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Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 11, Pages 1988–1997 (Mi zvmmf4967)  

This article is cited in 5 scientific papers (total in 5 papers)

Effect of the pipe curvature on internal elastic wave propagation

V. A. Rukavishnikov, O. P. Tkachenko

Computer Center, Far East Division, Russian Academy of Sciences, ul. Kim Yu Chena 65, Khabarovsk, 680000 Russia

Abstract: A mathematical model of internal elastic wave propagation in a bent pipe is developed. For slightly bent pipes, a method is devised for reducing the equations to a lower dimension problem. It is shown that the wave dynamics are described by the Korteweg-de Vries and Klein–Gordon–Fock equations. Thus, the class of problems to which these equations apply is expanded.

Key words: nonlinear waves in bent pipes, mathematical model of wave propagation, Korteweg-de Vries equation, Klein–Gordon–Fock equation, numerical method.

Full text: PDF file (234 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:11, 1886–1894

Bibliographic databases:

UDC: 519.634
Received: 25.02.2010
Revised: 25.03.2010

Citation: V. A. Rukavishnikov, O. P. Tkachenko, “Effect of the pipe curvature on internal elastic wave propagation”, Zh. Vychisl. Mat. Mat. Fiz., 50:11 (2010), 1988–1997; Comput. Math. Math. Phys., 50:11 (2010), 1886–1894

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Tkachenko O.P., “Chislennyi analiz dinamiki krivolineinogo truboprovoda”, Vychislitelnaya mekhanika sploshnykh sred = computational continuum mechanics, 5:3 (2012), 345–353  crossref  mathscinet  elib
    2. Tkachenko O., “Construction of the Mathematical Model of Complex Pipeline with Variable Geometry”, 15Th International Scientific Conference Underground Urbanisation as a Prerequisite For Sustainable Development, Procedia Engineering, 165, eds. Alpatov S., Prentkovskis O., Sterling R., Kaliampakos D., Elsevier Science BV, 2016, 1261–1274  crossref  isi  scopus
    3. Rukavishnikov V.A., Tkachenko O.P., “Numerical modeling of the fluid-filled pipelines in viscous medium”, INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2015 (ICNAAM 2015) (Rhodes, Greece, 22?28 September 2015), AIP Conference Proceedings, 1738, eds. Simos T., Tsitouras C., Amer Inst Physics, 2016, 030036  crossref  isi  scopus
    4. K. R. Aida-zade, Y. R. Ashrafova, “Numerical leak detection in a pipeline network of complex structure with unsteady flow”, Comput. Math. Math. Phys., 57:12 (2017), 1919–1934  mathnet  crossref  crossref  isi  elib
    5. Rukavishnikov V.A., Tkachenko O.P., “Dynamics of a Fluid-Filled Curvilinear Pipeline”, Appl. Math. Mech.-Engl. Ed., 39:6 (2018), 905–922  crossref  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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