Partially integrated transport modeling method for turbulence simulation with variable filters

The basis of the partially integrated transport modeling method was introduced in papers of Schiestel and Dejoan [Towards a new partially integrated transport model for coarse grid and unsteady turbulent flow simulations, Theor. Comput. Fluid Dyn. 18, 443 (2005)] and Chaouat and Schiestel [A new partially integrated transport model for subgrid-scale stresses and dissipation rate for turbulent developing flows, Phys. Fluids 17, 065106 (2005)]. This method provides a continuous approach for hybrid Reynolds averaged Navier-Stokes (RANS)-large eddy simulation (LES) simulations with seamless coupling between RANS and LES regions. The method, like in usual LES techniques, makes use of space filtering in the turbulent field. In the foundation papers cited above and in the main applications considered so far, the filter width has been supposed constant or at least slowly varying. In the present paper, we examine the effect of variable filter width in the model equations and how to account for this effect in practical numerical simulations. With the aim to illustrate the theoretical development of the effect of varying filter width in time and space on the governing equations of mass, momentum, and turbulence model, and to show the usefulness of the proposed approach, we perform then numerical simulations of isotropic decaying turbulence. (C) 2013 AIP Publishing LLC.