Rapidly decorrelating velocity-field model as a tool for solving one-point Fokker-Planck equations for probability density functions of turbulent reactive scalars

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Abstract
Light is shed upon Eulerian Monte Carlo methods and their application to the simulation of turbulent reactive flows. A rapid decorrelating velocity-field model is used to derive stochastic partial differential equations (SPDE’s) stochastically equivalent to the modeled one-point joint probability density function of turbulent reactive scalars. Those SPDE’s are shown to be hyperbolic, advection-reaction equations. They are dealt with in a generalized sense, so that discontinuities in the scalar fields can be treated. A numerical analysis is proposed and numerical tests are carried out. In particular, a comparison with the Lagrangian Monte Carlo method is performed.