  In this paper, we employ the lattice Boltzmann method to solve the Boltzmann
equation with the Shakhov model for the collision integral in the context of
the 3D planar Couette flow. The half-range Gauss-Hermite quadrature is used to
account for the wall-induced discontinuity in the distribution function. The
lattice Boltzmann simulation results are compared with direct simulation Monte
Carlo (DSMC) results for ${}^3{\rm He}$ and ${}^4{\rm He}$ atoms interacting
via ab initio potentials, at various values of the rarefaction parameter
$\delta$, where the temperature of the plates varies from $1\ {\rm K}$ up to
$3000\ {\rm K}$. Good agreement is observed between the results obtained using
the Shakhov model and the DSMC data at large values of the rarefaction
parameter. The agreement deteriorates as the rarefaction parameter is
decreased, however we highlight that the relative errors in the non-diagonal
component of the shear stress do not exceed $2.5\%$.
