  Finite-difference Lattice Boltzmann (LB) models are proposed for simulating
gas flows in devices with microscale geometries. The models employ the roots of
half-range Gauss-Hermite polynomials as discrete velocities. Unlike the
standard LB velocity-space discretizations based on the roots of full-range
Hermite polynomials, using the nodes of a quadrature defined in the half-space
permits a consistent treatment of kinetic boundary conditions. The
possibilities of the proposed LB models are illustrated by studying the
one-dimensional Couette flow and the two-dimensional driven cavity flow.
Numerical and analytical results show an improved accuracy in finite Knudsen
flows as compared with standard LB models.
