Rachida Chakir, PhD

As the population increases, cities must constantly reassess their urban planning. However, this must be done in such a way to preserve the quality of life of its inhabitants. Energy saving, sustainable water and air quality are some of the important challenges associated with growing cities.  In this context, the monitoring of the different urban flows (pollution, heat) is very important.  For instance data assimilation approach can be used in monitoring.  These methods incorporate available measurement data and mathematical model to provide improved approximations of the physical state. The effectiveness of modeling and simulation tools is essential.  Advanced physically based models could provide spatially rich small-scale solution, however the use of such models is challenging due to explosive computational times in real-world applications.  Beyond computational costs, physical models are often constrained by available knowledge on the physical system. To overcome these difficulties, we resort the Parameterized-Background Data-Weak (PBDW) method. The PBDW formulation combines a Reduced Basis (RB) from the physically based model and the experimental observations, in order to provide a real-time and state estimate in a non-intrusive manner. The RB is used to diminish the cost of using a high-resolution model by exploiting the parametric structure of the governing equations.  In addition, variational data-assimilation techniques are used to correct the model error.