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We apply a hybrid Molecular Dynamics and mesoscopic simulation technique tostudy the dynamics of two dimensional colloidal discs in confined geometries.We calculate the velocity autocorrelation functions, and observe the predicted$t^{-1}$ long time hydrodynamic tail that characterizes unconfined fluids, aswell as more complex oscillating behavior and negative tails for stronglyconfined geometries. Because the $t^{-1}$ tail of the velocity autocorrelationfunction is cut off for longer times in finite systems, the related diffusioncoefficient does not diverge, but instead depends logarithmically on theoverall size of the system.

Hydrodynamics of confined colloidal fluids in two dimensions