Computational simulation of coupled unsteady fluid mechanics and electromechanical actuation of a single synthetic jet can be performed with available CFD tools. Modeling of flow physics of large arrays of synthetic jets is computationally very challenging. This paper presents two complementary computational technologies: a high-fidelity physical model of a single jet, and a reduced (compact) model of the jet for modeling large array of synthetic jets. The high-fidelity model first has been validated against experimental data and then used to calibrate the compact model. The paper presents computational evaluation of accuracy and range of applicability of compact models and demonstrates them on multi-dimensional simulations of aerodynamic flow control and on electronics cooling applications.