A non-linear time-domain simulation has been developed to study the interaction between longitudinal beam dynamics and RF stations in the LHC rings. The motivation for this tool is to determine optimal LLRF configurations, to study system sensitivity on various parameters, and to define the operational and technology limits. It will be also used to study the effect of RF station noise, impedance, and perturbations on the beam life time and longitudinal emittance. It allows the study of alternative LLRF implementations and control algorithms. The insight and experience gained from our PEP-II simulation is important for this work. In this paper we discuss properties of the simulation tool that will be helpful in analyzing the LHC RF system and its initial results. Partial verification of the model with data taken during the LHC RF station commissioning is presented.