The Faver-average N-S equations are solved by using Beam-warning approximate factorization method combined with k-ε model and a high-order compact-difference scheme for the micro-jet actuator external flowfield,, at the same time, numerical simulation is performed to the compressible, two dimensional, time-dependent and viscous flowfield. Newton-like subiterations within each physical time step are employed to achieve temporal accuracy, remove factorization errors and reduce errors caused by linearization and the low spatial order of accuracy of the implicit operator. The implicit high-order compact-difference has high accuracy and good robustness. The algorithm demonstrates high accuracy compared to both second-order and upwind-biased methods. For several cases, particularly very low-Mach number flows, filtering is a superior alternative to damping. The calculating results tally with the experimental results.