  The mass flow rate of Poiseuille flow of rarefied gas through long ducts of
two-dimensional cross-sections with arbitrary shape are critical in the
pore-network modeling of gas transport in porous media. In this paper, for the
first time, the high-order hybridizable discontinuous Galerkin (HDG) method is
used to find the steady-state solution of the linearized Bhatnagar-Gross-Krook
equation on two-dimensional triangular meshes. The velocity distribution
function and its traces are approximated in the piecewise polynomial space (of
degree up to 4) on the triangular meshes and the mesh skeletons, respectively.
By employing a numerical flux that is derived from the first-order upwind
scheme and imposing its continuity on the mesh skeletons, global systems for
unknown traces are obtained with a few coupled degrees of freedom. To achieve
fast convergence to the steady-state solution, a diffusion-type equation for
flow velocity that is asymptotic-preserving into the fluid dynamic limit is
solved by the HDG simultaneously, on the same meshes. The proposed
HDG-synthetic iterative scheme is proved to be accurate and efficient.
Specifically, for flows in the near-continuum regime, numerical simulations
have shown that, to achieve the same level of accuracy, our scheme could be
faster than the conventional iterative scheme by two orders of magnitude, while
it is faster than the synthetic iterative scheme based on the finite difference
discretization in the spatial space by one order of magnitude. The
HDG-synthetic iterative scheme is ready to be extended to simulate rarefied gas
mixtures and the Boltzmann collision operator.
