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

Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jul;72(1 Pt 2):016301. doi: 10.1103/PhysRevE.72.016301. Epub 2005 Jul 6.


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.