The Features of the Solutions of Continuum Mechanics Problems

  • Sergey P. Kiselev
  • Evgenii V. Vorozhtsov
  • Vasily M. Fomin
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


In this chapter, we consider the similarity and dimensional methods, including the construction of self-similar solutions. We also present the theory of weak discontinuities (the characteristics) and strong discontinuities (shock waves and tangential discontinuities).


Shock Wave Cauchy Problem Strouhal Number Discontinuity Surface Tangential Discontinuity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Sedov, L.I.Similarity and Dimensional Methods in Mechanics(in Russian), Ninth Edition, Nauka, Moscow, 1987 [English translation made by A.G. Volkovets: Sedov, L.I.Similarity and Dimensional Methods in Mechanics, CRC Press, Boca Raton, 1993].Google Scholar
  2. 2.
    Birkhoff, G.Hydrodynamics. A Study in Logic Fact and SimilitudePrinceton University Press, Princeton, 1960.zbMATHGoogle Scholar
  3. 3.
    Ovsyannikov, L.V.Lectures on the Fundamentals of Gas Dynamics(in Russian), Nauka, Moscow, 1981.zbMATHGoogle Scholar
  4. 4.
    Landau, L.D. and Lifschitz, E.M.Hydrodynamics(in Russian), Nauka, Moscow, 1986.Google Scholar
  5. 5.
    Smirnov, V.I.A Course of Higher Mathematics Vol. IVBirkhäuser Verlag, Basel and Stuttgart, 1961.Google Scholar
  6. 6.
    Chorin, A.J. and Marsden, J.E.Mathematical Introduction to Fluid Mechanics.Second Edition, Springer-Verlag, New York, 1990.CrossRefGoogle Scholar
  7. 7.
    Godunov, S.K.Equations of the Mathematical Physics(in Russian), Nauka, Moscow, 1979.Google Scholar
  8. 8.
    Rozdestvenskii, B.L. and Janenko, N.N.Systems of Quasi-linear Equations and Their Applications to Gas Dynamics.Second Edition (in Russian), Nauka, Moscow, 1978. English transl.: Systems of Quasilinear Equations and Their Applications to Gas Dynamics, Translations of Mathematical Monographs, Vol. 55, American Mathematical Society, Providence, Rhode Island, 1983.Google Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Sergey P. Kiselev
    • 1
  • Evgenii V. Vorozhtsov
    • 1
  • Vasily M. Fomin
    • 1
  1. 1.Institute of Theoretical and Applied MechanicsRussian Academy of SciencesNovosibirskRussia

Personalised recommendations