Anisotropic scattering kernel

generalized and modified Maxwell boundary conditions

S. Kokou Dadzie, J. Gilbert Méolens

Research output: Contribution to journal › Article

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Abstract

This paper presents a model of a scattering kernel of boundary conditions for the Boltzmann equation. The proposed scattering kernel is based on an anisotropic accommodation argument. Three parameters equal to the momentum accommodation coeffcients are shown as characterizing the influence of each direction. First the new scattering kernel is derived from a phenomenological criticism of the first form of the scattering kernel proposed by Maxwell; then the same result is established from an analytic approach based on the spectral nature of the linear integral operator associated to the scattering kernel problem. As a result, the model provides a correct form of scattering kernel to handle the influence of each direction in particle collisions with the wall. Finally independent accommodation of each internal mode is added to extend the model to the case of polyatomic gases.
Original languageEnglish
Pages (from-to)1804-1819
Number of pages15
JournalJournal of Mathematical Physics
Volume45
Issue number5
DOIs
Publication statusPublished - 1 Apr 2004

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Scattering
boundary conditions
kernel
Boundary conditions
accommodation
scattering
polyatomic gases
particle collisions
Boltzmann Equation
Integral Operator
Linear Operator
Collision
Momentum
Model
Internal
momentum
operators
Form

Keywords

  • kinetic theory
  • gas-wall interaction
  • scattering kernel
  • accommodation coefficients
  • Boltzmann equation

Cite this

Dadzie, S. Kokou ; Méolens, J. Gilbert. / Anisotropic scattering kernel : generalized and modified Maxwell boundary conditions. In: Journal of Mathematical Physics. 2004 ; Vol. 45, No. 5. pp. 1804-1819.
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Dadzie, SK & Méolens, JG 2004, 'Anisotropic scattering kernel: generalized and modified Maxwell boundary conditions', Journal of Mathematical Physics, vol. 45, no. 5, pp. 1804-1819. https://doi.org/10.1063/1.1690491

Anisotropic scattering kernel : generalized and modified Maxwell boundary conditions. / Dadzie, S. Kokou; Méolens, J. Gilbert.

In: Journal of Mathematical Physics, Vol. 45, No. 5, 01.04.2004, p. 1804-1819.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Anisotropic scattering kernel

T2 - generalized and modified Maxwell boundary conditions

AU - Dadzie, S. Kokou

AU - Méolens, J. Gilbert

PY - 2004/4/1

Y1 - 2004/4/1

N2 - This paper presents a model of a scattering kernel of boundary conditions for the Boltzmann equation. The proposed scattering kernel is based on an anisotropic accommodation argument. Three parameters equal to the momentum accommodation coeffcients are shown as characterizing the influence of each direction. First the new scattering kernel is derived from a phenomenological criticism of the first form of the scattering kernel proposed by Maxwell; then the same result is established from an analytic approach based on the spectral nature of the linear integral operator associated to the scattering kernel problem. As a result, the model provides a correct form of scattering kernel to handle the influence of each direction in particle collisions with the wall. Finally independent accommodation of each internal mode is added to extend the model to the case of polyatomic gases.

AB - This paper presents a model of a scattering kernel of boundary conditions for the Boltzmann equation. The proposed scattering kernel is based on an anisotropic accommodation argument. Three parameters equal to the momentum accommodation coeffcients are shown as characterizing the influence of each direction. First the new scattering kernel is derived from a phenomenological criticism of the first form of the scattering kernel proposed by Maxwell; then the same result is established from an analytic approach based on the spectral nature of the linear integral operator associated to the scattering kernel problem. As a result, the model provides a correct form of scattering kernel to handle the influence of each direction in particle collisions with the wall. Finally independent accommodation of each internal mode is added to extend the model to the case of polyatomic gases.

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KW - gas-wall interaction

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KW - accommodation coefficients

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Dadzie SK, Méolens JG. Anisotropic scattering kernel: generalized and modified Maxwell boundary conditions. Journal of Mathematical Physics. 2004 Apr 1;45(5):1804-1819. https://doi.org/10.1063/1.1690491

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