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

Authors:
Michael Junk;Zhaoxia Yang
Affiliations:
FB Mathematik und Statistik, Universität Konstanz, Postfach D194, 78457 Konstanz, Germany;FB Mathematik und Statistik, Universität Konstanz, Postfach D194, 78457 Konstanz, Germany
Venue:
Computers & Mathematics with Applications
Year:
2008

Citing 6
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Abstract

Combining an asymptotic analysis of the lattice Boltzmann method [M. Junk, Z. Yang, Asymptotic analysis of lattice Boltzmann boundary conditions, J. Stat. Phys. 121 (2005) 3-35] with the stability estimate presented in [M. Junk, W.-A. Yong, Weighted L^2 stability of the lattice Boltzmann equation, Preprint], we are able to prove some strict convergence results. The proof applies to the lattice Boltzmann method with linear collision operator both in the case of periodic domains and bounded domains if the Dirichlet boundary condition is realized with the bounce back rule.