The objective of this study is to investigate the sensitivity and accuracy of the combustible flow field prediction for the LIMOUSINE combustor with regards to choices in computational mesh and turbulent combustion model. The LIMOUSINE combustor is a partially premixed bluff body stabilized natural gas combustor designed to operate at 40–80 kW and atmospheric pressure and used to study combustion instabilities. The transient simulation of a turbulent combusting flow with the purpose to study thermo-acoustic instabilities is a very time consuming process. For that reason the meshing approach leading to accurate numerical prediction, known sensitivity, and reduced amount of mesh elements is important. Since the numerical dissipation (and dispersion) is highly dependent on, and affected by, the geometrical mesh quality, it is of high importance to control the mesh distribution and element size across the numerical model. Typically, the structural mesh topology allows using much less grid elements compared to the unstructured grid, however an unstructured mesh is favorable for flows in complex geometries. To explore computational stability and accuracy, the numerical dissipation of the cold flow with mixing of fuel and air is studied first in the absence of the combustion process. Thereafter the studies are extended to combustible flows using standard available ANSYS-CFX combustion models. To validate the predicted variable fields of the combustor’s transient reactive flows, the numerical results for dynamic pressure and temperature variations, resolved under structured and unstructured mesh conditions, are compared with experimental data. The obtained results show minor dependence on the used mesh in the velocity and pressure profiles of the investigated grids under non-reacting conditions. More significant differences are observed in the mixing behavior of air and fuel flows. Here the numerical dissipation of the (unstructured) tetrahedral mesh topology is higher than in the case of the (structured) hexahedral mesh. For that reason, the combusting flow resolved with the use of the hexahedral mesh presents better agreement with experimental data and demands less computational effort. Finally in the paper the performance of the combustion model for reacting flow as a function of mesh configuration is presented, and the main issues of the applied combustion modeling are reviewed.