Controllable shock wave (CWS) parameters such as amplitude, operating area and number of operations are easy to control and have received extensive attention as a potential new technology for reservoir permeability enhancement. Based on the continuous-discontinuous element method (CDEM) and considering the coupling mechanism of reservoir deformation, failure, pore seepage and fracture flow, a multiphysical field coupling model of reservoir permeability enhancement under CWS is proposed. Under the fluid-solid coupling condition, the formation and development dynamic process of reservoir fractures are obtained, and the change of reservoir permeability is also obtained. The compression fracture zone, tensile fracture zone and undamaged zone are formed around the wellbore. After repeated impact, the number of fractures is more sensitive to tectonic stress, the fracture aperture is more sensitive to reservoir strength. Different from hydraulic fracturing, a large number of fractures in different directions will appear around the main fracture after repeated impact, forming a complex fracture network similar to spider web, which may be beneficial to improve reservoir permeability. The permeability of reservoirs with different tectonic stresses and strengths increases nonlinearly and monotonicly with repeated impacts. Based on CDEM, the change of reservoir permeability with tectonic stress, strength and impact times is obtained, which is a nonlinear monotonic three-dimensional relationship. Based on that relationship, the parameters of CWS can be controlled to predict the change of reservoir permeability, such as peak pressure, duration, impact times, etc. Therefore, it can optimize the reservoir fracturing scheme and improve the reservoir fracturing efficiency, which has considerable practical significance in engineering.