Geodesic
Taylor expansion method for analyzing bounce-back boundary conditions for lattice Boltzmann method
François Dubois1, 2 ; Pierre Lallemand3 ; Mohamed Mahdi Tekitek4, 5
1Structural Mechanics and Coupled Systems Laboratory, CNAM Paris, France.
2Department of Mathematics, University Paris-Sud, Orsay, France.
3Beijing Computational Science Research Center, Beijing, China.
4Faculty of Sciences of Tunis, University of Tunis El Manar, Tunis, Tunisia.
5Department 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},
     year = {2015},
     volume = {52},
     doi = {10.1051/proc/201552002},
     language = {en},
     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

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