  This paper describes the numerical simulation of the NASA Langley Research
Center supersonic H2 -Air combustion chamber performed using two approaches to
model the presumed probability density function (PDF) in the flamelet progress
variable (FPV) framework. The first one is a standard FPV model, built
presuming the functional shape of the PDFs of the mixture fraction, Z, and of
the progress parameter, {\Lambda}. In order to enhance the prediction
capabilities of such a model in high-speed reacting flows, a second approach is
proposed employing the statistically most likely distribution (SMLD) techcnique
to presume the joint PDF of Z and {\Lambda}, without any assumption about their
behaviour. The standard and FPV-SMLD models have been developed using the low
Mach number assumption. In both cases, the temperature is evaluated by solving
the total-energy conservation equation, providing a more suitable approach for
the simulation of supersonic combustion. By comparison with experimental data,
the proposed SMLD model is shown to provide a clear improvement with respect to
the standard FPV model, especially in the auto-ignition and stabilization
regions of the flame.
