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Numerical methods and programming, 2013, Volume 14, Issue 1, Pages 175–182 (Mi vmp104)  

This article is cited in 2 scientific papers (total in 2 papers)

Вычислительные методы и приложения

Stability analysis of the lattice Boltzmann schemes for solving the diffusion equation

G. V. Krivovichev

St. Petersburg State University, Faculty of Applied Mathematics and Control Processes
Full-text PDF (364 kB) Citations (2)
Abstract: The one-parameter families of lattice Boltzmann schemes for solving the linear diffusion equation in the cases of D2Q5, D2Q7 and D2Q9 velocity sets are considered. The comparison of various schemes proposed in previous studies is performed. The stability analysis of schemes is performed in the space of parameters. The stability with respect to initial conditions is studied by the von Neumann method. The optimal parameter values for which the absolute values of the largest-in-magnitude eigenvalues of the transition matrix are minimal are found.
Keywords: lattice Boltzmann method; linear diffusion equation; stability with respect to initial conditions; von Neumann method.
Received: 11.03.2013
Document Type: Article
UDC: 519.62+517.958:536.2
Language: Russian
Citation: G. V. Krivovichev, “Stability analysis of the lattice Boltzmann schemes for solving the diffusion equation”, Num. Meth. Prog., 14:1 (2013), 175–182
Citation in format AMSBIB
\Bibitem{Kri13}
\by G.~V.~Krivovichev
\paper Stability analysis of the lattice Boltzmann schemes for solving the diffusion equation
\jour Num. Meth. Prog.
\yr 2013
\vol 14
\issue 1
\pages 175--182
\mathnet{http://mi.mathnet.ru/vmp104}
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  • https://www.mathnet.ru/eng/vmp/v14/i1/p175
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Numerical methods and programming
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