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Matematicheskoe modelirovanie, 2011, Volume 23, Number 2, Pages 75–95 (Mi mm3075)  

Phase volume and canonicity preservation in finite-difference gas dynamic schemes constructed with the sequential variational method

Yu. A. Bondarenko

RFNC-VNIIEF, Sarov
References:
Abstract: The paper proves that the phase volume and canonicity (Hamiltonicity) are preserved in the finite-difference schemes of Lagrangiam gas dynamics constructed using the sequential variational method with Hamilton–Ostrogradskii principle of least action, which is discrete in time and space. It has been proved that in implicit finite-difference schemes with permanent “weight” θ=1/2 (in the equations for coordinates and velocity) the phase volume and canonicity are not preserved for an arbitrary varying time step independently of the way of selecting “hidden” generalized coordinates and “hidden” generalized momenta (such difference schemes cannot be constructed using the sequential variational method).
Keywords: Lagrangian gas dynamics, principle of least action, variational difference schemes, “cross”-type difference schemes, implicit difference schemes, schemes with “weights”, variable time step, phase volume, canonicity, “hidden” variables.
Received: 22.06.2010
English version:
Mathematical Models and Computer Simulations, 2011, Volume 3, Issue 5, Pages 646–660
DOI: https://doi.org/10.1134/S2070048211050073
Bibliographic databases:
Document Type: Article
UDC: 517.9+519.6+533
Language: Russian
Citation: Yu. A. Bondarenko, “Phase volume and canonicity preservation in finite-difference gas dynamic schemes constructed with the sequential variational method”, Mat. Model., 23:2 (2011), 75–95; Math. Models Comput. Simul., 3:5 (2011), 646–660
Citation in format AMSBIB
\Bibitem{Bon11}
\by Yu.~A.~Bondarenko
\paper Phase volume and canonicity preservation in finite-difference gas dynamic schemes constructed with the sequential variational method
\jour Mat. Model.
\yr 2011
\vol 23
\issue 2
\pages 75--95
\mathnet{http://mi.mathnet.ru/mm3075}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2848799}
\transl
\jour Math. Models Comput. Simul.
\yr 2011
\vol 3
\issue 5
\pages 646--660
\crossref{https://doi.org/10.1134/S2070048211050073}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928986772}
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    Abstract page:523
    Full-text PDF :237
    References:85
    First page:10
     
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