Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 10, Pages 1853–1859 (Mi zvmmf4774)  

This article is cited in 2 scientific papers (total in 2 papers)

Continuous compression waves in the two-dimensional Riemann problem

A. A. Charakhch'yan

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

Abstract: The interaction between a plane shock wave in a plate and a wedge is considered within the framework of the nondissipative compressible fluid dynamic equations. The wedge is filled with a material that may differ from that of the plate. Based on the numerical solution of the original equations, self-similar solutions are obtained for several versions of the problem with an iron plate and a wedge filled with aluminum and for the interaction of a shock wave in air with a rigid wedge. The behavior of the solids at high pressures is approximately described by a two-term equation of state. In all the problems, a two-dimensional continuous compression wave develops as a wave reflected from the wedge or as a wave adjacent to the reflected shock. In contrast to a gradient catastrophe typical of one-dimensional continuous compression waves, the spatial gradient of a two-dimensional compression wave decreases over time due to the self-similarity of the solution. It is conjectured that a phenomenon opposite to the gradient catastrophe can occur in an actual flow with dissipative processes like viscosity and heat conduction. Specifically, an initial shock wave is transformed over time into a continuous compression wave of the same amplitude.

Key words: shock waves, compression waves, shock wave reflection, Riemann problem, self-similar solution, gasdynamic equations.

Full text: PDF file (1023 kB)
References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2009, 49:10, 1774–1780

Bibliographic databases:

UDC: 519.634
Received: 26.06.2008
Revised: 12.03.2009

Citation: A. A. Charakhch'yan, “Continuous compression waves in the two-dimensional Riemann problem”, Zh. Vychisl. Mat. Mat. Fiz., 49:10 (2009), 1853–1859; Comput. Math. Math. Phys., 49:10 (2009), 1774–1780

Citation in format AMSBIB
\Bibitem{Cha09}
\by A.~A.~Charakhch'yan
\paper Continuous compression waves in the two-dimensional Riemann problem
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2009
\vol 49
\issue 10
\pages 1853--1859
\mathnet{http://mi.mathnet.ru/zvmmf4774}
\transl
\jour Comput. Math. Math. Phys.
\yr 2009
\vol 49
\issue 10
\pages 1774--1780
\crossref{https://doi.org/10.1134/S096554250910011X}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000270979900011}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-76349092877}


Linking options:
  • http://mi.mathnet.ru/eng/zvmmf4774
  • http://mi.mathnet.ru/eng/zvmmf/v49/i10/p1853

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. V. V. Milyavskii, V. E. Fortov, A. A. Frolova, K. V. Khishchenko, A. A. Charakhch'yan, L. V. Shurshalov, “On the mechanism of pressure increase with increasing porosity of the media compressed in conical and cylindrical targets”, Comput. Math. Math. Phys., 50:12 (2010), 2082–2094  mathnet  crossref  adsnasa
    2. Charakhch'yan A.A., Khishchenko K.V., Fortov V.E., Frolova A.A., Milyavskiy V.V., Shurshalov L.V., “Shock compression of some porous media in conical targets: numerical study”, Shock Waves, 21:1 (2011), 35–42  crossref  adsnasa  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Number of views:
    This page:230
    Full text:110
    References:22
    First page:4

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021