Topic
Rarefaction
About: Rarefaction is a research topic. Over the lifetime, 1852 publications have been published within this topic receiving 26943 citations.
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TL;DR: The main motivation for the study is to overcome the intense computational effort required by the large computational domain and the slow downstream variation and convergence in this problem, and to address some of the existing concerns with current models.
Abstract: This article addresses some analytical and numerical modeling issues regarding the simulation of pressure-driven nitrogen slip flow in long microchannels. The main motivation for the study is to overcome the intense computational effort required by the large computational domain and the slow downstream variation and convergence in this problem, and to address some of the existing concerns with current models. A parallel solver is developed and used along with a serial version to obtain the steady state solution. This approach is found to provide an efficient and accurate solution to the problem. A comparison with earlier results is used for validation, as well as for justifying this hybrid approach. Some implemental issues related to the parallel algorithm are discussed and solved. The effects of variable properties, rarefaction, and the source terms in energy equation are determined and are found to be significant, particularly for the case of uniform wall heat flux boundary condition.
16 citations
TL;DR: In this article, the authors investigated the properties of finite energy travelling waves to the nonlinear Schrodinger equation with nonzero conditions at infinity for a wide class of nonlinearities.
Abstract: We investigate the properties of finite energy travelling waves to the nonlinear Schrodinger equation with nonzero conditions at infinity for a wide class of nonlinearities. In space dimension two and three we prove that travelling waves converge in the transonic limit (up to rescaling) to ground states of the Kadomtsev-Petviashvili equation. Our results generalize an earlier result of F. Bethuel, P. Gravejat and J-C. Saut for the two-dimensional Gross-Pitaevskii equation, and provide a rigorous proof to a conjecture by C. Jones and P. H. Roberts about the existence of an upper branch of travelling waves in dimension three.
16 citations
01 Jan 1958
TL;DR: In this article, the regions of nonstability of a stationary magnetohydrodyanamical shock wave with respect to onedimensional perturbations were determined, and it was shown that two types of stable shock waves exist.
Abstract: The regions of nonstability of a stationary magnetohydrodyanamical shock wave with respect to onedimensional perturbations were determined. It is shown that two types of stable shock waves exist. The types of shock waves which can follow each other are ascertained. (tr-nuth)
16 citations
TL;DR: In this paper, a mathematical analysis of a supersonic jet stream out of an orifice into the atmosphere is presented, which involves the interaction of steady rarefaction waves, and the interactions of a rarefraction wave by the interface of the jet stream.
16 citations
TL;DR: In this paper, the authors considered the response of a gas in a microchannel to instantaneous (small-amplitude) non-periodic motion of its boundaries in the normal direction.
Abstract: We consider the response of a gas in a microchannel to instantaneous (small-amplitude) non-periodic motion of its boundaries in the normal direction. The problem is formulated for an ideal monatomic gas using the Bhatnagar, Gross, and Krook (BGK) kinetic model, and solved for the entire range of Knudsen (Kn) numbers. Analysis combines analytical (collisionless and continuum-limit) solutions with numerical (low-variance Monte Carlo and linearized BGK) calculations. Gas flow, driven by motion of the boundaries, consists of a sequence of propagating and reflected pressure waves, decaying in time towards a final equilibrium state. Gas rarefaction is shown to have a “damping effect” on equilibration process, with the time required for equilibrium shortening with increasing Kn. Oscillations in hydrodynamic quantities, characterizing gas response in the continuum limit, vanish in collisionless conditions. The effect of having two moving boundaries, compared to only one considered in previous studies of time-periodic systems, is investigated. Comparison between analytical and numerical solutions indicates that the collisionless description predicts the system behavior exceptionally well for all systems of the size of the mean free path and somewhat larger, in cases where boundary actuation acts along times shorter than the ballistic time scale. The continuum-limit solution, however, should be considered with care at early times near the location of acoustic wavefronts, where relatively sharp flow-field variations result in effective increase in the value of local Knudsen number.
16 citations