This thesis aims to explore and enable parameter estimation using the data assimilation method of the ensemble Kalman filter (EnKF). More specillically applied to the quasi-steady flow field, measured using particle image velocimetry (PIV), of a plasma actuator in quiescent ow where the parameters to be estimated are those describing the force field generated. The ensemble Kalman filter combines experimental observations together with a prior, created through numerical simulation, in a stochastic framework, to compute a closer estimation of the true state of the system together with an estimation of the error. This method has already proven to be able to improve the spacial and temporal accuracy experimental observations, as well as providing an estimation of the parameters describing the system. The EnKF has not yet been used in the _eld of plasma actuators, and can prove a valuable tool in improving upon existing experimental methods, including the calculation of the pressure field, and the time dependent force field. The calculation of the pressure field has mostly been ignored, and the determination of the time dependent force field has been done with limited success so far using only experimental methods only.

In the present thesis report the author synthetizes 9 months of work at the DSNA department of ONERA in Chatillon, France. The topic of the thesis is goal oriented mesh adaptation with particular application to unstructured grids and to _nite volume methods. The motivation of the present work is the application to unstructured meshes of a novel indicator for mesh adaptation, based on the total derivative of the goal function with respect to mesh nodes coordinates, introduced by Peter et al. in [6], [7] and that has been tested until now on structured grids only. In chapter 1 a brief literature survey is presented, with the aim of introducing the theoretical background of the work and the state of the art of goal oriented mesh adaptation techniques. In chapter 2 the author gives a description of the gradient computation module of the CFD software elsA, developed by ONERA, that has been the main tool used for ow simulations and mesh adaptation and the core of the code development work.