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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. [ABSTRACT FROM AUTHOR]

In the present paper, we consider a number of problems related to nonclassical transport phenomena in gas flows in regions with membranes. Our simulations focus on complex flows that might be of interest given the current trends in developing new membrane technologies. The methodological basis of this study is numerical modeling within the framework of solving the Boltzmann equation by various methods. Comparison between direct methods for solving the Boltzmann equation and the direct Monte Carlo modeling makes the assessment of the potential of both methods and better estimation of the accuracy of calculations possible. Flows through one or two consecutive membranes are considered for the classes of one-dimensional (1D) and two-dimensional (2D) problems. Several approaches to modeling thin membranes are discussed. Supersonic 2D flows in rectangular regions are considered. The results obtained confirm the assumptions of the 1D model of the membrane with additional explanation. The effects of nonclassical transfer are shown in 1D and 2D cases. [ABSTRACT FROM AUTHOR]

The possibilities of direct methods for solving the Boltzmann equation in comparison with direct simulation Monte Carlo are discussed. The general features of these different methods are considered, in particular, from the point of view of application of different variants of discretization in phase space. The advantages and disadvantages of both approaches are clarified. Comparative solutions of some simple problems are given. An important issue concerns anomalous heat transfer and validation of the effect by calculations based on these two methods. The solutions of the stationary one-dimensional heat transfer problem between two infinite plates with nonclassical nonequilibrium reflection from the surface are obtained; the anomalous heat transfer with a temperature gradient and a heat flux having the same sign is observed. One-dimensional and two-dimensional (in the square domain) problems with nonequilibrium "membranelike" boundary conditions are solved numerically; the anomalous heat transfer for all the considered cases is demonstrated. [ABSTRACT FROM AUTHOR]