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Weighted L2 Stability of the Lattice Boltzmann Method

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2009

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Yong, Wen-An

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http://nbn-resolving.de/urn:nbn:de:bsz:352-opus-106443
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https://doi.org/10.1137/060675216
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SIAM Journal on Numerical Analysis. 2009, 47(3), pp. 1651-1665. Available under: doi: 10.1137/060675216

Zusammenfassung

This article is concerned with the linearized stability of the lattice Boltzmann method both on periodic domains and on bounded domains with the bounce-back rule used at the boundaries. Under a structural hypothesis, we prove that a weighted L2-norm of the solutions to the linearized lattice Boltzmann method is decreasing with time. Moreover, we show that the structural hypothesis holds true for many lattice Boltzmann models.

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Fachgebiet (DDC)
510 Mathematik

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lattice Boltzmann method, bounce-back rule, stability analysis, weighted L2-estimate

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ISO 690JUNK, Michael, Wen-An YONG, 2009. Weighted L2 Stability of the Lattice Boltzmann Method. In: SIAM Journal on Numerical Analysis. 2009, 47(3), pp. 1651-1665. Available under: doi: 10.1137/060675216
BibTex
@article{Junk2009Weigh-834,
  year={2009},
  doi={10.1137/060675216},
  title={Weighted L2 Stability of the Lattice Boltzmann Method},
  number={3},
  volume={47},
  journal={SIAM Journal on Numerical Analysis},
  pages={1651--1665},
  author={Junk, Michael and Yong, Wen-An}
}
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