A combustion system, comprising: a combustion channel having an inlet end and an exit end and being configured to contain a combustion process comprising a transient pulse combustion event, and wherein an ignition source and a flame accelerator configured to accelerate the combustion process are disposed within the combustion channel; wherein, during operation, the inlet end of the combustion channel is supplied with fuel and oxidizer in a filling phase, wherein mass flows of the fuel and oxidizer in the filling phase are in a predominant flow direction from the inlet end toward the exit end of the combustion channel; the ignition source ignites the fuel and oxidizer to initiate the transient pulse combustion event, wherein a mass flow of combustion products resulting from the transient pulse combustion event is in the predominant flow direction and the combustion products are exhausted from the combustion channel, wherein the transient pulse combustion event yields a combustion flame front and compression wave traveling in an opposite direction to the predominant flow direction of the mass flows of the fuel, oxidizer and combustion products; and wherein the flame accelerator includes a discrete roughness element comprising an upstream flow surface and a downstream flow surface, the upstream flow surface being configured to provide a more gradual flow area contraction in the predominant flow direction and a less gradual flow area contraction in the opposite direction, the discrete roughness element thereby being configured to yield a higher pressure drop in flow in the opposite direction than the pressure drop in flow in the predominant flow direction. a combustion channel having an inlet end and an exit end and being configured to contain a combustion process comprising a transient pulse combustion event, and wherein an ignition source and a flame accelerator configured to accelerate the combustion process are disposed within the combustion channel; wherein, during operation, the inlet end of the combustion channel is supplied with fuel and oxidizer in a filling phase, wherein mass flows of the fuel and oxidizer in the filling phase are in a predominant flow direction from the inlet end toward the exit end of the combustion channel; the ignition source ignites the fuel and oxidizer to initiate the transient pulse combustion event, wherein a mass flow of combustion products resulting from the transient pulse combustion event is in the predominant flow direction and the combustion products are exhausted from the combustion channel, wherein the transient pulse combustion event yields a combustion flame front and compression wave traveling in an opposite direction to the predominant flow direction of the mass flows of the fuel, oxidizer and combustion products; and wherein the flame accelerator includes a discrete roughness element comprising an upstream flow surface and a downstream flow surface, the upstream flow surface being configured to provide a more gradual flow area contraction in the predominant flow direction and a less gradual flow area contraction in the opposite direction, the discrete roughness element thereby being configured to yield a higher pressure drop in flow in the opposite direction than the pressure drop in flow in the predominant flow direction.