  This paper provides an improved flamelet/progress variable (FPV) model for
the simulation of turbulent combustion, employing the statistically most likely
distribution (SMLD) approach for the joint probability density function (PDF)
of the mixture fraction, Z, and of the progress parameter, {\Lambda} .
Steady-state FPV models are built presuming the func- tional shape of the joint
PDF of Z and {\Lambda} in order to evaluate Favre-averages of thermody- namic
quantities. The mixture fraction is widely assumed to behave as a passive
scalar with a mono-modal behaviour modelled by a \b{eta} -distribution.
Moreover, under the hypothesis that Z and {\Lambda} are statistically
independent, the joint PDF coincides with the product of the two marginal PDFs.
In this work we discuss these two constitutive hypotheses. The proposed model
evaluates the most probable joint distribution of Z and {\Lambda} , relaxing
some crucial as- sumption on their statistical behaviour. This provides a more
general model in the context of FPV approach and an effective tool to verify
the adequateness of widely used hypotheses. The model is validated versus
experimental data of well-known test cases, namely, the San- dia flames. The
results are also compared with those obtained by the standard FPV approach,
analysing the role of the PDF functional form on turbulent combustion
simulations.
