Abstract
The order of magnitude method offers an alternative to the Chapman-Enskog and Grad methods to derive macroscopic transport equations for rarefied gas flows. This method yields the regularized 13 moment equations (R13) and a generalization of Grad’s 13 moment equations for non-Maxwellian molecules. Both sets of equations are presented and discussed. Solutions of these systems of equations are considered for steady state Couette flow. The order of magnitude method is used to further reduce the generalized Grad equations to the non-linear bulk equations, which are of second order in the Knudsen number. Knudsen layers result from the linearized R13 equations, which are of the third order. Superpositions of bulk solutions and Knudsen layers show good agreement with DSMC calculations for Knudsen numbers up to 0.5.
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Communicated by M. Slemrod.
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Struchtrup, H., Thatcher, T. Bulk equations and Knudsen layers for the regularized 13 moment equations. Continuum Mech. Thermodyn. 19, 177–189 (2007). https://doi.org/10.1007/s00161-007-0050-0
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DOI: https://doi.org/10.1007/s00161-007-0050-0