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

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

Reis, Tim ORCID: 0000-0003-2671-416X and Dellar, Paul J. (2012) Lattice Boltzmann simulations of pressure-driven flows in microchannels using Navier-Maxwell slip boundary conditions. Physics of Fluids, 24:112001. ISSN 1070-6631 (Print), 1089-7666 (Online) (doi:https://doi.org/10.1063/1.4764514)

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Abstract

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, and 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 and 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 and 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 and other common boundary conditions that impose conditions on the higher moments, not on the local tangential velocity itself.

Item Type: Article
Uncontrolled Keywords: lattice Boltzmann, slip flow, moment-based boundary conditions
Subjects: Q Science > QA Mathematics
Faculty / Department / Research Group: Faculty of Architecture, Computing & Humanities
Faculty of Architecture, Computing & Humanities > Department of Mathematical Sciences
Last Modified: 14 Apr 2019 00:51
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
Selected for GREAT 2019: None
URI: http://gala.gre.ac.uk/id/eprint/23344

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