Surface dielectric barrier discharges (sDBD) are efficient and scalable plasma sources for plasma-based gas conversion. One prominent feature of an sDBD in this application is its ionic wind, which exerts a force on the neutrals, thus leading to an efficient mixing of plasma and a passing gas stream. This becomes apparent by the creation of upstream and downstream vortices in the vicinity of the plasma. In this study, these vortices are monitored by Schlieren imaging diagnostic to benchmark a simulation of the sDBD using a plasma and a flow simulation. The plasma simulation models the streamer over typically 10 ns starting from the electrode and propagating along a dielectric surface. This is the source of charges, accelerated as ion wind by the applied voltage from the sDBD power supply. The flow simulation models this ion wind as a time-averaged volume force acting on the passing gas stream. The conversion of the time-resolved forces from the nanosecond plasma simulation into the steady state volume force in the flow simulation indicates that the force from the plasma lasts much longer than the actual nanosecond plasma phase. This is explained by the fact that the charges in the streamer channel remain for almost 100 ns, according to their recombination time constant, and the electric fields from the powered sDBD electrode remain for a few microseconds. This quantitatively explains the thrust from the ion wind, which must be inserted in the flow simulation to model the measured Schlieren images.