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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2023 Volume 63, Number 12, Pages 2025–2034 (Mi zvmmf11668)

Mathematical physics

Study of nonclassical transport by applying numerical methods for solving the Boltzmann equation

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

Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, 119333, Moscow, Russia

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.

UDC: 519.635

Received: 11.06.2023
Revised: 15.07.2023
Accepted: 22.08.2023

DOI: 10.31857/S0044466923120050


 English version:
Computational Mathematics and Mathematical Physics, 2023, 63:12, 2306–2314

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© Steklov Math. Inst. of RAS, 2024