Convergence to a model in sparse-Lagrangian FDF simulations

This work investigates the problem of distinguishing modelling assumptions and numerical errors in sparseLagrangian FDF (Filtered Density Function) methods. A new interpretation of sparse modelling with Curl’s mixing, which does not require an additional observation scale nor filtering, is given. The diffusion effects induced by mixing, which were previously interpreted as numerical errors, are now treated as modelling instruments. This ability of controlling numerical errors with the purpose of modelling physical quantities is one of the advantages of Lagrangian particle methods in turbulent reacting flows. The development of stochastic methods which use Lagrangian particles has been ongoing for many years, although the exact interpretation of the nature of such particles varies within the literature. Here we briefly discuss these interpretations and introduce the new term – “Pope particles” – to unify terminology used for the particle simulations of turbulent reacting flows.