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The effect of airflow, including the electrohydrodynamic (EHD) flow produced by the electric corona discharge, and the flow generated externally on the corona discharge has been investigated numerically in this paper. Contrary to the common assumption that the corona discharge and the EHD flow can be decoupled by neglecting the convection term in the current density equation, the equations for electric field, charge transport, and fluid flow have been solved simultaneously. The numerical algorithm is based on boundary and finite element methods, the method of characteristics, and the finite volume method. The simulation results confirm that the EHD flow has a very small effect on the corona discharge. However, in some configurations, the external airflow may have considerable effect on the I- V characteristics of the system and the current density distribution on the ground electrode.