# American Institute of Mathematical Sciences

January & 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 analysis of this lattice Boltzmann scheme in terms of a single numerical infinitesimal 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 & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 221-248. doi: 10.3934/dcds.2009.23.221
 [1] Agnaldo José Ferrari, Tatiana Miguel Rodrigues de Souza. Rotated $A_n$-lattice codes of full diversity. Advances in Mathematics of Communications, 2020  doi: 10.3934/amc.2020118 [2] Jian Zhang, Tony T. Lee, Tong Ye, Liang Huang. An approximate mean queue length formula for queueing systems with varying service rate. Journal of Industrial & Management Optimization, 2021, 17 (1) : 185-204. doi: 10.3934/jimo.2019106 [3] Hao Wang. Uniform stability estimate for the Vlasov-Poisson-Boltzmann system. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 657-680. doi: 10.3934/dcds.2020292 [4] Mehdi Badsi. Collisional sheath solutions of a bi-species Vlasov-Poisson-Boltzmann boundary value problem. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2020052

2019 Impact Factor: 1.338