Inverse-Reynolds-Dominance approach to transient fluid dynamics

Understand

We consider the evolution equations for the bulk viscous pressure, diffusion current and shear tensor derived within second-order relativistic dissipative hydrodynamics from kinetic theory.

• By matching the higher order moments directly to the dissipative quantities, all terms which are of second order in the Knudsen number Kn vanish, leaving only terms of order $\mathcal{O}(\textrm{Re}^{-1} \textrm{Kn})$ and $\mathcal{O}(\textrm{Re}^{-2})$ in the relaxation equations, where $\textrm{Re}^{-1}$ is the inverse Reynolds number.
• We therefore refer to this scheme as the Inverse-Reynolds-Dominance (IReD) approach.
• The remaining (non-vanishing) transport coefficients can be obtained exclusively in terms of the inverse of the collision matrix.