Probabilistic approach for rarefied gas dynamics: Linearized Couette flow
type: Item
instance of: scholarly article
title: Probabilistic approach for rarefied gas dynamics: Linearized Couette flow
zbMATH Open document ID: 0822.76082
DOI: 10.1016/0096-3003(94)00099-P
published in: Applied Mathematics and Computation
publication date: 1995-10-05T00:00:00Z
review text: Extending a new probabilistic approach for radiative transfer to the linear version of the Boltzmann equation based on the Krook kinetic model, an integral equation for the one-dimensional reflection function \(R(\tau; u, u_ 0)\) is derived from the Chapman-Kolmogorov equation in modified form. It is assumed that the joint probability of the molecular diffuse reflection at the moving wall has the Markovian character of the multiple scattering of particles. Then, the requisite perturbation velocity distribution at the moving wall is expressed in terms of the integrated \(R\)-function.
Mathematics Subject Classification ID: 76P05
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 761772
zbMATH Keywords: reciprocity principle
zbMATH Keywords: reflection function
zbMATH Keywords: Krook kinetic model
zbMATH Keywords: integral equation
zbMATH Keywords: Chapman-Kolmogorov equation
zbMATH Keywords: joint probability
zbMATH Keywords: multiple scattering
zbMATH Keywords: perturbation velocity distribution
author: Sueo Ueno
MaRDI profile type: Publication
cites work: The invariant imbedding method for transport problems. II: Resolvent in photon diffusion equation
cites work: Q5796557
cites work: Functional Equations in the Theory of Dynamic Programming--VII. A Partial Differential Equation for the Fredholm Resolvent
cites work: The probabilistic method for problems of radiative transfer. XIII: Diffusion matrix
cites work: INVARIANT IMBEDDING AND RAREFIED GAS DYNAMICS
cites work: Q3263585
cites work: A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems
cites work: Boundary value problems in kinetic theory of gases
cites work: Comparison of Kinetic Theory Analyses of Linearized Couette Flow
cites work: Q5585271
cites work: A cauchy method for an integral equation of linearized couette flow
cites work: Q4139876
cites work: Stochastic approach to the Cauchy problem of linearized Couette flow
cites work: Q3225947
cites work: Q5827321
full work available at URL: 0096-3003(94)00099-p
OpenAlex ID: W1964781074
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description: scientific article; zbMATH DE number 761772