Assisted generation of complex computational kernels in solid mechanics

The behavior laws used in numerical simulations describe the physical characteristics of simulated materials. As our understanding of these materials evolves, the complexity of these laws increases. Integrating these laws is a critical step for the performance and robustness of scientific computations. Therefore, this step can lead to intrusive and complex developments in the code.

Many digital platforms, such as FEniCS, FireDrake, FreeFEM, and Comsol, offer Just-In-Time (JIT) code generation techniques to handle various physics. This JIT approach significantly reduces the time required to implement new simulations, providing great versatility to the user. Additionally, it allows for optimization specific to the cases being treated and facilitates porting to various architectures (CPU or GPU). Finally, this approach hides implementation details; any changes in these details are invisible to the user and absorbed by the code generation layer.

However, these techniques are generally limited to the assembly steps of the linear systems to be solved and do not include the crucial step of integrating behavior laws.

Inspired by the successful experience of the open-source project mgis.fenics [1], this thesis aims to develop a Just-In-Time code generation solution dedicated to the next-generation structural mechanics code Manta [2], developed by CEA. The objective is to enable strong coupling with behavior laws generated by MFront [3], thereby improving the flexibility, performance, and robustness of numerical simulations.

The selected PhD candidate should have a solid background in computational science and a strong interest in numerical simulation and C++ programming. They should be capable of working independently and demonstrate initiative. The doctoral student will benefit from guidance from the developers of MFront and Manta (CEA), as well as the developers of the A-Set code (a collaboration between Mines-Paris Tech, Onera, and Safran). This collaboration within a multidisciplinary team will provide a stimulating and enriching environment for the candidate.

Furthermore, the thesis work will be enhanced by the opportunity to participate in conferences and publish articles in peer-reviewed scientific journals, offering national and international visibility to the thesis results.

The PhD will take place at CEA Cadarache, in south-eastern France, in the Nuclear Fuel Studies Department of the Institute for Research on Nuclear Systems for Low-Carbon Energy Production (IRESNE)[4]. The host laboratory is the LMPC, whose role is to contribute to the development of the physical components of the PLEIADES digital platform [5], co-developed by CEA and EDF.

[1] https://thelfer.github.io/mgis/web/mgis_fenics.html
[2] MANTA : un code HPC généraliste pour la simulation de problèmes complexes en mécanique. https://hal.science/hal-03688160
[3] https://thelfer.github.io/tfel/web/index.html
[4] https://www.cea.fr/energies/iresne/Pages/Accueil.aspx
[5] PLEIADES: A numerical framework dedicated to the multiphysics and multiscale nuclear fuel behavior simulation https://www.sciencedirect.com/science/article/pii/S0306454924002408

Multiphysic modeling of sintering of nuclear fuel pellet: effect of atmosphere on shrinkage kinetics

Uranium dioxide (UO2) fuels used in nuclear power plants are ceramics, for which solid-phase sintering is a key manufacturing step. The sintering stage involves heat treatment under controlled partial O2 pressure that induces coarsening of UO2 grain and then consolidation and densification of the material. Grain growth induce material densification and macroscopic shrinkage of the pellet. If the green pellet (powder obtained by pressing, manufacturing step before sintering) admit a highly heterogeneous density, this gradient leading to differential shrinkage and the appearance of defects. Furthermore, the sintering atmosphere, i.e., the gas composition in the furnace, impacts grain growth kinetics and thus the shrinkage of the pellet. Advanced simulation is the key to improving understanding of the mechanisms observed as well as optimizing manufacturing cycles.

The PhD thesis aims at developing a Thermo-chemo-mechanical modeling of sintering to simulate the impact of the gas composition and properties on the pellet densification. This scale will enable us to take into account not only the density gradients resulting from pressing, but also the oxygen diffusion kinetics that have a local impact on the densification rate, which in turn impacts the transport process. Therefore, a multiphysics coupling phenomenon has to be modelled and simulated.

This thesis will be conducted within the MISTRAL joint laboratory (Aix-Marseille Université/CNRS/Centrale Marseille CEA-Cadarache IRESNE institute). The PhD student will leverage his results through publications and participation in conferences and will have gained strong skills and expertise in a wide range of academic and industrial sectors.