(untitled) (Communications in Computational Physics, 2019)
This paper presents an implicit discrete unified gas-kinetic scheme (DUGKS) for steady state flow simulation in all flow regimes. The DUGKS is a multi-scale finite volume method (FVM), which is able to recover accurately the Navier-Stokes solutions in the continuum regime and the free molecular transport in collisionless regime. In the transition regime, the DUGKS can present reliable solution as well due to the close coupling of particle transport and collision in the flux evaluation at a cell interface. In this paper, an implicit DUGKS is constructed with predicted iterative steps for the updating of macroscopic flow variables, then the updating of microscopic gas distribution function in a discrete 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 a large CFL number. Some numerical test cases, including the Couette flow, the lid-driven cavity flows under different Knudsen numbers and the hypersonic flow in transition flow regime around a circular cylinder, have been performed to validate the proposed IDUGKS. The computational efficiency of the IDUGKS for steady state flow computations in all flow regimes can be improved by one or two orders of magnitude in comparison with the explicit DUGKS.