  Nonequilibrium flows have been frequently encountered in various aerospace
engineering applications. To understand nonequilibrium physics, multiscale
effects, and the dynamics in these applications, an effective and reliable
multiscale scheme for all flow regimes is required. Following the direct
modeling methodology, the adaptive unified gas-kinetic scheme employs discrete
velocity space (DVS) to accurately capture the non-equilibrium physics,
recovering the original unified gas-kinetic scheme (UGKS), and adaptively
employs continuous distribution functions based on the Chapman-Enskog expansion
to achieve better efficiency. Different regions are dynamically coupled at the
cell interface through the fluxes from the discrete and continuous gas
distribution functions, thereby avoiding any buffer zone between them. In the
current study, an implicit adaptive unified gas-kinetic scheme (IAUGKS) is
constructed to further enhance the efficiency of steady-state solutions. The
current scheme employs implicit macroscopic governing equations and couples
them with implicit microscopic governing equations within the non-equilibrium
region, resulting in high convergence efficiency in all flow regimes. A series
of numerical tests were conducted for high Mach number flows around diverse
geometries such as a cylinder, a sphere, an X-38-like vehicle, and a space
station. The current scheme can capture the non-equilibrium physics and provide
accurate predictions of surface quantities. In comparison with the original
UGKS, the velocity space adaptation, unstructured DVS, and implicit iteration
significantly improve the efficiency by one or two orders of magnitude. Given
its exceptional efficiency and accuracy, the IAUGKS serves as an effective tool
for nonequilibrium flow simulations.
