This work attempts to develop a generalized flamelet progress variable (FPV) method in conjunction with the Reynolds-averaged Navier–Stokes (RANS) approach, employing nonpremixed and premixed-based chemistry tabulation in the OpenFOAM platform. For this, a normalized progress variable was used for the parameterisation of reactive scalers, and a new transport equation for the normalized progress variable was solved. The additional source term resulting from the normalization of the progress variable C, representing the contribution of the nonpremixed combustion mode, was modeled and implemented in the OpenFOAM solver. A turbulent bluff-body stabilized CH4–H2 flame was selected to validate the coupling process. A presumed probability density function (PDF) approach was employed to obtain the mean reactive scalars as a function of mixture fraction, mixture fraction (Z), variance of mixture fraction ( \(\tilde{Z}^{{\prime\prime 2}}\) ), and normalized progress variable (Cn) using both premixed and nonpremixed tabulation techniques. In both approaches, the PDFs of Z and Cn were modeled using beta-PDF and delta function distribution, respectively. The modified k−ε model was employed for turbulence modeling. The predicted mean temperature and H2O mass fraction fields obtained by premixed and nonpremixed tabulation approaches were compared against the experimental values. It was observed that the FPV formulation with both the premixed and nonpremixed tabulated libraries exhibited reasonable predictions compared to the experiments. Further, an artificial neural network (ANN) was coupled with the standard FPV approach to handle the high memory requirements of the FPV. Thus, 32 species and temperatures were trained in an ANN model and coupled with OpenFOAM, while the reaction rate was obtained from the flamelet library. The ANN-predicted data reasonably validated data obtained from the standard FPV approach and thus replaced the FPV flamelet library for the trained variables. The mean reactive variables computed by this combined ANN-FPV approach were in reasonable agreement with the results of the standard FPV approach. A significant memory saving of 99.85% was achieved using the ANN-FPV approach compared to the standard FPV approach.