New forms of non-relativistic and relativistic hydrodynamic equations as derived by the renormalization-group method - possible functional ansatz in the moment method consistent with Chapman-Enskog theory -

2012/05/31 by Kyosuke Tsumura, Teiji Kunihiro · 1 citation
Mathematics · Physics and Astronomy · #math-ph #math.MP #nucl-th #physics.flu-dyn

paper · pdf · doi:10.1143/ptps.195.19

Typos are corrected. Accepted version. 10 pages. To be published in Suppl. Prog. Theor. Phys

arxiv created 2012/06/02 · arxiv updated 2015/06/05

Abstract

After a brief account of the derivation of the first-order relativistic hydrodynamic equation as a construction of the invariant manifold of relativistic Boltzmann equation, we give a sketch of derivation of the second-order hydrodynamic equation (extended thermodynamics) both in the nonrelativistic and relativistic cases. We show that the resultant equation suggests a novel ansatz for the functional form to be used in Grad moment method, which turns out to give the same expressions for the transport coefficients as those given in the Chapman-Enskog theory as well as the novel expressions for the relaxation times and lenghts allowing natural physical interpretaion.

Cited by

• Derivation of relativistic hydrodynamic equations consistent with relativistic Boltzmann equation by renormalization-group method