Velocity-scalar filtered mass density function for large eddy simulation of turbulent reacting flows

A methodology termed the “velocity-scalar filtered mass density function” (VSFMDF) is developed and implemented for large eddy simulation (LES) of variable-density turbulent reacting flows. This methodology is based on the extension of the previously developed “velocity-scalar filtered density function” method for constant-density flows. In the VSFMDF, the effects of the unresolved subgrid scales (SGS) are taken into account by considering the joint probability density function of the velocity and scalar fields. An exact transport equation is derived for the VSFMDF in which the effects of SGS convection and chemical reaction are in closed forms. The unclosed terms in this equation are modeled in a fashion similar to that in Reynolds-averaged simulation procedures. A set of stochastic differential equations (SDEs) are considered which yield statistically equivalent results to the modeled VSFMDF transport equation. The SDEs are solved numerically by a Lagrangian Monte Carlo procedure in which the Ito-Gikhma...