Pressure-Velocity-Scalar Filtered Mass Density Function for Large Eddy Simulation of Compressible Turbulent Flow

A new model is developed which accounts for the effects of subgrid scale pressure in the context of the filtered density function (FDF) formulation. This results in a pressure-velocity-scalar filtered mass density function (PVS-FMDF), which is suitable for large eddy simulation of compressible turbulence. Following its mathematical definition, an exact transport equation is derived for the PVS-FMDF. This equation is modeled in a probabilistic manner by a system of stochastic differential equations (SDEs). The consistency and the predictive capability of the model are established by conducting LES of a three-dimensional compressible mixing layer, and comparison with direct numerical simulation (DNS) data.