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On the lattice Boltzmann deviatoric stress: analysis, boundary conditions, and optimal relaxation times

On the lattice Boltzmann deviatoric stress: analysis, boundary conditions, and optimal relaxation times

Reis, Timothy ORCID: 0000-0003-2671-416X (2020) On the lattice Boltzmann deviatoric stress: analysis, boundary conditions, and optimal relaxation times. SIAM Journal on Scientific Computing. ISSN 1064-8275 (Print), 1095-7197 (Online) (In Press)

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Abstract

We analytically solve the {two dimensional, nine-velocity,} lattice Boltzmann model in planar channel flow and determine its deviatoric stress tensor. The shear component of its stress takes the expected Navier-Stokes form but the tangential component contains second order in Knudsen number contributions that one finds in solutions to the Burnett equations. Boundary conditions that neglect this Burnett contribution cause spurious grid-scale oscillations in the computed stress field within the computational domain. A moment-based boundary condition which considers the non--zero deviatoric stress is analysed and shown to completely eliminate the spurious oscillations seen in solutions using other boundary conditions. The analysis offers an explanation of previously reported optimal relaxation times in terms of the recurrence relation for the tangential stress and gives them an interpretation in terms of compact finite difference schemes.

Item Type: Article
Uncontrolled Keywords: Lattice Boltzmann equation, Burnett stress, compact finite difference schemes, boundary conditions, two relaxation time models
Subjects: Q Science > QA Mathematics
Faculty / Department / Research Group: Faculty of Liberal Arts & Sciences
Faculty of Liberal Arts & Sciences > Department of Mathematical Sciences
Last Modified: 24 Jan 2020 11:27
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/26766

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