  A hybrid transport approach for the bulk evolution of viscous QCD matter
produced in ultra-relativistic heavy-ion collisions is presented. The expansion
of the dense deconfined phase of the reaction is modeled with viscous
hydrodynamics while the dilute late hadron gas stage is described
microscopically by the Boltzmann equation. The advantages of such a hybrid
approach lie in the improved capability of handling large dissipative
corrections in the late dilute phase of the reaction, including a realistic
treatment of the non-equilibrium hadronic chemistry and kinetic freeze-out. By
varying the switching temperature at which the hydrodynamic output is converted
to particles for further propagation with the Boltzmann cascade we test the
ability of the macroscopic hydrodynamic approach to emulate the microscopic
evolution during the hadronic stage and extract the temperature dependence of
the effective shear viscosity of the hadron resonance gas produced in the
collision. We find that the extracted values depend on the prior hydrodynamic
history and hence do not represent fundamental transport properties of the
hadron resonance gas. We conclude that viscous fluid dynamics does not provide
a faithful description of hadron resonance gas dynamics with predictive power,
and that both components of the hybrid approach are needed for a quantitative
description of the fireball expansion and its freeze-out.
