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The observation of fluid-like behavior in nucleus-nucleus, proton-nucleus andhigh-multiplicity proton-proton collisions motivates systematic studies of howdifferent measurements approach their fluid-dynamic limit. We have developednumerical methods to solve the ultra-relativistic Boltzmann equation forsystems of arbitrary size and transverse geometry. Here, we apply thesetechniques for the first time to the study of azimuthal flow coefficients $v_n$including non-linear mode-mode coupling and to an initial condition withrealistic event-by-event fluctuations. We show how both linear and non-linearresponse coefficients extracted from $v_n$ develop as a function of opacityfrom free streaming to perfect fluidity. We note in particular that away fromthe fluid-dynamic limit, the signal strength of linear and non-linear responsecoefficients does not reduce uniformly, but that their hierarchy and relativesize shows characteristic differences.

Hydrodynamization in systems with detailed transverse profiles