Numerical Issues of Monte Carlo PDF for Large Eddy Simulations of Turbulent Flames

Monte Carlo simulations of joint PDF approaches have been extensively developed in the past largely with Reynolds Averaged Navier Stokes (RANS) equations. Current interests are in the extension of PDF approaches to Large Eddy Simulation (LES). As LES intends to resolve the large scales of turbulence in time, the coupling between Monte Carlo simulation and the flow field becomes an important issue. It is crucial to ensure some sort of coherency between the scalar field solution obtained via finite-volume methods and that from the stochastic solution of the PDF. In this paper, we first review the advantages and disadvantages of Eulerian and Lagrangian approaches. In order to clarify the coherency feature of a solution method, we introduce the concept of stochastic convergence for hybrid methods. Secondly, we present some preliminary results of an ongoing study with the Eulerian approach that reveals the numerical issues needing to be resolved. Results are presented for simulations of a pure mixing jet and Sandia Flame D using a steady-state flamelet model