Towards a new partially integrated transport model for coarse grid and unsteady turbulent flow simulations

Abstract

A new two-equation model is proposed for large eddy simulations (LESs) using coarse grids. The modeled transport equations are obtained from a direct transposition of well- known statistical models by using multiscale spectrum splitting given by the filtering operation applied to the Navier–Stokes equations. The model formulation is compatible with the two ex- treme limits that are on one hand a direct numerical simulation and on the other hand a full statistical modeling. The characteristic length scale of subgrid turbulence is no longer given by the spatial discretization step size, but by the use of a dissipation equation. The proposed method is applied to a transposition of the well-known k-ε statistical model, but the same method can be developed for more advanced closures. This approach is intended to contribute to non-zonal hybrid models that bridge Reynolds-averaged Navier–Stokes (RANS) and LES, by using a continuous change rather than matching zones. The main novelty in the model is the derivation of a new ε equation for LES that is formally consistent with RANS when the filter width is very large. This approach is dedicated to applications to non-equilibrium turbulence and coarse grid simulations. An illustration is made of large eddy simulations of turbulence submitted to periodic forcing. The model is also an alternative approach to hybrid models.