Lattice Boltzmann simulations of pressure-driven flows in microchannels using Navier–Maxwell slip boundary conditions

Tim Reis, Paul J. Dellar

Research output: Contribution to journalArticlepeer-review

41 Scopus citations


We present lattice Boltzmann simulations of rarefied flows driven by pressure drops along two-dimensional microchannels. Rarefied effects lead to non-zero cross-channel velocities, nonlinear variations in the pressure along the channel. Both effects are absent in flows driven by uniform body forces. We obtain second-order accuracy for the two components of velocity the pressure relative to asymptotic solutions of the compressible Navier-Stokes equations with slip boundary conditions. Since the common lattice Boltzmann formulations cannot capture Knudsen boundary layers, we replace the usual discrete analogs of the specular diffuse reflection conditions from continuous kinetic theory with a moment-based implementation of the first-order Navier-Maxwell slip boundary conditions that relate the tangential velocity to the strain rate at the boundary. We use these conditions to solve for the unknown distribution functions that propagate into the domain across the boundary. We achieve second-order accuracy by reformulating these conditions for the second set of distribution functions that arise in the derivation of the lattice Boltzmann method by an integration along characteristics. Our moment formalism is also valuable for analysing the existing boundary conditions. It reveals the origin of numerical slip in the bounce-back other common boundary conditions that impose conditions on the higher moments, not on the local tangential velocity itself. © 2012 American Institute of Physics.
Original languageEnglish (US)
Pages (from-to)112001
JournalPhysics of Fluids
Issue number11
StatePublished - Nov 8 2012
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: The authors thank Dr. Sam Bennett for useful conversations. The authors' research is supported by Award No. KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST); and by an Advanced Research Fellowship from the Engineering and Physical Sciences Research Council [Grant No. EP/E0546251].
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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