Many engineering fields require to solve numerically partial differential equations (PDE) modeling physical phenomenon.

When we focus on a mathematical model that describes the physical behavior of a system based on one or more parametrized PDEs (geometrical or physical parameters), it may be desirable to rapidly and reliably evaluate the output of the model (quantity of interest)
for different parameter values.
The real-time context, needed to perform command-control, and contexts asking many evaluations of model outputs (typically for optimization methods or uncertainty and sensitivity analysis) lend themselves perfectly.

The certified reduced basis method is an intrusive reduction method beacause, unkike non-intrusive methods, the reduction is based on the projection of operators associated to physical model PDEs.
This method allow to obtain rapidly, for a given set of parameter values, an approximation of the evaluation of the model output.
One of the strengths of the method is the "certified" aspect to estimate the approximation error of the model output evaluation.

The goal of the post-doctorate is to develop a computational framework for the certified reduced basis method. This framework should be based on the TRUST platform (https://sourceforge.net/projects/trust-platform/) developed at CEA and will be generic enough to be used to deal with different types of problems (linear or not, stationary or not, coercive or not...)
The framework will be used in the case of a two-fluid mixing model.