@book{38471,
  keywords = {hydrodynamics, example, simulation, models, flow, backward-facing step, limit, navier-stokes equations},
  author = {Ansumali and Chikatamarla and Frouzakis and Karlin and Kevrekidis and Gorban and Kazantzis and Kevrekidis and Ottinger and Theodoropoulos},
  title = {Lattice Boltzmann method and kinetic theory},
  abstract = { 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{\textquoteright}s approximation is used to formulate a novel outflow boundary condition for lattice Boltzmann simulations. },
  year = {2006},
  publisher = {Springer-Verlag Berlin},
  address = {Berlin},
  isbn = {3-540-35885-4},
  language = {English},
}