The acoustic characteristics of a liquid-propellant rocket engine were studied using numerical simulations with constantfrequency excitations. The simulated geometry included a porous catalyst, a retainer, a combustion chamber and a converging-diverging nozzle. Realistic profiles of flow parameters were imposed onto the internal flow volume, which was excited by a cloud of randomly phased monopole sources at frequencies up to 20 kHz. Acoustic modes were identified using an array of virtual microphones and maps of acoustic pressure. Several types of finite element meshes and local mesh refinements were tested with the aim of identifying the most accurate and computationally efficient configuration. The results showed that quadratic interpolation is significantly more efficient than linear, but only at sufficiently high frequencies. Furthermore, polyhedral meshes were found to be both more accurate and more efficient than tetrahedral, with further gains provided by uniform refinement of the surface mesh.