The Volvo burner features the canonical configuration of a bluff-body stabilized premixed flame. This configuration was studied experimentally under the Volvo Flygmotor AB program. Two cases are considered in this study: a non-reacting case with an inlet flow speed of 16.6 m/s and a reacting case with equilibrium ratio of 0.65 and inflow speed of 17.3 m/s. The characteristic vortex shedding in the wake behind the bluff body is present in the non-reacting case, while two oscillation modes are intermittently present in the reacting case. A series of large-eddy simulations are performed on this configuration using two solvers, one using a high-resolution finite-volume (FV) scheme and the other featuring a high-order discontinuous-Galerkin (DG) discretization. The FV calculations are conducted on hexahedral meshes with three different resolution (4mm, 2mm, and 1mm). The DG calculations are performed using two different polynomial orders on the same tetrahedral mesh. For the non-reacting cases, good agreement with respect to the experimental data is achieved by both solvers at high numerical resolution. The reacting cases are calculated using a two-step global mechanism in combination with the thickened-flame model. Reasonable agreement with experiments is obtained by both solvers at higher resolution. Models for combustion-turbulence interaction are necessary for the reacting case as it contains the length scale of the flame, which is smaller than the grid resolution in all calculations. The impact of such models on the flame stability and flow/flame dynamics is the subject of future research.