The polynomial expansion method for boundary value problems of transport in rarefied gases
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The principles of rarefied gas dynamics are finding application in many areas of practical interest ranging from aerosol science to micro–fabrication to vacuum and space applications. Many methods have become available for solving the Boltzmann equation which is the complicated integro–differential equation that describes the distribution of the gas molecules and forms the basis for the field of rarefied gas dynamics. Moments methods are among the most popular of these solution techniques due to their relative simplicity and overall versatility. In the half–range moment method of solving boundary value problems based on the Boltzmann equation, difficult bracket integrals are encountered. We discuss here a simplification of such integrals specific to the spherical geometry and applicable for arbitrary values of the Knudsen number. A polynomial expansion in velocity space is used to represent the discontinuous factor in these integrals. The accuracy of the method is verified by a comparison of the analytical results with available numerical results.
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