A synthetic jet is an oscillatory jet, with zero time-averaged mass-flux, used to manipulate boundary layer characteristics for flow control applications such as drag reduction, detachment delay, etc. The objective of this work is the comparison and assessment of some numerical models of synthetic jets, in the framework of compressible flows governed by Reynolds- averaged Navier-Stokes (RANS) equations. More specifically, we consider three geometrical models, ranging from a simple boundary condition, to the account of the jet slot and the computation of the flow in the underlying cavity. From numerical point of view, weak and strong oscillatory boundary conditions are tested. Moreover, a systematic grid and time-step refinement study is carried out. Finally, a comparison of the flows predicted with two turbulence closures (Spalart-Allmaras and Menter SST k − ω models) is achieved.