Lagrangian particles with mixing. II. Sparse-Lagrangian methods in application for turbulent reacting flows

Both parts of this work present a more detailed and specific analysis of ideas introduced in the previously published letter [Phys. Fluids 19, 031702 (2007)]. In Paper I [Phys. Fluids 19, 065101 (2009)], we show that the continuous scalar transport and diffusion can be accurately specified by means of mixing between randomly walking Lagrangian particles with scalar properties. Here, in Paper II, we deal with the situation where the number of particles is not sufficient to resolve all scales in turbulent flows and Lagrangian particles with mixing become an approximate model rather than a stochastic framework for solving exact scalar transport equations. We consider sparse-Lagrangian methods that use relatively small numbers of particles compared to the number of Eulerian grid points and discuss similarities and differences with conventional large eddy simulations-filtered density function (LES-FDF) methods. Special attention is paid to multiple mapping conditioning (MMC) formulation for sparse-Lagrangian simulations. Physical and simulated equations for joint FDFs of reactive scalars are compared and analyzed. The efficiency of the MMC-LES approach that was demonstrated in several recent publications is explained from a methodological perspective.