Study of transport coefficients in ultrarelativistic kinetic theory

Abstract

A spatially-periodic longitudinal wave is considered in relativistic dissipative hydrodynamics. At sufficiently small wave amplitudes, an analytic solution is obtained in the linearised limit of the macroscopic conservation equations within the first- and second-order relativistic hydrodynamics formulations. A kinetic solver is used to obtain the numerical solution of the relativistic Boltzmann equation for massless particles in the Anderson-Witting approximation for the collision term. It is found that, at small values of the Anderson-Witting relaxation time $\tau$, the transport coefficients emerging from the relativistic Boltzmann equation agree with those predicted through the Chapman-Enskog procedure, while the relaxation times of the heat flux and shear pressure are equal to $\tau$. These claims are further strengthened by considering a moment-type approximation based on orthogonal polynomials under which the Chapman-Enskog results for the transport coefficients are exactly recovered.

34 pages (double column), 15 figures. Version accepted for publication in PRC

References in corpus (10)

• Dissipative relativistic fluid dynamics: a new way to derive the equations of motion from kinetic theory
• Transport Coefficients of Bulk Viscous Pressure in the 14-moment approximation
• Relativistic third-order viscous corrections to the entropy four-current from kinetic theory
• Relativistic quantum transport coefficients for second-order viscous hydrodynamics
• Quasiparticle second-order viscous hydrodynamics from kinetic theory
• Kinetic approach to relativistic dissipation
• Kelvin-Helmholtz instability of the Dirac fluid of charge carriers on graphene
• Equilibration and freeze-out of an expanding gas in a transport approach in a Friedmann-Robertson-Walker metric
• Towards a unified lattice kinetic scheme for relativistic hydrodynamics
• Transport coefficients in second-order non-conformal viscous hydrodynamics

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