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P. Lallemand and L.-S. Luo, “Theory of the Lattice Boltzmann Method: Dispersion, Dissipation, Isotropy, Galilean Invariance, and Stability,” Physical Review E, Vol. 61, No. 6, 2000, pp. 6546-6562. doi:10.1103/PhysRevE.61.6546

has been cited by the following article:

• TITLE: Lattice Boltzmann Simulations in the Slip and Transition Flow Regime with the Peano Framework

  AUTHORS: Philipp Neumann, Till Rohrmann

  KEYWORDS: Lattice Boltzmann; Microflows; Knudsen Number; Channel Flow; Transition Flow; Slip Flow

  JOURNAL NAME: Open Journal of Fluid Dynamics, Vol.2 No.3, September 21, 2012

  ABSTRACT: We present simulation results of flows in the finite Knudsen range, that is in the slip and transition flow regime. Our implementations are based on the Lattice Boltzmann method and are accomplished within the Peano framework. We validate our code by solving two- and three-dimensional channel flow problems and compare our results with respective experiments from other research groups. We further apply our Lattice Boltzmann solver to the geometrical setup of a microreactor consisting of differently sized channels and a reactor chamber. Here, we apply static adaptive grids to further reduce computational costs. We further investigate the influence of using a simple BGK collision kernel in coarse grid regions which are further away from the slip boundaries. Our results are in good agreement with theory and non-adaptive simulations, demonstrating the validity and the capabilities of our adaptive simulation software for flow problems at finite Knudsen numbers.