Equilibrating Effect of Maxwell-Type Boundary Condition in Highly Rarefied Gas

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We study the equilibrating effects of the boundary and intermolecular collision in the kinetic theory for rarefied gases. We consider the Maxwell-type boundary condition, which has weaker equilibrating effect than the commonly studied diffuse reflection boundary condition. The gas region is the spherical domain in (Formula presented.)=1,2. First, without the equilibrating effect of the collision, we obtain the algebraic convergence rates to the steady state of free molecular flow with variable boundary temperature. The convergence behavior has intricate dependence on the accommodation coefficient of the Maxwell-type boundary condition. Then we couple the boundary effect with the intermolecular collision and study their interaction. We are able to construct the steady state solutions of the full Boltzmann equation for large Knudsen numbers and small boundary temperature variation. We also establish the nonlinear stability with exponential rate of the stationary Boltzmann solutions. Our analysis is based on the explicit formulations of the boundary condition for symmetric domains.

Original languageEnglish
Pages (from-to)743-800
Number of pages58
JournalJournal of Statistical Physics
Volume161
Issue number3
DOIs
Publication statusPublished - 2015 Nov 1

Fingerprint

Rarefied Gas
rarefied gases
boundary conditions
Boundary conditions
Collision
collisions
free molecular flow
accommodation coefficient
Knudsen number
Boundary Effect
Knudsen flow
Nonlinear Stability
Kinetic Theory
Steady-state Solution
kinetic theory
Boltzmann Equation
Ludwig Boltzmann
Convergence Rate
formulations
temperature

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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abstract = "We study the equilibrating effects of the boundary and intermolecular collision in the kinetic theory for rarefied gases. We consider the Maxwell-type boundary condition, which has weaker equilibrating effect than the commonly studied diffuse reflection boundary condition. The gas region is the spherical domain in (Formula presented.)=1,2. First, without the equilibrating effect of the collision, we obtain the algebraic convergence rates to the steady state of free molecular flow with variable boundary temperature. The convergence behavior has intricate dependence on the accommodation coefficient of the Maxwell-type boundary condition. Then we couple the boundary effect with the intermolecular collision and study their interaction. We are able to construct the steady state solutions of the full Boltzmann equation for large Knudsen numbers and small boundary temperature variation. We also establish the nonlinear stability with exponential rate of the stationary Boltzmann solutions. Our analysis is based on the explicit formulations of the boundary condition for symmetric domains.",
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Equilibrating Effect of Maxwell-Type Boundary Condition in Highly Rarefied Gas. / Kuo, Hung-Wen.

In: Journal of Statistical Physics, Vol. 161, No. 3, 01.11.2015, p. 743-800.

Research output: Contribution to journalArticle

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