Transport coefficients for bulk viscous evolution in the relaxation time approximation

Understand

We derive the form of the viscous corrections to the phase-space distribution function due to the bulk viscous pressure and shear stress tensor using the iterative Chapman-Enskog method.

• We then calculate the transport coefficients necessary for the second-order hydrodynamic evolution of the bulk viscous pressure and the shear stress tensor.
• We demonstrate that the transport coefficients obtained using the Chapman-Enskog method are different than those obtained previously using the 14-moment approximation for a finite particle mass.
• Specializing to the case of boost-invariant and transversally homogeneous longitudinal expansion, we show that the transport coefficients obtained using the Chapman-Enskog method result in better agreement with the exact solution of the Boltzmann equation in the relaxation-time approximation compared to results obtained in the 14-moment approximation.