  The observation of fluid-like behavior in nucleus-nucleus, proton-nucleus and
high-multiplicity proton-proton collisions motivates systematic studies of how
different measurements approach their fluid-dynamic limit. We have developed
numerical methods to solve the ultra-relativistic Boltzmann equation for
systems of arbitrary size and transverse geometry. Here, we apply these
techniques for the first time to the study of azimuthal flow coefficients $v_n$
including non-linear mode-mode coupling and to an initial condition with
realistic event-by-event fluctuations. We show how both linear and non-linear
response coefficients extracted from $v_n$ develop as a function of opacity
from free streaming to perfect fluidity. We note in particular that away from
the fluid-dynamic limit, the signal strength of linear and non-linear response
coefficients does not reduce uniformly, but that their hierarchy and relative
size shows characteristic differences.
