In this paper we introduce a numerical procedure for performing dynamic data driven simulations (DDDAS). The main ingredient of our simulation is the multiscale interpolation technique that maps the sensor data into the solution space. We test our method on various synthetic examples. In particular we show that frequent updating of the sensor data in the simulations can significantly improve the prediction results and thus important for applications. The frequency of sensor data updating in the simulations is related to streaming capabilities and addressed within DDDAS framework. A further extension of our approach using local inversion is also discussed.