Lattice boltzmann method and kinetic theory

One of the classical questions of non-equilibrium thermodynamics is the validity of various closure approximations in nontrivial flows. We study this question for a lid-driven cavity flow using a minimal molecular model derived from the Boltzmann equation. In this nontrivial flow, we quantify the model as a superset of the Grad moment approximation and visualize the quality of the Chapman-Enskog and Grad closure approximations. It is found that the Grad closure approximation is strikingly more robust than the Chapman-Enskog approximation at all Knudsen numbers studied. Grad's approximation is used to formulate a novel outflow boundary condition for lattice Boltzmann simulations.