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High-accuracy deterministic solution of the Boltzmann equation for the shock wave structure

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Abstract

A new deterministic method of solving the Boltzmann equation has been proposed. The method has been employed in numerical studies of the plane shock wave structure in a hard sphere gas. Results for Mach numbers \(M=4\) and \(M=8\) have been compared with predictions of the direct simulation Monte Carlo (DSMC) method, which has been used to obtain the reference solution. Particular attention in estimating the solution accuracy has been paid to a fine structural effect: the presence of a total temperature peak exceeding the temperature value further downstream. The results of solving the Boltzmann equation for the shock wave structure are in excellent agreement with the DSMC predictions.

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Acknowledgments

This work was supported by the Russian Government under the grant “Measures to Attract Leading Scientists to Russian Educational Institutions” (Contract No. 14.Z50.31.0019).

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Authors and Affiliations

  1. Khristianovich Institute of Theoretical and Applied Mechanics SB RAS, Novosibirsk, Russia

    E. A. Malkov, Ye. A. Bondar, A. A. Kokhanchik, S. O. Poleshkin & M. S. Ivanov

  2. Novosibirsk State University, Novosibirsk, Russia

    E. A. Malkov, Ye. A. Bondar, A. A. Kokhanchik, S. O. Poleshkin & M. S. Ivanov

Authors
  1. E. A. Malkov
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  2. Ye. A. Bondar
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  3. A. A. Kokhanchik
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  4. S. O. Poleshkin
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  5. M. S. Ivanov
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Corresponding author

Correspondence to E. A. Malkov.

Additional information

Communicated by D. Ranjan.

M. S. Ivanov is deceased.

This paper is based on work that was presented at the 29th International Symposium on Shock Waves, Madison, WI, USA, July 14–19, 2013.

Appendix. Code listing

Appendix. Code listing

figure a
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Malkov, E.A., Bondar, Y.A., Kokhanchik, A.A. et al. High-accuracy deterministic solution of the Boltzmann equation for the shock wave structure. Shock Waves 25, 387–397 (2015). https://doi.org/10.1007/s00193-015-0563-6

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  • DOI: https://doi.org/10.1007/s00193-015-0563-6

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