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Num. Meth. Prog., 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

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.

Full text: PDF file (692 kB)
UDC: 519.62
Received: 12.03.2015

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. V. Krivovichev, “Issledovanie ustoichivosti raznostnykh skhem metoda reshetochnykh uravnenii Boltsmana dlya modelirovaniya diffuzii”, Kompyuternye issledovaniya i modelirovanie, 8:3 (2016), 485–500  mathnet  crossref
  • Numerical methods and programming
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