Geodesic
Taylor expansion method for analyzing bounce-back boundary conditions for lattice Boltzmann method
François Dubois1, 2 ; Pierre Lallemand3 ; Mohamed Mahdi Tekitek4, 5
1 Structural Mechanics and Coupled Systems Laboratory, CNAM Paris, France.
2 Department of Mathematics, University Paris-Sud, Orsay, France.
3 Beijing Computational Science Research Center, Beijing, China.
4 Faculty of Sciences of Tunis, University of Tunis El Manar, Tunis, Tunisia.
5 Department of Mathematics, Conservatoire National des Arts et Métiers, 292, rue Saint Martin, Paris, 75003, France.
ESAIM. Proceedings, Tome 52 (2015), pp. 25-46.

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In this contribution, we propose a new method of analysis for the lattice Boltzmann scheme’s boundary conditions. We develop this approach for bounce-back with a given velocity between two mesh points. We develop a “accordion” test case for linear stationary Stokes problem with an analytic expression. Numerical experiment show a good agreement at first and second order accuracy. This study has been also applied to the computation of momentum transfer.
DOI : 10.1051/proc/201552002

François Dubois 1, 2 ; Pierre Lallemand 3 ; Mohamed Mahdi Tekitek 4, 5

1 Structural Mechanics and Coupled Systems Laboratory, CNAM Paris, France.
2 Department of Mathematics, University Paris-Sud, Orsay, France.
3 Beijing Computational Science Research Center, Beijing, China.
4 Faculty of Sciences of Tunis, University of Tunis El Manar, Tunis, Tunisia.
5 Department of Mathematics, Conservatoire National des Arts et Métiers, 292, rue Saint Martin, Paris, 75003, France. 
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     author = {Fran\c{c}ois Dubois and Pierre Lallemand and Mohamed Mahdi Tekitek},
     title = {Taylor expansion method for analyzing bounce-back boundary conditions for lattice {Boltzmann} method},
     journal = {ESAIM. Proceedings},
     pages = {25--46},
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     doi = {10.1051/proc/201552002},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201552002/}
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François Dubois; Pierre Lallemand; Mohamed Mahdi Tekitek. Taylor expansion method for analyzing bounce-back boundary conditions for lattice Boltzmann method. ESAIM. Proceedings, Tome 52 (2015), pp. 25-46. doi : 10.1051/proc/201552002. http://geodesic.mathdoc.fr/articles/10.1051/proc/201552002/

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