The effects of numerical boundary conditions on the accuracy of simulation of synthetic jet actuators are analyzed. The flowfield surrounding a synthetic jet actuator located on a flat plate is simulated numerically by solving the 2-D unsteady compressible NavierStokes equations. Time-accurate solutions are obtained by an explicit finite difference method which is 4th-order accurate in both time and space. The numerical simulation is based on treating the actuator as a suction/blowing boundary condition imposed inside the throat of the actuator. Numerical results have shown that the conventional boundary conditions based on the normal momentum equation do not provide mass conservation.

As follows from our calculations, the maximum mass rate error, which occurs during the suction stage, is of the order of 15% if the normal momentum equation is used as a boundary condition for pressure. Note that the error introduced into the numerical solution increases as the boundary condition is imposed closer to the plate surface. To overcome this problem, new characteristic boundary conditions based on the moving mesh technique are proposed. The new method simulates the 2-D actuator by solving the 1-D Euler equations on a moving grid. The simplified actuator model has several advantages. First, this approach provides conservation of not only mass, but also momentum and energy. Furthermore, the new method is much more efficient in terms of computational time compared with the full 2-D simulation of the flowfield in the actuator. Numerical examples demonstrating efficiency and accuracy of the new strategy are presented.