Reconstruction of RDWs after being influenced by shock waves is numerically studied here. Shock waves will induce two counter-rotating detonation waves when meeting the reactants near the combustor inlet. One collides with the old RDW to fail while the other grows up to be a steady RDW by DDT. The collision produces a weak explosion wave decaying quickly. When the RDW meets the explosion products, the RDW weakens and falls behind the oblique shock wave in lack of enough reactants, causing gaps of low temperature reactants which flow out of the combustor. The gaps start from the weak detonation position and later the gaps are sewn gradually because the accelerating RDW catches up with the old detonation products by DDT while the contact surface is being formed from the outlet towards the inlet. Thus, a steady RDW is finally formed. It means RDWs are easily reconstructed after interacting with shock and RDW structure is relatively robust. During the reconstruction the RDW moves axially and the specific impulse has fluctuations as pressure changes in the combustor affect the mass flow rate. The walls of the combustor head help to form and intensify reflected compression waves which may induce explosions and new RDWs. Decreasing the areas of the walls of the combustor head by widening the injector areas will weaken compression waves, as prevents new detonation waves from being formed.