Transport coefficients for bulk viscous evolution in the relaxation time approximation

We derive the form of the viscous corrections to the phase-space distribution function due to 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. Finally, we explicitly confirm that the time evolution of the bulk viscous pressure is significantly affected by its coupling to the shear stress tensor.

Note:

8 pages, 6 figures; v2 - PRC version

47.75.+f
24.10.Nz
25.75.-q
tensor: energy-momentum
viscosity: correction
Boltzmann equation: solution
expansion: longitudinal
pressure
distribution function
hydrodynamics

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Figures(6)

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