The combustion dynamics observed in a sub-scale rocket combustor with optical access and operated with the propellant combination of liquid oxygen and methane at supercritical chamber pressures are investigated numerically. This combustion chamber shows a very intermittent behavior which is extremely difficult to simulate. Temperature and pressure measurements at the wall as well as \(\textrm{OH}^{*}\) radiation images from inside the combustor are used to validate the numerical solver. All simulations are performed with the in-house code TASCOM3D using a spatial discretization up to fifth order. The scalability of TASCOM3D is briefly discussed. It will be shown that TASCOM3D achieves high efficiencies for both weak and strong scaling. Comparison of the time-resolved data with the experiment reveals an excellent agreement concerning the frequencies of the eigenmodes of the combustion chamber. The flame characteristics are similar, too. The presented analysis additionally focuses on the methane combustion process at rocket combustor conditions.