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

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

2007-03-29

arxiv.org/abs/cond-mat/0703791v2

Phys. Rev. E 75, 051204 (2007) (10 pages)

Physics

Condensed Matter

Statistical Mechanics

23 pages, 5 figures, to appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.75.051204

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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