Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
General information
Latest issue
Impact factor

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Zh. Vychisl. Mat. Mat. Fiz.:

Personal entry:
Save password
Forgotten password?

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
\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
\jour Comput. Math. Math. Phys.
\yr 2009
\vol 49
\issue 10
\pages 1774--1780

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
    First page:4

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