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

M. Colangeli·I. V. Karlin·M. Kroger
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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 thirteen moment Grad system.

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M. Colangeli, I. V. Karlin, M. Kroger. 2007-04-04. From hyperbolic regularization to exact hydrodynamics for linearized Grad's equations. https://doi.org/10.1103/physreve.75.051204

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