  We investigate Poiseuille channel flow through intrinsically curved media,
equipped with localized metric perturbations. To this end, we study the flux of
a fluid driven through the curved channel in dependence of the spatial
deformation, characterized by the parameters of the metric perturbations
(amplitude, range and density). We find that the flux depends only on a
specific combination of parameters, which we identify as the average metric
perturbation, and derive a universal flux law for the Poiseuille flow. For the
purpose of this study, we have improved and validated our recently developed
lattice Boltzmann model in curved space by considerably reducing discrete
lattice effects.
