Abstract: A general discretization of Boltzmann-Shakhov model equation along the characteristic line is obtained, where the time integration of collision term is handled as a weighted average between the implicit and explicit part. Moreover, the value of weight factor depends on the local Knudsen number, which represents the local flow regime and scale. With the aid of this weight factor, a scale adaptive discrete unified gas kinetic scheme (SADUGKS) has been developed as an improvement of the existing discrete unified gas kinetic scheme (DUGKS). Some typical compressible flows in different flow regimes are numerically simulated to demonstrate the validity and the property of scale adaption of SADUGKS. It turns out that the present SADUGKS is a valid numerical method for multiscale flow problems.