Nanosecond dielectric barrier discharge (NS-DBD) plasma actuators is relatively new means of flow control. It has several advantages compared to more conventional means of flow control, such as small size, low weight, fast response time and controllability. It has been demonstrated to be able to promote transition of boundary layers and to postpone flow separation on aerodynamic surfaces. This makes the NS-DBD actuator a promising technology for many applications in aerospace and wind energy industries. This thesis presents a study of NS-DBD actuator effects by numerical simulations. For the purposes of simulations of fluid-dynamic effects of the actuation, complex plasma dynamic processes are modeled by their thermal effects. This is possible due to a large separation of scales between plasmadynamic, thermodynamic and fluid dynamic phenomena. The resulting model is embedded into the compressible computational fluid dynamics (CFD) simulation using Navier- Stokes equations. This model is then used in numerical simulations in two model flows: a laminar boundary and a free shear layer. These model flows are relevant for promotion of laminar to turbulent boundary layer transition and laminar leading edge separation elimination. For the laminar boundary case, the effect of a burst of discharges on a flat plate boundary layer is studied. The shape, wavelength and propagation speed of the disturbance introduced into the boundary layer by actuation are compared to experimental results and found to be in agreement. This indicates that the thermal model is adequate at predicting phenomenological effects of the actuation in this case. POD analysis of the CFD flow fields is employed to identify the dominating modes of the disturbance. The dominating mode is found to be the same as the least stable mode predicted by linear stability theory. A compression wave, however, is not found to play an important role, and the burst of pulses is found to produce the same effects as the long pulse with the same total energy. For the free shear layer case, the model of the actuator is placed on a centerline in the beginning of a free shear layer. As a result of constant frequency actuation, early formation of vortices and shear layer breakdown are observed. Each actuation event produces a convective disturbance in the flow field. Dynamics of the disturbances are analyzed and growth rates are found to be in agreement with the predictions of linear stability theory. A parametric study is carried out to study scalability of the actuator effects to change of actuation frequency and energy per pulse. A saturation effect with the increase of actuation frequency is observed. For both studied cases, the effect of NS-DBD actuation is excitation of natural instability modes, which then evolve according to the stability properties of the flow.@en