A Finite-Difference Lattice Boltzmann Approach for Gas Microflows (Communications in Computational Physics, 2018)
Finite-difference Lattice Boltzmann (LB) models are proposed for simulatinggas flows in devices with microscale geometries. The models employ the roots ofhalf-range Gauss-Hermite polynomials as discrete velocities. Unlike the standard LBvelocity-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 treatmentof kinetic boundary conditions. The possibilities of the proposed LB models areillustrated by studying the one-dimensional Couette flow and the two-dimensionalsquare driven cavity flow. Numerical and analytical results show an improved accuracyin finite Knudsen flows as compared with standard LB models.