Topic
Knudsen number
About: Knudsen number is a research topic. Over the lifetime, 5052 publications have been published within this topic receiving 104278 citations.
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TL;DR: In this article, the characteristic parameters of the Knudsen and Poiseuille transport mechanisms were determined from gas permeation experiments using helium, air and argon and direct contact membrane distillation (DCMD) experiments using distilled water.
75 citations
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TL;DR: In this paper, an analytical solution to the Brownian coagulation of aerosol particles in the low Knudsen number regime is presented which provides time evolution of the particle size distribution.
75 citations
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TL;DR: In this article, a domain decomposition approach for the coupling of Boltzmann and Euler equations is presented, which leads to a simple implementation of the coupling procedure and to natural interface conditions between the two domains.
75 citations
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TL;DR: In this article, an implicit-explicit (IMEX) time discretization was proposed for the initial value problem of the ES-BGK kinetic equation, where the convection is explicit while the relaxation term is implicit to overcome the stiffness.
Abstract: In this paper, we study a time discrete scheme for the initial value problem of the ES-BGK kinetic equation. Numerically solving these equations are challenging due to the nonlinear stiff collision (source) terms induced by small mean free or relaxation time. We study an implicit-explicit (IMEX) time discretization in which the convection is explicit while the relaxation term is implicit to overcome the stiffness. We first show how the implicit relaxation can be solved explicitly, and then prove asymptotically that this time discretization drives the density distribution toward the local Maxwellian when the mean free time goes to zero while the numerical time step is held fixed. This naturally imposes an asymptotic-preserving scheme in the Euler limit. The scheme so designed does not need any nonlinear iterative solver for the implicit relaxation term. Moreover, it can capture the macroscopic fluid dynamic (Euler) limit even if the small scale determined by the Knudsen number is not numerically resolved. We also show that it is consistent to the compressible Navier-Stokes equations if the viscosity and heat conductivity are numerically resolved. Several numerical examples, in both one and two space dimensions, are used to demonstrate the desired behavior of this scheme.
75 citations
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TL;DR: The correct form of the diffusion equation in the case of an inhomogeneous medium, whose temperature may also vary in space, has been the subject of some debate in this paper.
75 citations