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.

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 allows to resolve the large scales of turbulence in time and space, a joint LESPDF approach holds the promise to ease the modelling requirements (e.g. mixing models). In the past we have implemented a joint scalar PDF approach into LES with the amelet model using an Eulerian approach. Our preliminary results demonstrated that careful implementation of the Eulerian approach can be fully consistent with the counterpart nite-volume method. In this paper, results of recent LES of a pilot CH4/Air ame (Sandia/TUD ame D) with realistic nite-rate chemistry will be reported using three di erent mixing models including modi ed Curl (MC), Interaction by Exchange with the Mean (IEM), and Eucledian Minimum Spanning Tree (EMST). The calculations were performed with a 12-step reduced chemistry that has been well tested in RANS simulations of Sandia Flame D. In constrast to established RANS results which showed unphysical extinction with selected mixing models, LES results with di erent mixing models all lead to stable combustion and somewhat similar extinction patterns. These results suggest that the requirements of mixing models may be relaxed if large variations in scalar composition are coherently resolved as shown by our implementation of a joint LES-Eulerian PDF approach.