Frequency-velocity-scalar filtered mass density function for large eddy simulation of turbulent flows

A methodology termed "frequency-velocity-scalar filtered mass density function" (FVS-FMDF) is developed for large eddy simulation (LES) of turbulent flows. The FVS-FMDF takes account of unresolved subgrid scales (SGSs) by considering the joint probability density function (PDF) of the frequency, the velocity, and the scalar fields. An exact transport equation is derived for the FVS-FMDF in which the effects of convection and chemical reaction are in closed forms. The unclosed terms in this equation are modeled in a fashion similar to PDF methods in Reynolds-averaged Navier-Stokes simulations. The FVS-FMDF transport is modeled via a set of stochastic differential equations (SDEs). The numerical solution procedure is based on a hybrid finite-difference (FD)/Monte Carlo (MC) method in which the LES filtered transport equations are solved by the FD, and the set of SDEs is solved by a Lagrangian MC procedure. LES of a temporally developing mixing layer is conducted via the FVS-FMDF, and the results are compared with those via the Smagorinsky SGS closure. All these results are also assessed by comparison with those obtained by direct numerical simulation (DNS). The FVS-FMDF predictions show favorable agreements with DNS data.