A physical and numerical model for surface dielectric barrier discharge evolution in atmospheric air was developed and tested against experimental data for discharge parameters. Both discharge formation and relaxation phases were simulated successfully using a new approach of non-local air ionization by electron impact and ab initio boundary conditions on the electrode and dielectric surface. The main features of the physical and numerical model of the discharge simulation have been discussed. It was shown that discharge relaxation phase contributes primarily to momentum and heat sources relevant for flow control. The momentum source spatial distribution has a complex structure with the regions of upstream and downstream body force direction and qualitatively depends on applied voltage polarity and voltage pulse waveform. For different conditions it could lead to either near-surface flow acceleration or vortex generation.