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Convergence of lattice Boltzmann methods for Navier–Stokes flows in periodic and bounded domains

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Abstract

Combining an asymptotic analysis of the lattice Boltzmann method with a stability estimate, we are able to prove some convergence results which establish a strict relation to the incompressible Navier–Stokes equation. The proof applies to the lattice Boltzmann method in the case of periodic domains and for specific bounded domains if the Dirichlet boundary condition is realized with the bounce back rule.

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Authors and Affiliations

  1. FB Mathematik und Statistik, Universität Konstanz, 78457, Konstanz, Germany

    Michael Junk & Zhaoxia Yang

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  1. Michael Junk
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  2. Zhaoxia Yang
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Correspondence to Michael Junk.

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Junk, M., Yang, Z. Convergence of lattice Boltzmann methods for Navier–Stokes flows in periodic and bounded domains. Numer. Math. 112, 65–87 (2009). https://doi.org/10.1007/s00211-008-0196-0

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  • DOI: https://doi.org/10.1007/s00211-008-0196-0

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