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  • Open Access

Exact nonlocal hydrodynamics predict rarefaction effects

Florian Kogelbauer* and Ilya Karlin†

  • Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland

  • *Contact author: floriank@ethz.ch
  • †Contact author: ikarlin@ethz.ch
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Phys. Rev. E 112, 014119 – Published 17 July, 2025

DOI: https://doi.org/10.1103/4gkn-7s3x

Abstract

We combine the theory of slow spectral closure for linearized Boltzmann equations with Maxwell's kinetic boundary conditions to derive optimal hydrodynamics with arbitrary accommodation. Focusing on shear-mode dynamics, we obtain explicit steady state solutions in terms of Fourier integrals and closed-form expressions for the mean flow and the stress. We demonstrate that the exact nonlocal fluid model correctly predicts several rarefaction effects with accommodation, including the Couette flow and thermal creep in a plane channel.

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References (38)

  1. C. Cercignani, Rarefied Gas Dynamics: From Basic Concepts to Actual Calculations (Cambridge University Press, Cambridge, 2000), Vol. 21.
  2. C. Cercignani and M. Lampis, Transp. Theory Stat. Phys. 1, 101 (1971).
  3. J. C. Maxwell, Philos. Trans. R. Soc. London 170, 231 (1879).
  4. D. Hilbert, Bull. Am. Math. Soc. 37, 407 (2000).
  5. S. Chapman and T. Cowling, The Mathematical Theory of Non-uniform Gases, Cambridge Mathematical Library (Cambridge University Press, Cambridge, 1990).
  6. A. V. Bobylev, in Akademiia Nauk SSSR Doklady (Moscow, 1982), Vol. 262, pp. 71–75.
  7. N. G. Hadjiconstantinou, Phys. Fluids 18, 111301 (2006).
  8. H. Struchtrup, Z. Angew. Math. Phys. 51, 346 (2000).
  9. X.-J. Gu and D. R. Emerson, J. Comput. Phys. 225, 263 (2007).
  10. F. Kogelbauer and I. Karlin, Phys. Rev. E 110, 055105 (2024).
  11. F. Kogelbauer, C. Zheng, and I. Karlin, arXiv:2501.13938.
  12. M. Torrilhon and H. Struchtrup, J. Comput. Phys. 227, 1982 (2008).
  13. X. Li, B. Hu, and L. Wu, Phys. Fluids 36 (2024).
  14. P.-L. Lions and N. Masmoudi, Arch. Ration. Mech. Anal. 158, 173 (2001).
  15. P.-L. Lions and N. Masmoudi, Arch. Ration. Mech. Anal. 158, 195 (2001).
  16. I. Gallagher and I. Tristani, Ann. Henri Lebesgue 3, 561 (2020).
  17. A. N. Gorban, Philos. Trans. R. Soc. A 376, 20170238 (2018).
  18. A. Gorban and I. Karlin, Bull. Am. Math. Soc. 51, 187 (2014).
  19. A. N. Gorban and I. V. Karlin, Phys. Rev. Lett. 77, 282 (1996).
  20. F. Kogelbauer, Continuum Mech. Thermodyn. 32, 1141 (2020).
  21. H. Struchtrup and M. Torrilhon, Phys. Rev. Lett. 99, 014502 (2007).
  22. S. Ansumali, I. V. Karlin, S. Arcidiacono, A. Abbas, and N. I. Prasianakis, Phys. Rev. Lett. 98, 124502 (2007).
  23. P. Anzini, G. M. Colombo, Z. Filiberti, and A. Parola, Phys. Rev. Lett. 123, 028002 (2019).
  24. S. Loyalka, N. Petrellis, and T. Storvick, Z. Angew. Math. Phys. 30, 514 (1979).
  25. L. B. Barichello, M. Camargo, P. Rodrigues, and C. Siewert, Z. Angew. Math. Phys. 52, 517 (2001).
  26. F. Kogelbauer and I. Karlin, Physica D 459, 134014 (2024).
  27. G. Berkooz, P. Holmes, and J. L. Lumley, Annu. Rev. Fluid Mech. 25, 539 (1993).
  28. F. Kogelbauer and I. Karlin, Continuum Mech. Thermodyn. 36, 1685 (2024).
  29. F. Kogelbauer, Continuum Mech. Thermodyn. 33, 431 (2021).
  30. C. Cercignani, The Boltzmann Equation (Springer, New York, 1988).
  31. M. Williams, Z. Angew. Math. Phys. 52, 500 (2001).
  32. L. Hörmander, The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis, Classics in Mathematics (Springer Berlin Heidelberg, Heidelberg, 2015).
  33. M. Razavy, Quantum Theory of Tunneling (World Scientific, Singapore, 2013).
  34. H. Grad, Commun. Pure Appl. Math. 2, 331 (1949).
  35. S. K. Loyalka, Jr. and J. Cipolla, Phys. Fluids 14, 1656 (1971).
  36. P. L. Bhatnagar, E. P. Gross, and M. Krook, Phys. Rev. 94, 511 (1954).
  37. S. D. Baalrud, Phys. Plasmas 20, 012118 (2013).
  38. W. Su, P. Wang, H. Liu, and L. Wu, J. Comput. Phys. 378, 573 (2019).

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Phys. Rev. E 112, 014119– Published 17 July, 2025
  • Received 8 November 2024
  • Revised 9 April 2025
  • Accepted 25 June 2025
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