In order to simulate accurately the interaction of shock wave/complex flows, hybrid schemes combining the compact scheme and weighted essentially non-oscillatory(WENO) schemes are beneficial, due to the high order low diffusion schemes used in smooth regions. There are two key issues for a hybrid scheme, one is how to detect the discontinuity, the other is how to implement the high order low diffusion scheme to ensure the accuracy, robustness and efficiency. In this paper, several high order schemes are used with the fifth order WENO scheme to form the hybrid schemes based on the discontinuity detector proposed by Shen and Zha(Y. Shen, G.Zha, J. Compu. Phys., 2011, 230:4419-4436). The different hybrid schemes are compared for their accuracy and convergence.