This research study investigates the effects of hydrogen enrichment on bluff-body stabilized turbulent premixed methane flames in the lean combustion regime. To this end, a premixed combustion modelling closure is proposed for RANS (Reynolds Averaged Navier-Stokes), SAS (Scale Adaptive Simulation) and LES (Large Eddy Simulation) simulations of atmospheric turbulent premixed CH4/H2/air flames. The model solves the progress variable equation, and the reaction rate source term is modelled with an algebraic closure which is a function of a turbulent flame speed. The turbulent flame speed has been derived by building on correlations in the literature, and specifically calibrated against atmospheric spherically expanding turbulent premixed CH4/H2/air flame speed measurements including stretch effects. Stretch and heat loss effects, responsible for the correct flame stabilization, are taken into account by means of tabulated laminar consumption speeds. Tabulation is done by solving one-dimensional conservation equations with a detailed chemistry approach in a fresh-to-burnt counter flow flame configuration for different strain and heat loss levels in CANTERA. The hydrogen enrichment effect is accounted for by means of an effective Lewis number incorporated into the turbulent flame speed. The model has been implemented in RANS, SAS, and LES context CFD (Computational Fluid Dynamics) simulations, and validated against atmospheric bluff body stabilized turbulent flame experiments ranging from pure methane to pure hydrogen. The performance of the model in flame dynamics predictions has been tested by extracting FTFs (Flame Transfer Functions) and UIRs (Unit Impulse Responses) from SAS and LES simulations and comparing them against those from experiments. Results indicate that the model predicts the correct flame stabilizations for RANS, SAS, and LES contexts and is capable of predicting flame dynamics.