Plasma addressed liquid crystal ͑PALC͒ is a promising technology for large size flat display devices, which uses gas discharges as electrical switches for the addressing of a liquid crystal ͑LC͒ layer. This work presents a comprehensive two-dimensional fluid model, that we developed for the simulation of the microdischarges occurring in PALC displays. The model comprises continuity equations and drift-diffusion equations for plasma particle species, a balance equation for the electron energy, and Poisson's equation for the electric field. Using this model, we succeeded in simulating the full PALC operation, reproducing a series of discharge pulses and afterglows in three consecutive PALC discharge channels. Results are presented for helium and helium-hydrogen mixtures. The results include: calculated particle densities, current-voltage curves, plasma decay times, surface charges, and LC transmission profiles. The influence of electrical crosstalk between adjacent channels is demonstrated.