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We investigate the applicability of fluid dynamics in ultrarelativistic heavyion (AA) collisions and high multiplicity proton nucleus (pA) collisions. Inorder for fluid dynamics to be applicable the microscopic and macroscopicdistance/time scales of the system have to be sufficiently separated. Thedegree of separation is quantified by the ratio between these scales, usuallyreferred to as the Knudsen number. In this work, we calculate the Knudsennumbers reached in fluid dynamical simulations of AA and pA collisions at RHICand LHC energies. For this purpose, we consider different choices of shearviscosity parametrizations, initial states and initialization times. We thenestimate the values of shear viscosity for which the fluid dynamicaldescription of ultrarelativistic AA and pA collisions breaks down. Inparticular, we study how such values depend on the centrality, in the case ofAA collision, and multiplicity, in the case of pA collision. We found that themaximum viscosity in AA collisions is of the order $\eta/s \sim 0.1 \ldots0.2$, which is similar in magnitude to the viscosities currently employed insimulations of heavy ion collisions. For pA collisions, we found that suchlimit is significantly lower, being less than $\eta/s=0.08$

How large is the Knudsen number reached in fluid dynamical simulations of ultrarelativistic heavy ion collisions?