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.

中文翻译：

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应用数值方法求解玻尔兹曼方程研究非经典输运

摘要

本文概述了非经典输运非平衡气体流动的研究现状，其中违反了斯托克斯和傅里叶定律（因此，查普曼-恩斯科格方法不适用）。为了可靠地验证反常输运效应，我们使用不同性质的计算方法：玻尔兹曼方程的直接求解和蒙特卡罗的直接模拟。非经典反常输运表现为 5-10 平均自由程的尺度，这证实了高度非平衡流动是检测效应的先决条件这一事实。考虑二维流动问题，即瞬态状态下平板上的超音速流动和穿过膜（晶格）的超音速流动，其中晶格后面的流动对应于空间非均匀弛豫问题。在该区域中，形成了表现出异常传输的非平衡分布。讨论了该效应与热力学第二定律的关系，考虑了实验验证的可能性，并概述了在此基础上创建新型微型器件的前景。