  The recently-developed general synthetic iterative scheme (GSIS) is efficient
in simulating multiscale rarefied gas flows due to the coupling of mesoscopic
kinetic equation and macroscopic synthetic equation: for linearized Poiseuille
flow where the boundary flux is fixed at each iterative step, the steady-state
solutions are found within dozens of iterations in solving the gas kinetic
equations, while for general nonlinear flows the iteration number is increased
by about one order of magnitude, caused by the incompatible treatment of the
boundary flux for the macroscopic synthetic equation. In this paper, we propose
a generalized boundary treatment (GBT) to further accelerate the convergence of
GSIS. The main idea is, the truncated velocity distribution function at the
boundary, similar to that used in the Grad 13-moment equation, is reconstructed
by the macroscopic conserved quantities from the synthetic equation, and the
high-order correction of non-equilibrium stress and heat flux from the kinetic
equation; therefore, in each inner iteration solving the synthetic equation,
the explicit constitutive relations facilitate real-time updates of the
macroscopic boundary flux, driving faster information exchange in the flow
field, and consequently achieving quicker convergence. Moreover, the high-order
correction derived from the kinetic equation can compensate the approximation
by the truncation and ensure the boundary accuracy. The accuracy of GSIS-GBT is
validated by the direct simulation Monte Carlo method, the previous versions of
GSIS, and the unified gas-kinetic wave-particle method. For the efficiency, in
the near-continuum flow regime and slip regime, GSIS-GBT can be faster than the
conventional iteration scheme in the discrete velocity method and the previous
versions of GSIS by two- and one-order of magnitude, respectively.
