Axisymmetric cavity combustors are not subjected to the corner boundary-layer effects present in planar combustors, making them an attractive configuration for robust flameholding. Experiments at the University of Illinois have investigated ethylene combustion in an axisymmetric combustor using a cavity flameholder with inlet flow at Mach 4.5. Cavity flameholding was achieved for a range of fuel equivalence ratios. This paper presents preliminary results in using the Naval Research Laboratory’s discontinuous Galerkin finite element method code, JENRE®, to simulate the operation of the University of Illinois ACT-II cavity combustor facility. The overall goal of this ongoing effort is to gain further insight into combustion dynamics in an axisymmetric supersonic cavity combustor. Two and three dimensional simulations were performed using a reduced model for ethylene-air combustion. Robust, cavity-stabilized combustion was achieved and results are compared to experimental data.