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Method for describing the steady-state reaction front in a two-dimensional flow

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Abstract

It has been shown that the complete system of hydrodynamic equations describing the position of the steady-state reaction front in a two-dimensional incompressible flow can be reduced to a closed system of surface equations using the method for reducing the dimension in overdetermined systems of differential equations. This system of surface equations allows the determination of the position of the steady-state front and all other quantities characterizing a hydrodynamic flow through it.

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References

  1. Ya. B. Zeldovich, Ya. B. Barenblat, V. B. Librovich, et al., Mathematical Theory of Combustion and Explosion (Nauka, Moscow, 1980; Plenum, New York, 1985).

    Google Scholar 

  2. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 6: Fluid Mechanics (Nauka, Moscow, 1986; Pergamon, New York, 1987).

    Google Scholar 

  3. F. A. Williams, Combustion Theory (Addison-Wesley, Redwood City, CA, 1985).

    Google Scholar 

  4. C. K. Law, Combustion Physics (Cambridge Univ., New York, 2006).

    Book  Google Scholar 

  5. G. I. Sivashinsky, Acta Astronaut. 4, 1177 (1977).

    Article  MATH  MathSciNet  Google Scholar 

  6. P. Pelce and P. Clavin, J. Fluid Mech. 124, 219 (1982).

    Article  MATH  ADS  Google Scholar 

  7. V. V. Bychkov, S. M. Golberg, M. A. Liberman, et al., Phys. Rev. E 54, 3713 (1996).

    Article  ADS  Google Scholar 

  8. S. Kadowaki, Phys. Fluids 11, 3426 (1999).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  9. V. V. Bychkov, Phys. Fluids 10, 2091 (1998).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  10. H. EL-Rabii, G. Joulin, and K. Kazakov, Phys. Rev. Lett. 100, 174501 (2008).

    Article  ADS  Google Scholar 

  11. G. Joulin, H. El-Rabii, and K. Kazakov, J. Fluid Mech. 608, 217 (2008).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  12. K. A. Kazakov, Phys. Rev. Lett. 94, 094501 (2005).

    Article  ADS  Google Scholar 

  13. V. Bychkov, M. Zaytsev, and V. Akkerman, Phys. Rev. E 68, 026312 (2003).

    Article  ADS  Google Scholar 

  14. A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics (Nauka, Moscow, 1966) [in Russian].

    Google Scholar 

  15. M. L. Zaytsev and V. B. Akkerman, in Proceedings of the 52nd MFTI Scientific Conference on Modern Problems of Fundamental and Applied Sciences, Pt. VI: Aeromechanics and Flight Engineering (MFTI, Moscow, 2009), p. 10.

    Google Scholar 

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Correspondence to M. L. Zaytsev.

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Original Russian Text © M.L. Zaytsev, V.B. Akkerman, 2010, published in Pis’ma v Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2010, Vol. 92, No. 11, pp. 813–816.

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Zaytsev, M.L., Akkerman, V.B. Method for describing the steady-state reaction front in a two-dimensional flow. Jetp Lett. 92, 731–734 (2010). https://doi.org/10.1134/S0021364010230037

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  • DOI: https://doi.org/10.1134/S0021364010230037

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