The composition PDF transport model, like the EDC model, should be used when you are interested in simulating finite-rate chemical kinetic effects in turbulent reacting flows. With an appropriate chemical mechanism, kinetically controlled species such as CO and NOx, as well as flame extinction and ignition, can be predicted. ANSYS FLUENT has two different discretizations of the composition PDF transport equation, namely Lagrangian and Eulerian. The Lagrangian method is strictly more accurate than the Eulerian method but requires significantly longer run time to converge. Turbulent combustion is governed by the reacting Navier-Stokes equations. While this equation set is accurate, its direct solution (where all turbulent scales are resolved) is far too expensive for practical turbulent flows. In Species Transport and Finite-Rate Chemistry, the species equations are Reynolds averaged, which leads to unknown terms for the turbulent scalar flux and the mean reaction rate.
ref: ANSYS Fluent Theory Guide