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The three-dimensional Couette flow between parallel plates is addressed usingmixed lattice Boltzmann models which implement the half-range and thefull-range Gauss-Hermite quadratures on the Cartesian axes perpendicular andparallel to the walls, respectively. The ability of our models to simulaterarefied flows are validated through comparison against previously reportedresults obtained using the linearized Boltzmann-BGK equation for values of theKnudsen number (Kn) up to $100$. We find that recovering the non-linear part ofthe velocity profile (i.e., its deviation from a linear function) at ${\rm Kn}\gtrsim 1$ requires high quadrature orders. We then employ the Shakhov modelfor the collision term to obtain macroscopic profiles for Maxwell moleculesusing the standard $\mu \sim T^\omega$ law, as well as for monatomic Helium andArgon gases, modeled through ab-initio potentials, where the viscosity isrecovered using the Sutherland model. We validate our implementation bycomparison with DSMC results and find excellent match for all macroscopicquantities for ${\rm Kn} \lesssim 0.1$. At ${\rm Kn} \gtrsim 0.1$, smalldeviations can be seen in the profiles of the diagonal components of thepressure tensor, the heat flux parallel to the plates, and the velocityprofile, as well as in the values of the velocity gradient at the channelcenter. We attribute these deviations to the limited applicability of theShakhov collision model for highly out of equilibrium flows.

Half-range lattice Boltzmann models for the simulation of Couette flow using the Shakhov collision term