Transported probability density function methods for Reynolds-averaged and large-eddy simulations

Probability density function (PDF) methods provide an elegant and effective resolution to the closure problems that arise from averaging or filtering chemical source terms and other nonlinear terms in the equations that govern chemically reacting turbulent flows. PDF methods traditionally have been associated with studies of turbulence-chemistry interactions in laboratory-scale, atmospheric pressure, nonluminous, statistically-stationary nonpremixed turbulent flames; and Lagrangian particle-based Monte Carlo numerical algorithms have become the predominant method for solving modeled PDF transport equations. The emphasis in this chapter is on recent advances, new trends and perspectives in PDF methods. These include advances in particle-based algorithms, alternatives to particle-based algorithms (e.g., Eulerian field methods), treatment of combustion regimes beyond low-to-moderate-Damk̈ohler-number nonpremixed systems (e.g., premixed flamelets), extensions to include radiation heat transfer and multiphase systems (e.g., soot and fuel sprays), and the use of PDF-based methods as the basis for modeling in largeeddy simulation.