Two different operating conditions of the hydrodynamic and mixing study of thermoacoustically excited rocket (HAMSTER) experiment are simulated using a LES approach. The HAMSTER experiment is a new potential validation case for combustion instability, which builds on lessons learned from previous experiments. The two operating conditions show qualitatively similar behavior and provide an excellent agreement with the experimental longitudinal mode frequency. The simulations predict a bulk mode, which is within 40 Hz of the experiment. The bulk mode amplitude is higher in the simulations compared with the experiment. Dynamic mode decomposition analysis of the bulk mode shows a nearly uniform change in the pressure of the combustor over the course of a cycle. The simulations show that fuel rich vortices impinge on the combustor wall during the cycle, this impingement coincides with the returning acoustic wave and amplification of the combustion. Periods of low amplitude oscillations are present in the simulations; these periods are shown to be a result of a periodic higher temperature recirculation region. For one of the operating conditions, the frequency of these events is correlated to the bulk mode.