In this study, a single injector methane-oxygen rocket combustor is numerically studied. The simulations included in this study are based on the hardware and experimental data from the Technical University of Munich. The focus is on the recently developed generalized k–ω turbulence model (GEKO) and the effect of its adjustable coefficients on the pressure and on wall heat flux profiles, which are compared with the experimental data. It was found that the coefficients of ‘jet’, ‘near-wall’, and ‘mixing’ have a major impact, whereas the opposite can be deduced about the ‘separation’ parameter Csep, which highly influences the pressure and wall heat flux distributions due to the changes in the eddy-viscosity field. The simulation results are compared with the standard k–ε model, displaying a qualitatively and quantitatively similar behavior to the GEKO model at a Csep equal to unity. The default GEKO model shows a stable performance for three oxidizer-to-fuel ratios, enhancing the reliability of its use. The simulations are conducted using two chemical kinetic mechanisms: Zhukov and Kong and the more detailed RAMEC. The influence of the combustion model is of the same order as the influence of the turbulence model. In general, the numerical results present a good or satisfactory agreement with the experiment, and both GEKO at Csep = 1 or the standard k–ε model can be recommended for usage in the CFD simulations of rocket combustion chambers, as well as the Zhukov–Kong mechanism in conjunction with the flamelet approach.