistical properties of the turbulence. Considering the limitations of RANS and the desire to study more complex flows, more sophisticated methods are called for. An approach that fulfills these requirements is large-eddy simulation (LES) which attempts to resolve the dynamics of the large-scale flow, while modeling only the effects of the small-scale fluctuations. The limitations of LES are, however, closely tied to the subgrid model, which invariably relies on the use of eddy-viscosity models. Turbulent flows of practical importance involve inherently three-dimensional unsteady features, often subjected to strong inhomogeneous effects and rapid deformation that cannot be captured by isotropic models. As an alternative to the filtering approach fundamental to LES, we here consider the homogenization method, which consists of finding a so-called homogenized problem, i.e. finding a homogeneous “material” whose overall response is close to that of the heterogeneous “material” when the size of the inhomogeneity is small. Here, we develop a homogenization-based LES-model using a multiple-scales expansion technique and taking advantage of the scaling properties of the Navier-Stokes equations. To study the model simulations of forced homogeneous isotropic turbulence and channel flow are carried out, and comparisons are made with LES, direct numerical simulation and experimental data.