Ionic wind devices or electrostatic fluid accelerators are becoming of increasing interest as tools for thermal management, in particular for semiconductor devices. In this work, we present a numerical model for predicting the performance of such devices; its main benefit is the ability to accurately predict the amount of charge injected from the corona electrode. Our multiphysics numerical model consists of a highly nonlinear, strongly coupled set of partial differential equations including the Navier-Stokes equations for fluid flow, Poisson's equation for electrostatic potential, charge continuity, and heat transfer equations. To solve this system we employ a staggered solution algorithm that generalizes Gummel's algorithm for charge transport in semiconductors. Predictions of our simulations are verified and validated by comparison with experimental measurements of integral physical quantities, which are shown to closely match.