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The ability to enhance detonation wave transmission at a diffraction plane through various shock reflection/focusing conditions was evaluated numerically. The geometry dimensions were generally representative of the condition existing in a valve-less pulse detonation engine developed by the Naval Postgraduate School and consisted of a small cylindrical initiator combustor which transmitted a shock wave to a larger diameter combustor. The wall cross section of the larger combustor was varied to evaluate the increase in reflected shock temperature and pressure conditions ultimately revealing the dramatic increase in local temperature for a scalloped outer wall condition over the cylindrical cross section cases. The initiator diameter was held constant and the larger combustor diameters varied in order to evaluate the effects of diameter ratio on the shock reflection conditions for both cylindrical and scalloped geometries. A computational fluid dynamics (CFD) solver known as OVERFLOW was used to model the fluid dynamic processes but was limited in capability to shock wave Mach numbers less than about 4.2.