Higher-order Continuum Approximation for Rarefied Gases

Abstract

The Hilbert-Chapman-Enskog expansion of the kinetic equations in mean flight times is believed to be asymptotic rather than convergent. It is therefore inadvisable to use lower order results to simplify the current approximation as is done in the traditional Chapman-Enskog procedure, since that is an iterative method. By avoiding such recycling of lower order results, one obtains macroscopic equations that are asymptotically equivalent to the ones found in the Chapman-Enskog approach. The new equations contain higher order terms that are discarded in the Chapman-Enskog method. These make a significant impact on the results for such problems as ultrasound propagation. In this paper, it is shown that these results turn out well with relatively little complication when the expansions are carried to second order in the mean free time, for the example of the relaxation or BGK model of kinetic theory.

20 pages, 2 figures, RevTeX 4 macros

References in corpus (4)

• A Continuum Description of Rarefied Gas Dynamics (I)--- Derivation From Kinetic Theory
• A Continuum Description of Rarefied Gas Dynamics (II)--- The Propagation of Ultrasound
• A Continuum Description of Rarefied Gas Dynamics (III)--- The Structures of Shock Waves
• The Radiative Stress Tensor

Cited by in corpus (7)

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• Causal Relativistic Fluid Dynamics
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• Shear viscosity of nuclear matter
• Ultrasonic waves in classical gases
• One-dimensional ultrasound propagation at stratified gas: Gross-Jackson model
• A volume-based hydrodynamic approach to sound wave propagation in a monatomic gas