**Article: **Nouri, AG; Nik, MB; Givi, P; Livescu, D; Pope, SB; *“Self-Contained Filtered Density Function”,* Physical Review Fluids, 2 (**9**)

**Abstract:** The filtered density function (FDF) closure is extended to a “self-contained” format to include the subgrid-scale (SGS) statistics of all of the hydro-thermo-chemical variables in turbulent flows. These are the thermodynamic pressure, the specific internal energy, the velocity vector, and the composition field. In this format, the model is comprehensive and facilitates large-eddy simulation (LES) of flows at both low and high compressibility levels. Atransport equation is developed for the joint pressure-energy-velocity-composition filtered mass density function (PEVC-FMDF). In this equation, the effect of convection appears in closed form. The coupling of the hydrodynamics and thermochemistry is modeled via a set of stochastic differential equation for each of the transport variables. This yields a self-contained SGS closure. For demonstration, LES is conducted of a turbulent shear flow with transport of a passive scalar. The consistency of the PEVC-FMDF formulation is established, and its overall predictive capability is appraised via comparison with direct numerical simulation (DNS) data.

Funding Acknowledgement: AFOSR [FA9550-12-1-0057]; NSF [CBET-1603131, CBET-1609120]

Funding Text: This work is sponsored by AFOSR under Grant No. FA9550-12-1-0057 and by NSF under Grants No. CBET-1603131 and No. CBET-1609120. Computational resources are provided by the University of Pittsburgh Center for Research Computing.