  This paper presents an implicit method for the discrete unified gas-kinetic
scheme (DUGKS) to speed up the simulations of the steady flows in all flow
regimes. The DUGKS is a multi-scale scheme finite volume method (FVM) for all
flow regimes because of its ability in recovering the Navier-Stokes solution in
the continuum regime and the free transport mechanism in rarefied flow, which
couples particle transport and collision in the flux evaluation at cell
interfaces. In this paper the predicted iterations are constructed to update
the macroscopic variables and the gas distribution functions in discrete
microscopic velocity space. The lower-upper symmetric Gauss-Seidel (LU-SGS)
factorization is applied to solve the implicit equations. The fast convergence
of implicit discrete unified gas-kinetic scheme (IDUGKS) can be achieved
through the adoption of a numerical time step with large CFL number. Some
numerical test cases, including the Couette flow, the lid-driven cavity flows
under different Knudsen number and the hypersonic flow in transition flow
regime around a circular cylinder, have been performed to validate this
proposed IDUGKS. The computational efficiency of the IDUGKS to simulate the
steady flows in all flow regimes can be improved by one or two orders of
magnitude in comparison with the explicit DUGKS.
