Modeling for oceanic and atmospheric flows
Current numerical oceanic and atmospheric models suffer from a number of well-identified issues. They are mainly related to the lack of horizontal and vertical resolution thus requiring the parameterization of unresolved (subgrid scales) processes and the control of discretization errors to fulfill criteria related to the particular underlying physics of rotating and strongly stratified flows. Oceanic and atmospheric coupled models are increasingly used on a wide range of applications from global to regional scales. The assessment of the reliability of those coupled models is an emerging topic nowadays as the spread among the answers of existing models (e.g. for climate change predictions) has not been reduced with the new generation models compared to the elder ones.
Advanced methods for the modeling of 3D rotating and stratified flows
Ocean Atmosphere interactions and formulation of coupled models
Model reduction / multiscale algorithms
The high computational cost of the applications is a common and major concern to have in mind when deriving new methodological approaches. This cost increases with the use of sensivity analysis or parameter estimation methods and more generally with methods that require a potentially large number of integrations of the model trajectory. A dimension reduction using either stochastic or deterministic methods, is a way to reduce the number of degrees of freedom, and therefore the calculation time, of a numerical model.
Model reduction for sensitivity analysis and parameter estimation
Reduced models for coupling applications
Reduced models for multiscale optimization
Dealing with uncertainties
There are many sources of uncertainties in numerical models. They are due to imperfect external forcing, poorly known parameters, missing physics and discretization errors. Studying these uncertainties and their impact on the simulations is a challenge mostly because of the high dimensionality and non-linear nature of the systems. To deal with uncertainties we propose three axes of research, that are actually linked: sensitivity analysis, parameter estimation and risk assessment. They are based on either stochastic or deterministic methods.
High performance computing
According to the computational cost of our applications, the evolution of high performance computing platforms has to be taken into account for several reasons. Grid computing softwares offer the possibility to manage the large number of model evaluations often required by our mathematical tools. In addition, there is an increase need to propose efficient numerical algorithms specifically designed for new (or future) computing architectures.