# American Institute of Mathematical Sciences

February  2009, 23(1&2): 221-248. doi: 10.3934/dcds.2009.23.221

## Third order equivalent equation of lattice Boltzmann scheme

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

Received  September 2007 Published  September 2008

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.
Citation: François Dubois. Third order equivalent equation of lattice Boltzmann scheme. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 221-248. doi: 10.3934/dcds.2009.23.221
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