Third order equivalent equation of lattice Boltzmann scheme

François Dubois

doi:10.3934/dcds.2009.23.221

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2009, Volume 23, Issue 1&2: 221-248. Doi: 10.3934/dcds.2009.23.221

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Third order equivalent equation of lattice Boltzmann scheme

François Dubois^1,

1.
Numerical Analysis and Partial Differential Equations, Department of Mathematics, University Paris Sud, Bat. 425, F-91405 Orsay Cedex

Received: September 2007

Published: May 2009

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Abstract

We recall the origin of lattice Boltzmann scheme and detail the version due to D'Humières [8]. We present a formal analysisof this lattice Boltzmann scheme in terms of a single numericalinfinitesimal parameter. We derive third order equivalent partial differential equation of this scheme.Both situations of single conservation law and fluid flow with mass and momentum conservations are detailed. We apply our analysis to so-called D1Q3 and D2Q9 lattice Boltzmann schemes in one and two space dimensions.

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Mathematics Subject Classification: Primary: 65Q05, 82C20; Secondary: 76N15.

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