Advertisement

Numerical Simulation of Shock Wave Diffraction on the Sphere in the Shock Tube

  • Sergey N. Martyushov
  • Yanina G. Martyushova
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5434)

Abstract

In non-stationary problems of flows, for example problem of shock wave diffraction on a flying body, the impulse of appearing drag force generates non-stationary forward and rotary movement of the body. The describing mathematical model is nonlinear not only with respect to coefficients of system of the equations, but also in the sense of dependence of the system of equations and boundary conditions from integral characteristics of the decision (drag force and its moment relative to the center of mass of the body). The purpose of this work is realization of computing aspects of numerical simulation of such problems by modern numerical algorithms on the example of model problem of shock wave diffraction on sphere in the shock tube. The problem was numerically simulated on the basis of the difference scheme of second order accuracy [1,2]. The 3-D structured grids construction was performed by algorithm based on the Poisson equations decision [5,6].

Keywords

Shock Wave Drag Force Shock Tube Total Variation Diminishing Rear Stagnation Point 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Yee, H.C., Warming, R.E., Harten, A.: Implicit Total Variation Diminishing (TVD) Schemes for Steady-State Calculation. J. Comp. Phys. 57, 327–361 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Martyushov, S.N.: Calculation of two non stationary problems of diffraction by explicit algorithm of second order of accuracy. Comp. Technol., Novosibirsk. 1(4), 82–89 (1996)zbMATHGoogle Scholar
  3. 3.
    Vinokur, M.: An Analysis of Finite-Difference and Finite-Volume Formulations of Conservation Lows. J. Comp. Phys. 81, 1–51 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Il’in, S.A., Timofeev, E.V.: Comparison of quasi monotony difference scheme. N 2 FTI Ioffe Institute publishing, St. Petersburg. 1550 (1991)Google Scholar
  5. 5.
    Thompson, J.F., Warsi, Z.U.A., Mastin, C.W.: Numerical Grid Generation, p. 306. North Holland, NY (1985)zbMATHGoogle Scholar
  6. 6.
    Martyushov, S.N.: Numerical grid generation in computational field simulation. In: Proceedings of the 6-th International Conf. Greenwich Great Britain, p. 249 (1998)Google Scholar
  7. 7.
    Tanno, H., Itoh, K., Saito, T., Abe, A., Tokayama, K.: Interaction of a shock wave with a sphere suspended in vertical shock tube. Shock Waves 13, 249 (2003)CrossRefGoogle Scholar
  8. 8.
    Sun, M., Saito, T., Tokayama, K., Tanno, H.: Unsteady drag on a sphere by shock wave loading. Shock Waves 14, 3 (2005)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Sergey N. Martyushov
    • 1
  • Yanina G. Martyushova
    • 1
  1. 1.State Duma of Russian Federation, Moscow, Russia, Moskovsky Aviacionny Institute-Technical UniversityMoscowRussia

Personalised recommendations