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.

@article{LBSITSATFR12,
	author	 = {Philipp Neumann and Till Rohrmann},
	title	 = {{Lattice Boltzmann Simulations in the Slip and Transition Flow Regime with the Peano
      Framework}},
	year	 = {2012},
	editor	 = {Heuy-Dong Kim},
	publisher	 = {Scientific Research Publishing},
	journal	 = {Open Journal of Fluid Dynamics},
	series	 = {2(3)},
	pages	 = {101--110},
	issn	 = {2165-3852},
	doi	 = {http://dx.doi.org/10.4236/ojfd.2012.23010},
	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.},
}