Weighted $\mathbb{L}^2$-Stability of the Lattice Boltzmann Method

Authors:
Michael Junk;Wen-An Yong
Affiliations:
michael.junk@uni-konstanz.de;wayong@mail.tsinghua.edu.cn
Venue:
SIAM Journal on Numerical Analysis
Year:
2009

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Abstract

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 $\mathbb{L}^2$-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.