This research work presents the numerical simulations of multispecies multi-dimensional fluid model of atmospheric pressure discharge. The semi-implicit sequential iterative scheme is used to solve the coupled system of plasma fluid model equations with a proper set of boundary conditions. A one- dimensional self consistent drift-diffusion fluid model is developed to investigate the characteristics of atmospheric pressure discharge in pure helium and He-N2 gases. The uniform atmospheric pressure glow and Townsend discharge modes are examined under different operating conditions. The intricate dynamic patterns are evolved with the temporal evolution of discharge current densities at lower frequencies (≲7 kHz), which represent the discharge plasma operation between atypical lower and higher ionization modes in several consecutive cycles. To deduce different aspects of internal distributions of atmospheric pressure discharge, a two-dimensional fluid model is advanced with symmetric boundary conditions in the parallel plate reactor geometry. The filamentary and uniform behavior of discharge is emerged by the presence and removal of specific imposed conditions in APD. The periodic stationary pattern of various discharge parameters are exhibited at different times during the prebreakdown, breakdown, formation of cathode fall layer and decay phases. The Penning ionization process performs an outstanding role during the different phases of a complete cycle, which is explored with the temporal evolution of averaged chemical reaction rates. The analysis of spatio- temporal species distribution demonstrates that they are distinguished with their distinctive properties in various regimes of APD. In the presence of bulk gas flow, the two-dimensional symmetric uniform distributions of discharge species are transformed into non-symmetric form. The transport effects of heavy species, such as He+, He2+, N2+, He* and He2* are considered for the numerical solution of gas temperature equation and the numerical magnitude of gas temperature in the glow mode decreases with the increase of imposed bulk gas flow speed. The temporal profiles of discharge current density provide an insight in different bulk gas flow regimes, which are elucidated with the spatial structures of discharge species densities in the uniform, filamentary and constricted filamentary modes of APD. Finally, the three-dimensional fluid model is developed and employed to describe the space and time variations of discharge variables in the uniform and filamentary discharges. The homogeneous uniform slice distributions of electrons density are compared at different frequencies, which show the trapping of electrons in the positive column at higher frequencies. The non-uniform distribution of axial electric field illustrates that the field strength is higher in the constricted part than the smooth part of the dielectric barrier surface. The shape and configuration of filaments exhibit that they are directed from the anode towards the cathode barrier in the filamentary APD. The noticeable structures of filaments are prominently observed from 5 to 20 kHz than higher frequencies because of the coalescence of filaments at higher frequencies, leading to the formation of uniform APD. The temporal evolution of discharge current density exhibits that it represents the composite behavior in different driving frequency regimes from 20 to 100 kHz. The numerical simulation study reveals that it is useful to deliver a satisfactory information for the uniform and filamentary atmospheric pressure discharges, and describes the origin of non-uniformities.