Abstract

We have considered the theory of breakdown of an arbitrary gas-dynamic discontinuity for the space-time dimension equal to two. The link of this task with the geometrical theory of reconfiguration of shock-waves and wave fronts is shown. We consider the Riemann problem of the breakdown of an arbitrary discontinuity of parameters at angular collision of two flat flows. The problem is solved as accurate stated. We consider the solution region with different types of the shock-wave structure. The Mach number region is discovered and the angles of flows interaction for which there is no solution. We demonstrate the generality of solutions for one-dimensional non-stationary and two-dimensional stationary cases.

Keywords:

Computational gas dynamics, contact discontinuity, discontinuity breakdown scheme, Riemann wave, shock-wave,

References

1. Arnold, V.I., 1978. Additional Chapters of the Theory of Ordinary Differential Equation. Book for the Physical and Mathematical Students of Universities. Publishing House ‘Nauka’. Main Editorial Board of Physical and Mathematical Literature, Moscow.
   
2. Karman, T. and I. Burgers, 1939. Theoretical aerodynamics of perfect liquids, pp: 408.
   
3. Kobzeva, T. and N. Moiseev, 2003. Method of undetermined coefficients for solution of the discontinuity breakdown problem, VANT. Ser. Mathematical Modeling of Physical Processes. Scientific-and-technical Collected Articles, Issue 1.
   
4. Kotchine, N.E., 1927. Detetmination rigoureuse des ondes permanentes d'ampleur finie a la surface de separation de deux liquides de profodeur finie. Math. Ann., 98: 582-615.
   CrossRef    
5. Landau, L. and E. Lifshits, 1953. Mechanics of Continua: Hydrodynamics. Fizmatlit, Moscow, pp: 736.
   
6. Uskov, V.N., 1980. Shock-waves and their Interaction: Textbook. Mechanical Institute, Leningrad, pp: 90.
   
7. Uskov, V.N., V. Glaznev et al., 2000. Jet Streams and Non-stationary Streams in the Gas Dynamics. Publ. House SO Russian Academy of Science, Novosibirsk, pp: 200.
   
8. Zeldovich, Y., 1970. Gravitational instability: An approximation theory for large density perturbation. Astron. Astrophys., 5(1): 85-89.
   

Competing interests

The authors have no competing interests.

Open Access Policy

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Copyright

The authors have no competing interests.