Advertisement

High-Gradient Method for the Solution of First Order Hyperbolic Type Systems with Partial Differential Equations

  • Vladimir V. Demchenko
Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 133)

Abstract

The effective difference method based on characteristic directions isolation and consequent approximation of partial derivatives in pre-assigned finite-dimensional space is suggested for the numerical simulation of physical processes with the strong discontinues in mechanics of continua and plasma physics.

Keywords

High-gradient method Numerical simulation Convergence 

References

  1. 1.
    Magomedov, K.M., Kholodov, A.S.: The Grid-characteristic Methods. Nauka, Moscow (1988). (in Russian)zbMATHGoogle Scholar
  2. 2.
    Belotserkovskii, O.M., Demchenko, V.V., Kosarev, V.I., Kholodov, A.S.: Numerical simulation of some problems of the laser compression of shells. Zh. Vychisl. Mat. Mat. Fiz. 18(2), 420–444 (1978). (in Russian)CrossRefGoogle Scholar
  3. 3.
    Demchenko, V.V.: An Arbitrary Gas Dynamical Discontinuity Decay. MIPT, Moscow (1998). (in Russian)Google Scholar
  4. 4.
    Demchenko, V.V., Nemchinov, I.V.: Three-dimensional gas motions by break-down at several points on circle. Fizika Gorenija i Vzryva 6, 131–134 (1990). (in Russian)Google Scholar
  5. 5.
    Aleshin, A.N., Demchenko, V.V., Zaytsev, S.G., Lazareva, E.V.: The interaction of shock waves with undulating tangential discontinuity. Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza 5, 168–174 (1992). (in Russian)Google Scholar
  6. 6.
    Demchenko, V.V.: Numerical simulation of Richtmyer-Meshkov instability. Russ. J. Comput. Mech. 1(2), 51–66 (1993)Google Scholar
  7. 7.
    Belotserkovskii, O.M., Demchenko, V.V., Oparin, A.M.: A sequential transition to turbulence in Richtmyer-Meshkov instability. Physics-Doklady 39(2), 118–120 (1994). [translated from Doklady Academii Nauk, 334(5), 581–583 (1994)]Google Scholar
  8. 8.
    Belotserkovskii, O.M., Demchenko, V.V., Oparin, A.M.: Unsteady three-dimensional numerical simulation of the Richtmyer-Meshkov instability. Physics-Doklady 42(5), 273–276 (1997). [translated from Doklady Academii Nauk 354(2), 190–193(1997)]zbMATHGoogle Scholar
  9. 9.
    Yakovlev, N.V.: the contact boundary instability of metal colliding surfaces. Fizika Gorenija i Vzryva 9(3), 447–452 (1973). (in Russian)Google Scholar
  10. 10.
    Deribas, A.A., Zakharov, V.S., Sobolenko, T.M., Teslenko, T.S.: About the surface relief transfer by the shock waves in the metals. Fizika Gorenija i Vzryva 10(5), 931–932 (1974). (in Russian)Google Scholar
  11. 11.
    Demchenko, V.V., Sergeev, M.A.: Instability of a collision surface during high-velocity impact. Fluid Dynamics 38(6), 923–932 (2003). [translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti I Gaza 6, 111–121 (2003)]CrossRefGoogle Scholar
  12. 12.
    Demchenko, V.V., Sergeev, M.A.: The gas dynamical instability during high-velocity impact. Mat. Model. 14(10), 87–94 (2002)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Moscow Institute of Physics and Technology (MIPT)DolgoprudnyRussian Federation

Personalised recommendations