Advanced numerical techniques are required to accurately analyze turbulent combustion at a minimal computational cost. In the current study, the use of automatic mesh refinement based on velocity and temperature curvatures was used. In order to speed up kinetic calculations, computational cells with similar temperatures, pressures, and composition were grouped as "zones" and kinetics were solved once per zone per time step. These techniques, previously validated for internal combustion engines, are applied to study premixed combustion in a constant-volume combustor. Innovative post-processing techniques are suggested to estimate the flame surface area and local flame thickness. Pressure, heat release, vorticity, Mach number, and normal strains on the flame were evaluated to understand the mechanisms behind flame surface area increase and wrinkling, and enhanced fuel burning rates, following interactions with shock waves. Predicted in-channel pressures are validated against experimental measurements.