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

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 extreme 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.