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Study of Nonclassical Transport by Applying Numerical Methods for Solving the Boltzmann Equation

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Abstract

This paper overviews the state of the art in the study of nonequilibrium gas flows with nonclassical transport, in which the Stokes and Fourier laws are violated (and, accordingly, the Chapman–Enskog method is inapplicable). For a reliable validation of anomalous transport effects, we use computational methods of different nature: the direct solution of the Boltzmann equation and direct simulation Monte Carlo. Nonclassical anomalous transport is manifested on scales of 5–10 mean free paths, which confirms the fact that a highly nonequilibrium flow is a prerequisite for the detection of the effects. Two-dimensional flow problems are considered, namely, the supersonic flow over a flat plate in the transient regime and the supersonic flow through membranes (lattices), where the flow behind the lattice corresponds to the spatially nonuniform relaxation problem. In this region, nonequilibrium distributions demonstrating anomalous transport are formed. The relationship of the effect with the second law of thermodynamics is discussed, the possibilities of experimental verification are considered, and the prospects of creating new microdevices on this basis are outlined.

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Funding

This work was supported by the Ministry of Science and Higher Education of the Russian Federation, project no. 075-15-2020-799. The numerical computations were carried out using the infrastructure of Joint Supercomputer Center of the Russian Academy of Sciences.

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Authors and Affiliations

  1. Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 119333, Moscow, Russia

    V. V. Aristov, I. V. Voronich & S. A. Zabelok

Authors
  1. V. V. Aristov
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  2. I. V. Voronich
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  3. S. A. Zabelok
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Correspondence to V. V. Aristov.

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Dedicated to Professor E.M. Shakhov on the occasion of his 90 birthday

Translated by I. Ruzanova

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Aristov, V.V., Voronich, I.V. & Zabelok, S.A. Study of Nonclassical Transport by Applying Numerical Methods for Solving the Boltzmann Equation. Comput. Math. and Math. Phys. 63, 2306–2314 (2023). https://doi.org/10.1134/S0965542523120047

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  • DOI: https://doi.org/10.1134/S0965542523120047

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