Volume viscosity and internal energy relaxation: Symmetrization and Chapman-Enskog expansion

Vincent Giovangigli, Wen-An Yong
2014 Kinetic and Related Models  
We analyze a mathematical model for the relaxation of translational and internal temperatures in a nonequilibrium gas. The system of partial differential equations-derived from the kinetic theory of gases-is recast in its natural entropic symmetric form as well as in a convenient hyperbolic-parabolic symmetric form. We investigate the Chapman-Enskog expansion in the fast relaxation limit and establish that the temperature difference becomes asymptotically proportional to the divergence of the
more » ... divergence of the velocity field. This asymptotic behavior yields the volume viscosity term of the limiting one-temperature fluid model.
doi:10.3934/krm.2015.8.79 fatcat:tcqouownubewpkc3qqhuwcfixe