In this paper we discuss numerical techniques involved in dynamic data driven application simulations (DDDAS). We present an interpolation technique and update procedures. A multiscale interpolation technique is designed to map the sensor data into the solution space. 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 (Douglas et al., 2003). We discuss the update of permeability and initial data.