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Title: Numerical solution of the linearized Boltzmann equation for an arbitrary intermolecular potential

Abstract

A numerical procedure to solve the linearized Boltzmann equation with an arbitrary intermolecular potential by the discrete velocity method is elaborated. The equation is written in terms of the kernel, which contains the differential cross section and represents a singularity. As an example, the Lennard-Jones potential is used and the corresponding differential cross section is calculated and tabulated. Then, the kernel is calculated so that to overcome its singularity. Once, the kernel is known and stored it can be used for many kinds of gas flows. In order to test the method, the transport coefficients, i.e. thermal conductivity and viscosity for all noble gases, are calculated and compared with those obtained by the variational method using the Sonine polynomials expansion. The fine agreement between the results obtained by the two different methods shows the feasibility of application of the proposed technique to calculate rarefied gas flows over the whole range of the Knudsen number.

Authors:
 [1];  [1]
  1. Departamento de Fisica, Universidade Federal do Parana, Caixa Postal 19044, Curitiba, 81531-990 (Brazil)
Publication Date:
OSTI Identifier:
21313071
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 228; Journal Issue: 9; Other Information: DOI: 10.1016/j.jcp.2009.01.016; PII: S0021-9991(09)00039-4; Copyright (c) 2009 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOLTZMANN EQUATION; DIFFERENTIAL CROSS SECTIONS; KNUDSEN FLOW; LENNARD-JONES POTENTIAL; NUMERICAL SOLUTION; POLYNOMIALS; RARE GASES; SINGULARITY; THERMAL CONDUCTIVITY; VARIATIONAL METHODS; VISCOSITY

Citation Formats

Sharipov, Felix, and Bertoldo, Guilherme. Numerical solution of the linearized Boltzmann equation for an arbitrary intermolecular potential. United States: N. p., 2009. Web. doi:10.1016/j.jcp.2009.01.016.
Sharipov, Felix, & Bertoldo, Guilherme. Numerical solution of the linearized Boltzmann equation for an arbitrary intermolecular potential. United States. https://doi.org/10.1016/j.jcp.2009.01.016
Sharipov, Felix, and Bertoldo, Guilherme. 2009. "Numerical solution of the linearized Boltzmann equation for an arbitrary intermolecular potential". United States. https://doi.org/10.1016/j.jcp.2009.01.016.
@article{osti_21313071,
title = {Numerical solution of the linearized Boltzmann equation for an arbitrary intermolecular potential},
author = {Sharipov, Felix and Bertoldo, Guilherme},
abstractNote = {A numerical procedure to solve the linearized Boltzmann equation with an arbitrary intermolecular potential by the discrete velocity method is elaborated. The equation is written in terms of the kernel, which contains the differential cross section and represents a singularity. As an example, the Lennard-Jones potential is used and the corresponding differential cross section is calculated and tabulated. Then, the kernel is calculated so that to overcome its singularity. Once, the kernel is known and stored it can be used for many kinds of gas flows. In order to test the method, the transport coefficients, i.e. thermal conductivity and viscosity for all noble gases, are calculated and compared with those obtained by the variational method using the Sonine polynomials expansion. The fine agreement between the results obtained by the two different methods shows the feasibility of application of the proposed technique to calculate rarefied gas flows over the whole range of the Knudsen number.},
doi = {10.1016/j.jcp.2009.01.016},
url = {https://www.osti.gov/biblio/21313071}, journal = {Journal of Computational Physics},
issn = {0021-9991},
number = 9,
volume = 228,
place = {United States},
year = {Wed May 20 00:00:00 EDT 2009},
month = {Wed May 20 00:00:00 EDT 2009}
}