A series of large eddy simulations of the Volvo bluff-body stabilized combustion experiment are performed with a high-order, unstructured-grid, finite-volume solver. Standard subgrid-scale models are used, along with a two-step global kinetics model for the premixed propane-air reactions. A conserved scalar is solved in conjuction with the conservation equations to represent the ignition delay; its source term is set to represent the experimentally-measured ignition delay time for propane-air combustion. When the ignition delay scalar reaches a critical value, the global model is activated. No other subgrid-scale chemistry-turbulence interaction models are used. Four different grids are used, ranging in size from 0.3 to 58.6 million elements. The simulations are conducted with a sixth-order accurate numerical flux function and a novel method for limiting species mass fraction excursions. It is found that the non-reacting simulations agree very well with the experimental data and show grid convergence between the coarse and medium grids. The reacting simulations are more sensitive to the grid resolution, and show variations between the grids even at the highest resolution. The present results agree with previous simulations, and generally agree with the experimental trends.