Microfabricated arrays of synthetic jets are being explored for applications in aerodynamic flow control, in cooling of electronic packages, and in mixing in microchemical reactors. 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 techniques: a three-dimensional high-fidelity model for detailed simulation of a single jet, and a reduced "singlecell" model of a jet for simulation of large arrays of synthetic jets. The high-fidelity model is also used to calibrate the compact model. The paper shows examples of multi-dimensional simulations of aerodynamic flow control ("virtual flight control") and of active electronics cooling with 2D arrays of synthetic jets.