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Numerical methods and programming, 2015, Volume 16, Issue 2, Pages 196–204 (Mi vmp532)  

This article is cited in 1 scientific paper (total in 1 paper)

Stability study of finite-difference-based lattice Boltzmann schemes with upwind differences of high order approximation

G. V. Krivovichev, S. A. Mikheev

Saint Petersburg State University
Full-text PDF (692 kB) Citations (1)
Abstract: The stability of three-level finite-difference-based lattice Boltzmann schemes of third and fourth orders of approximation with respect to spatial variables is studied. The stability analysis with respect to initial conditions is performed on the basis of a linear approximation. These studies are based on the Neumann method. It is shown that the stability of the schemes can be improved by the approximation convective terms in internal nodes of the grid stencils in use. In this case the stability domains are larger compared to the case of approximation in boundary nodes.
Keywords: lattice Boltzmann method, lattice Boltzmann schemes, stability with respect to initial conditions, Neumann method.
Received: 12.03.2015
UDC: 519.62
Language: Russian
Citation: G. V. Krivovichev, S. A. Mikheev, “Stability study of finite-difference-based lattice Boltzmann schemes with upwind differences of high order approximation”, Num. Meth. Prog., 16:2 (2015), 196–204
Citation in format AMSBIB
\Bibitem{KriMik15}
\by G.~V.~Krivovichev, S.~A.~Mikheev
\paper Stability study of finite-difference-based lattice Boltzmann schemes with upwind differences of high order approximation
\jour Num. Meth. Prog.
\yr 2015
\vol 16
\issue 2
\pages 196--204
\mathnet{http://mi.mathnet.ru/vmp532}
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  • https://www.mathnet.ru/eng/vmp/v16/i2/p196
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    Numerical methods and programming
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