Application of mixed quadrature lattice Boltzmann models for the simulation of Poiseuille flow at non-negligible values of the Knudsen number

We consider the 2D force-driven Poiseuille flow between parallel plates, on which diffuse reflection boundary conditions apply. We present a systematic procedure for the construction of the force term in lattice Boltzmann models based on mixed Cartesian quadratures, where the quadrature on each axis is selected independently. We find that, at non-negligible value of the Knudsen number, half-range quadratures outperform the full-range Gauss-Hermite quadratures for the direction perpendicular to the diffuse-reflecting plates, while the quadrature on the periodic direction along the flow is the full-range Gauss-Hermite quadrature. Our results are validated against numerical results available in the literature.