  In this work, we have theoretically analyzed and numerically evaluated the
accuracy of high-order lattice Boltzmann (LB) models for capturing
non-equilibrium effects in rarefied gas flows. In the incompressible limit, the
LB equation is proved to be equivalent to the linearized Bhatnagar-Gross-Krook
(BGK) equation. Therefore, when the same Gauss-Hermite quadrature is used, LB
method closely assembles the discrete velocity method (DVM). In addition, the
order of Hermite expansion for the equilibrium distribution function is found
not to be correlated with the approximation order in terms of the Knudsen
number to the BGK equation, which was previously suggested by
\cite{2006JFM...550..413S}. Furthermore, we have numerically evaluated the LB
models for a standing-shear-wave problem, which is designed specifically for
assessing model accuracy by excluding the influence of gas molecule/surface
interactions at wall boundaries. The numerical simulation results confirm that
the high-order terms in the discrete equilibrium distribution function play a
negligible role. Meanwhile, appropriate Gauss-Hermite quadrature has the most
significant effect on whether LB models can describe the essential flow physics
of rarefied gas accurately. For the same order of the Gauss-Hermite quadrature,
the exact abscissae will also modestly influence numerical accuracy. Using the
same Gauss-Hermite quadrature, the numerical results of both LB and DVM methods
are in excellent agreement for flows across a broad range of the Knudsen
numbers, which confirms that the LB simulation is similar to the DVM process.
Therefore, LB method can offer flexible models suitable for simulating
continuum flows at Navier Stokes level and rarefied gas flows at the linearized
Boltzmann equation level.
