I am a PhD student in Numerical Analysis at CERMICS, École des Ponts ParisTech, in partnership with EDF R&D. With my advisors Alexandre Ern (CERMICS) and Jérôme Bonelle (EDF R&D), we are developing the Compatible Discrete Operator (CDO) schemes for the Navier-Stokes equations.
CDO is a framework of low-order numerical methods for PDEs and it belongs to the broad class of compatible, or structure-preserving, discretizations. The key role is played by the Hodge operator, the discrete counterpart of the Hodge-star operator used in differential geometry, which links a primal and a dual mesh. The main advantage of CDO is that it naturally applies to general, polyhedral meshes: an asset that is particularly attractive for industrial applications.
The CDO schemes have been devised and developed at CERMICS and EDF over the last few years. They were originally introduced for the diffusion and Stokes problems and then applied to the transport problem. They have been implemented and validated in the EDF CFD industrial code Code_Saturne.
The aim of this PhD is to extend the CDO framework to the unsteady Navier-Stokes equations for incompressible flows.
I attended a Double Degree program of École Polytechnique and Politecnico di Milano. In both establishments, my major was Applied Mathematics and Computer Sciences, with special interest in PDEs. A detailed resume can be found here (English version).
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