  This paper provides an extension of the standard flamelet progress variable
(FPV) approach for turbulent combustion, applying the statistically most likely
distribution (SMLD) framework to the joint PDF of the mixture fraction, Z, and
the progress variable, C. In this way one does not need to make any assumption
about the statistical correlation between Z and C and about the behaviour of
the mixture fraction, as required in previous FPV models. In fact, for
state-of-the-art models, with the assumption of very-fast-chemistry,Z is widely
accepted to behave as a passive scalar characterized by a $\beta$-distribution
function. Instead, the model proposed here, evaluates the most probable joint
distribution of Z and C without any assumption on their behaviour and provides
an effective tool to verify the adequateness of widely used hypotheses, such as
their statistical independence. The model is validated versus three well-known
test cases, namely, the Sandia flames. The results are compared with those
obtained by the standard FPV approach, analysing the role of the PDF functional
form on turbulent combustion simulations.
