Research

My research activities are very varied and evolve according to collaborations. In summary, I try to develop some numerical tools using finite “things” (element or volume) applied to some natural phenomena highly non-linear and often coupled. All my computer developments were integrated until 2006 in the “SIC” research software, which is a toolbox for PDEs, then in the EOLENS & CM2 codes, then in the BBAMR code and now in the CERF & Rivage software platforms.

Wave propagation and wave breaking

In collaboration with P. Helluy, we have developed and validated bi-fluid flow model at low Mach applied to the propagation and breaking of a solitary wave. This model is integrated in a parallelized finite volume code on unstructured mesh. We have focused on optimizing the computing time in order to be able to perform 3D simulations (example). Subsequently, in collaboration with MIO laboratory and Principia company, this work continued with the study of breaking in the presence of macro-roughness (PhD A.N. Sambe, some examples here). I improved this model by introducing an efficient interface sharpening method and a block based adaptive mesh refinement method (BB-AMR), using the numerical production of entropy as a refinement criterion. Subsequently, Saint-Venant or relaxed SGN propagation models were integrated and coupled to the bi-fluid model (PhD K. Pons).

Fluid-Structure Interaction

As part of the regional project on the Hydro/aerodynamic Behavior of Floating Wind Turbines (CHEF), we developed a Fluid-Structure Interaction model based on a penalization Eulerian approach (PhD T. Altazin, some examples here). This approach is also very useful for imposing mobile or non-mobile boundaries, it is integrated in the BBAMR and CERF codes. Some examples here.

Erosion

In collaboration with INRAE, we study internal erosion phenomena. The Water/soil interface is modeled by a Level Set method coupled with a fictitious domain technique (PhD D. Lachouette, some examples here). In order to take advantage of the BB-AMR mesh refinement, we have developed DDFV (Discrete Duality Finite Volume) schemes which are a generalization of Mac schemes on non-conforming and unstructured meshes (PhD J. Lakhlili, CM2 code). As part of the CERF project, we are also developing erosion models for Eulerian or shallow water flows. Some examples here.

Flow in non-saturated porous media

We study flow phenomena in sandy beaches. This flow in non-saturated porous media is treated by a discontinuous finite element scheme and dynamic mesh in order to capture the very strong nonlinearities inherent in the advancement of the saturation front (PhD J-B. Clément, some examples here). This model has been improved and strongly coupled to shallow water flows (PhD C. Poussel, some examples here). These models are integrated in the Rivage code.