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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2013, Volume 281, Pages 162–169
DOI: https://doi.org/10.1134/S0371968513020131
(Mi tm3462)
 

This article is cited in 9 scientific papers (total in 9 papers)

On the acceleration of shock waves and concentration of energy

A. N. Golubyatnikov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow, Russia
Full-text PDF (149 kB) Citations (9)
References:
Abstract: By a series of simple examples related to exact solutions of problems in gas dynamics and magnetohydrodynamics, possible mechanisms of acceleration of shock waves and concentration of energy are elucidated. The acceleration of a shock wave is investigated in the problem of motion of a plane piston at a constant velocity in the case when the initial density of the medium drops in the presence of constant counterpressure. It is shown that in this situation a “blow-up” regime is induced by a shock wave going to infinity in finite time even for limited work of the piston. A simple spherically symmetric solution with a converging shock wave is constructed and shown to lead to the concentration of energy. A general method for solving one-dimensional non-self-similar problems related to matching the equilibrium state to a motion with homogeneous deformation on a shock wave is discussed; this method leads to a solution in quadratures.
Received in September 2012
English version:
Proceedings of the Steklov Institute of Mathematics, 2013, Volume 281, Pages 153–160
DOI: https://doi.org/10.1134/S0081543813040135
Bibliographic databases:
Document Type: Article
UDC: 533.95
Language: Russian
Citation: A. N. Golubyatnikov, “On the acceleration of shock waves and concentration of energy”, Modern problems of mechanics, Collected papers. Dedicated to Academician Andrei Gennad'evich Kulikovskii on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 281, MAIK Nauka/Interperiodica, Moscow, 2013, 162–169; Proc. Steklov Inst. Math., 281 (2013), 153–160
Citation in format AMSBIB
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\paper On the acceleration of shock waves and concentration of energy
\inbook Modern problems of mechanics
\bookinfo Collected papers. Dedicated to Academician Andrei Gennad'evich Kulikovskii on the occasion of his 80th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2013
\vol 281
\pages 162--169
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\crossref{https://doi.org/10.1134/S0371968513020131}
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\jour Proc. Steklov Inst. Math.
\yr 2013
\vol 281
\pages 153--160
\crossref{https://doi.org/10.1134/S0081543813040135}
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Linking options:
  • https://www.mathnet.ru/eng/tm3462
  • https://doi.org/10.1134/S0371968513020131
  • https://www.mathnet.ru/eng/tm/v281/p162
  • This publication is cited in the following 9 articles:
    1. A. V. Aksenov, A. N. Golubyatnikov, “Razvitie rabot shkoly L.I. Sedova na kafedre gidromekhaniki”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2024, no. 6, 88–93  mathnet  crossref  elib
    2. A. V. Aksenov, A. N. Golubyatnikov, “Development of Studies of the School of L.I. Sedov at the Chair of Hydromechanics”, Moscow Univ. Mech. Bull., 79:6 (2024), 183  crossref
    3. A. N. Golubyatnikov, D. V. Ukrainskii, “On the Problem of Energy Concentration”, Proc. Steklov Inst. Math., 322 (2023), 77–87  mathnet  crossref  crossref
    4. A. N. Golubyatnikov, D. V. Ukrainskii, “An Exact Solution on Compression of a Cavity in a Viscous Heat-Conducting Compressible Medium”, Fluid Dyn, 57:4 (2022), 494  crossref
    5. Ukrainskii D.V., “Exact Solutions of Gas Dynamics Equations in Series in the Lagrangian Coordinate and Their Numerical Realization”, Fluid Dyn., 55:6 (2020), 858–869  crossref  mathscinet  isi
    6. S. D. Kovalevskaya, “Propagation of a shock wave across a current sheet without reflection”, Fluid Dyn., 52:4 (2017), 463–467  crossref  mathscinet  zmath  isi  scopus
    7. A. N. Golubyatnikov, S. D. Kovalevskaya, “Acceleration of weak shock waves”, Fluid Dyn., 50:5 (2015), 705–710  crossref  mathscinet  zmath  isi  elib  scopus
    8. A. N. Golubyatnikov, S. D. Kovalevskaya, “Self-similar gas motions in a gravity field”, Fluid Dyn., 49:3 (2014), 407–415  crossref  mathscinet  zmath  isi  elib  scopus
    9. A. N. Golubyatnikov, S. D. Kovalevskaya, “Shock wave acceleration in a magnetic field”, Fluid Dyn., 49:6 (2014), 844–848  crossref  zmath  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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