In LES the chemical source term depends on the unresolved, sub-filter fluctuations of temperature and composition. A transported filtered density function (FDF) closes this term exactly, but solving for it directly is expensive.
ESF represents the FDF with a small ensemble of stochastic fields. Each field is a full set of species and enthalpy, solved on the same LES grid as an ordinary transport equation with an added stochastic (Wiener) term and a micromixing term. Averaging over the fields gives the filtered composition and its fluctuations, while the reaction rates are evaluated exactly in each field.
Because everything stays on the Eulerian mesh, ESF fits naturally into a finite-volume code, handles complex combustor geometries, and parallelizes like the flow solver itself.