Kinetic representation of fluid dynamics is essential for describing flows far beyond the Navier–Stokes regime. Existing lattice Boltzmann models suffer from discrete rotation artifacts at high Knudsen number (Kn). In this paper, we present a new approach that directly addresses this issue and...

Most of current lattice Boltzmann (LB) research is based on the single-time relaxation approximation of the continuum Boltzmann equation. In this note we present a few critical considerations on the reasons behind the success of such an approach and discuss new developments in the direction of...

We use the lattice Boltzmann method (LBM) for analysis of high and moderate Knudsen number phenomena. Simulation results are presented for microscale Couette and Poiseuille flows. The slip velocity, nonlinear pressure drop, and mass flow rate are compared with previous numerical results and/or...

We describe a general algorithmic concept for grid refinement in the lattice Boltzmann method. Unlike most of the previously known approaches, the present one is based on volumetric formulation so that conservation laws are exactly guaranteed.