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From hyperbolic regularization to exact hydrodynamics for linearized Grad's equations

From hyperbolic regularization to exact hydrodynamics for linearized Grad's equations
From hyperbolic regularization to exact hydrodynamics for linearized Grad's equations
Inspired by a recent hyperbolic regularization of Burnett's hydrodynamic equations [A. Bobylev, J. Stat. Phys. 124, 371 (2006)], we introduce a method to derive hyperbolic equations of linear hydrodynamics to any desired accuracy in Knudsen number. The approach is based on a dynamic invariance principle which derives exact constitutive relations for the stress tensor and heat flux, and a transformation which renders the exact equations of hydrodynamics hyperbolic and stable. The method is described in detail for a simple kinetic model-a 13 moment Grad system.
1539-3755
51204
Colangeli, M.
1748ae98-dc59-4aab-b122-eebbffccc7eb
Karlin, I.V.
3f0e01a2-c4d9-4210-9ef3-47e6c426cc8a
Kroger, M.
407ef526-39d0-40d7-b3f2-b54ec7bad1d6
Colangeli, M.
1748ae98-dc59-4aab-b122-eebbffccc7eb
Karlin, I.V.
3f0e01a2-c4d9-4210-9ef3-47e6c426cc8a
Kroger, M.
407ef526-39d0-40d7-b3f2-b54ec7bad1d6

Colangeli, M., Karlin, I.V. and Kroger, M. (2007) From hyperbolic regularization to exact hydrodynamics for linearized Grad's equations. Physical Review E, 75 (5), 51204. (doi:10.1103/PhysRevE.75.051204).

Record type: Article

Abstract

Inspired by a recent hyperbolic regularization of Burnett's hydrodynamic equations [A. Bobylev, J. Stat. Phys. 124, 371 (2006)], we introduce a method to derive hyperbolic equations of linear hydrodynamics to any desired accuracy in Knudsen number. The approach is based on a dynamic invariance principle which derives exact constitutive relations for the stress tensor and heat flux, and a transformation which renders the exact equations of hydrodynamics hyperbolic and stable. The method is described in detail for a simple kinetic model-a 13 moment Grad system.

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Published date: May 2007

Identifiers

Local EPrints ID: 49269
URI: https://eprints.soton.ac.uk/id/eprint/49269
ISSN: 1539-3755
PURE UUID: f17a3462-d0d3-4bcf-b589-1000fdc9c138

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Date deposited: 26 Oct 2007
Last modified: 13 Mar 2019 20:54

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