  The numerical simulation of rarefied gas mixtures with disparate mass and
concentration is a huge research challenge. Based on our recent kinetic
modelling for monatomic gas mixture flows, this problem is tackled by the
general synthetic iterative scheme (GSIS), where the mesoscopic kinetic and
macroscopic synthetic equations are alternately solved by the finite-volume
discrete velocity method. Three important features of GSIS are highlighted.
First, the synthetic equations are precisely derived from the kinetic equation,
naturally reducing to the Navier-Stokes equations in the continuum flow regime;
in other flow regimes, the kinetic equation provides high-order closure of the
constitutive relations to capture the rarefaction effects. Second, these
synthetic equations, which can be solved quickly, help to adjust the kinetic
system to relax rapidly toward the steady state. Furthermore, in such a two-way
coupling, the constraint on the spatial cell size is relieved. Third, the
linear Fourier stability analysis demonstrates that the error decay rate in
GSIS is smaller than 0.5 for various combinations of mass, concentration and
viscosity ratios, such that the error can be reduced by three orders of
magnitude after 10 iterations. The efficiency and accuracy of GSIS are
demonstrated through several challenging cases covering a wide range of mass
ratio, species concentration, and flow speed.
