dorsal/arxiv
View SchemaHigher-order Continuum Approximation for Rarefied Gases
| Authors | Edward A. Spiegel, Jean-Luc Thiffeault |
|---|---|
| Categories | |
| ArXiv ID | physics/0301021 |
| URL | https://arxiv.org/abs/physics/0301021 |
| DOI | 10.1063/1.1613280 |
| Journal | Physics of Fluids 15 (11), 3558-3567 (2003) |
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.
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"abstract": "The Hilbert-Chapman-Enskog expansion of the kinetic equations in mean flight\ntimes is believed to be asymptotic rather than convergent. It is therefore\ninadvisable to use lower order results to simplify the current approximation as\nis done in the traditional Chapman-Enskog procedure, since that is an iterative\nmethod. By avoiding such recycling of lower order results, one obtains\nmacroscopic equations that are asymptotically equivalent to the ones found in\nthe Chapman-Enskog approach. The new equations contain higher order terms that\nare discarded in the Chapman-Enskog method. These make a significant impact on\nthe results for such problems as ultrasound propagation. In this paper, it is\nshown that these results turn out well with relatively little complication when\nthe expansions are carried to second order in the mean free time, for the\nexample of the relaxation or BGK model of kinetic theory.",
"arxiv_id": "physics/0301021",
"authors": [
"Edward A. Spiegel",
"Jean-Luc Thiffeault"
],
"categories": [
"physics.flu-dyn"
],
"doi": "10.1063/1.1613280",
"journal_ref": "Physics of Fluids 15 (11), 3558-3567 (2003)",
"title": "Higher-order Continuum Approximation for Rarefied Gases",
"url": "https://arxiv.org/abs/physics/0301021"
},
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