We investigate the applicability of fluid dynamics (FD) in relativistic heavy-ion collisions by comparing its solutions to those of the relativistic Boltzmann equation (BE) . The latter can be solved numerically  and its FD limit is well known . We consider various (2+1)-dimensional boost-invariant scenarios, with realistic initial transverse profiles of energy and particle density. By varying the system size and the cross section we then identify regions where FD is a good approximation to the BE.
We observe that the space-time evolution of energy density and fluid velocity is well described by FD for all considered values of the cross section. However, the FD shear-stress tensor starts to deviate from its BE counterpart when the Knudsen number $\rm Kn$, defined as a mean free path times the local expansion rate, exceeds a value of one.
We furthermore study the elliptic flow generated for Glauber-type initial conditions. We consider various decoupling conditions in FD and identify the $\rm Kn$ regions where the elliptic flow is generated. Decoupling at a constant $\rm Kn \sim 2-3$ gives a good agreement with the solutions of the BE when the cross section is sufficiently large, i.e., when most of the elliptic flow is generated during the evolution where $\rm Kn < 1$. With decreasing cross section most of the flow signal is generated in regions where $\rm Kn > 1$. In this case, the FD elliptic flow starts to deviate from that generated by the BE.
 K. Gallmeister, H. Niemi, C. Greiner, D. H. Rischke, in preparation
 Z. Xu and C. Greiner, Phys. Rev. C71, 064901 (2005)
 G. Denicol, H. Niemi, E. Molnar and D. H. Rischke, Phys. Rev. D85, 114047 (2012)
|Centralised submission by Collaboration||Presenter name already specified|