This article presents a simulation of a model rocket combustor with continuously variable acoustic properties thanks to a variable-length injector tube. Fully compressible Large-Eddy Simulations are conducted using the AVBP code. An original flame stabilization mechanism is uncovered where the recirculation of hot gases in the corner recirculation zone creates a triple flame structure. An unstable operating point is then chosen to investigate the mech- anism of the instability. The simulations are compared to experimental results in terms of frequency and mode structure. Two-dimensional axi-symmetric computations are com- pared to full 3D simulations in order to assess the validity of the axi-symmetry assumption for the prediction of mean and unsteady features of this flow. Despite the inaccuracies in- herent to the 2D description of a turbulent flow, for this configuration and the particular operating point investigated, the axi-symmetric simulation qualitatively reproduces some features of the instability.