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Analysis of lattice Boltzmann boundary conditions. (English) Zbl 1354.76146
Summary: The correct implementation of Navier-Stokes boundary conditions in the framework of lattice Boltzmann schemes is complicated by the non-availability of analytical methods to assess the consistency of such discretizations. To close this gap, we propose a simple direct asymptotic analysis which is readily applicable to finite difference discretizations of initial boundary value problems in general and to lattice Boltzmann methods in particular. Results of the analysis applied to the classical lattice Boltzmann scheme with bounce back boundary condition are reported.

76M28 Particle methods and lattice-gas methods
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
Full Text: DOI
[1] Bouzidi, Physics of Fluids 13 pp 3452– (2001)
[2] He, J. Stat. Phys. 88 pp 927– (1997)
[3] : Kinetic theory and .uid dynamics, Birkhäuser, 2002.
[4] : Rigorous Navier-Stokes limit of the lattice Boltzmann equation, to appear in Asymptotic Anal..
[5] : Asymptotic analysis of finite difference methods, submitted to Applied Mathematics and Computation.
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