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

Colangeli, M.; Karlin, I. V.; Kroger, M.

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

Authors

Colangeli, M.

Karlin, I. V.

Kroger, M.

Description

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