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A Closed-Form Solution of a Kinetic Integral Equation for Rarefied Gas Flow in a Cylindrical Duct

¹ Departamento de Ciências Exatas e da Terra, Universidade Regional Integrada do Alto Uruguai e das Miss?es (URI), Frederico Westphalen, Brazil
² Departamento de Ciências Agron?micas e Ambientais, Universidade Federal de Santa Maria (UFSM), Frederico Westphalen, Brazil
³ Instituto de Matemática, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil

Applied Mathematics·Volume 05 (2014)·Pages 1516–1527·Published 22 May 2014·DOI10.4236/am.2014.510145

Abstract

A spectral method based on Hermite cubic splines expansions combined with a collocation scheme is used to develop a solution for the vector form integral S-model kinetic equation describing rarefied gas flows in cylindrical geometry. Some manipulations are made to facilitate the computational treatment of the singularities inherent to the kernel. Numerical results for the simulation of flows generated by pressure and thermal gradients, Poiseuille and thermal-creep problems, are presented.

KeywordsRarefied Gas DynamicsIntegral EquationS-ModelCollocation Schemes

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A Closed-Form Solution of a Kinetic Integral Equation for Rarefied Gas Flow in a Cylindrical Duct

Abstract

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