  One of the central problems in the study of rarefied gas dynamics is to find
the steady-state solution of the Boltzmann equation quickly. When the Knudsen
number is large, i.e. the system is highly rarefied, the conventional iteration
scheme can lead to convergence within a few iterations. However, when the
Knudsen number is small, i.e. the flow falls in the near-continuum regime,
hundreds of thousands iterations are needed, and yet the "converged" solutions
are prone to be contaminated by accumulated error and large numerical
dissipation. Recently, based on the gas kinetic models, the implicit unified
gas kinetic scheme (UGKS) and its variants have significantly reduced the
iterations in the near-continuum flow regime, but still much higher than that
of the highly rarefied gas flows. In this paper, we put forward a general
synthetic iteration scheme (GSIS) to find the steady-state solutions of general
rarefied gas flows within dozens of iterations at any Knudsen number. As the
GSIS does not rely on the specific kinetic model/collision operator, it can be
naturally extended to quickly find converged solutions for mixture flows and
even flows involving chemical reactions. These two superior advantages are also
expected to accelerate the slow convergence in simulation of near-continuum
flows via the direct simulation Monte Carlo method and its low-variance
version.
