Title: Boundary conditions for Grad's 13 moment equations

Authors: Toby Thatcher, Y. Zheng, H. Struchtrup

Addresses: Department of Mechanical Engineering, University of Victoria, Victoria BC, Canada. ' Department of Mechanical Engineering, University of Victoria, Victoria BC, Canada. ' Department of Mechanical Engineering, University of Victoria, Victoria BC, Canada

Abstract: A complete set of boundary conditions for Grad|s 13 moment equations is derived from Maxwell|s boundary conditions for the Boltzmann equation. The equations are solved for plane Couette flow. The results exhibit temperature jump and slip, and agree well with DSMC calculations for Knudsen numbers Kn ≤ 0.1. Non-linear effects lead to unphysical results at larger Knudsen numbers, and for very fast flows. A simplified version of the Grad 13 equations, the so-called bulk equations, gives meaningful results in conditions where the full set of equations fails.

Keywords: kinetic theory; microscale flows; Grad moment method; boundary conditions; plane Couette flow; bulk equations; Boltzmann equation.

DOI: 10.1504/PCFD.2008.018080

Progress in Computational Fluid Dynamics, An International Journal, 2008 Vol.8 No.1/2/3/4, pp.69 - 83

Available online: 30 Apr 2008 *

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