In this thesis we would like to contribute to the development of mathematical and numerical tools, appropriate for modelling of multi-scale, multi-physics and strongly coupled systems. More precisely, we plan to study geometric structures that appear naturally for such problems, and numerical methods that “respect” these structures. We also pay attention to efficient implementation of the designed algorithms. Our range of applications is motivated by mechanical problems, and fluid–structure interaction in particular, but the framework is not limited to those.
Description of the project Supervision and team
The PhD student will be supervised by Vladimir Salnikov (CNRS Researcher) and Aziz Hamdouni (Professor), both from La Rochelle University, France.
He/she will be working in the Laboratory of Engineering Sciences for Environment (LaSIE) in the La Rochelle University (https://lasie.univ-larochelle.fr/), team “Mathematical and Numerical Methods” (https://lasie.univ-larochelle.fr/E1-M2N).
Even if nowadays it is relatively easy to have access to serious computational resources, development of efficient methods remains a real challenge. Let us just name an example in this context :
In the fluid–structure interaction problem, the main difficulty is the size of data one needs to handle. On the one hand, one needs to take into account the geometry of the interface between the solid and the fluid, thus, introduce a very fine mesh. It is also important to have good discretization in time to capture the dynamics and especially deformations of the solid, that can influence the spacial mesh as well. On the other hand studied systems are usually very large, if one compares them with the scale of the interface and deformations. One thus needs to work with enormous mass of information, that results in algorithmic and technological issues, meaning that the“brute-force” approach of increasing the size of the calculator is not efficient. For this mentioned case, as well as for many others, one needs reliable numerical schemes, preferably with reasonable computational cost and necessarily scalable.
Candidate and tasks
We are searching either for a candidate specializing in mathematics (differential geometry or math- ematical aspects of theoretical physics), capable to understand problems coming from mechanics and having some knowledge about numerical methods, or for a candidate specializing in mechanics having a solid general mathematics background and a capacity to master geometric topics. He/she will work on some concrete examples of mechanical systems within the approach described in the introduction. Ideally, that would include the “full cycle” of formalizing the model, spelling-out the geometric coun- terpart of the governing differential equations, designing and implementing the appropriate numerical methods. Some programming skills are certainly useful but not strictly mandatory