  The flow regime of micro flow varies from collisionless regime to
hydrodynamic regime according to the Knudsen number. On the kinetic scale, the
dynamics of micro flow can be described by the linearized kinetic equation. In
the continuum regime, hydrodynamic equations such as linearized Navier-Stokes
equations and Euler equations can be derived from the linearized kinetic
equation by the Chapman-Enskog asymptotic analysis. In this paper, based on the
linearized kinetic equation we are going to propose a unified gas kinetic
scheme scheme (UGKS) for micro flow simulation, which is an effective
multiscale scheme in the whole micro flow regime. The important methodology of
UGKS is the following. Firstly, the evolution of microscopic distribution
function is coupled with the evolution of macroscopic flow quantities.
Secondly, the numerical flux of UGKS is constructed based on the integral
solution of kinetic equation, which provides a genuinely multiscale and
multidimensional numerical flux. The UGKS recovers the linear kinetic solution
in the rarefied regime, and converges to the linear hydrodynamic solution in
the continuum regime. An outstanding feature of UGKS is its capability of
capturing the accurate viscous solution even when the cell size is much larger
than the kinetic kinetic length scale, such as the capturing of the viscous
boundary layer with a cell size ten times larger than the particle mean free
path. Such a multiscale property is called unified preserving (UP) which has
been studied in \cite{guo2019unified}. In this paper, we are also going to give
a mathematical proof for the UP property of UGKS.
