In many industrial sectors, rapid transient phenomena are involved in accident scenarios. An example in the nuclear industry is the Loss of Primary Coolant Accident, in which an expansion wave propagates through the primary circuit of a Pressurized Water Reactor, potentially vaporizing the primary fluid and causing structural damage. Nowadays, the simulation of these fast transient phenomena relies mainly on "explicit" time integration algorithms, as they enable robust and efficient treatment of these problems, which are generally highly non-linear. Unfortunately, because of the stability constraints imposed on time steps, these approaches struggle to calculate steady-state regimes. Faced with this difficulty, in many cases, the kinematic quantities and internal stresses of the steady state of the system under consideration at the time of occurrence of the simulated transient phenomenon are neglected.

Furthermore, the applications in question involve solid structures interacting with the fluid, undergoing large-scale deformation and possibly fragmenting. A immersed boundary technique known as MBM (Mediating Body Method [1]) recently developed at the CEA enables structures with complex geometries and/or undergoing large deformations to be processed efficiently and robustly. However, this coupling between fluid and solid structure has only been considered in the context of "fast" transient phenomena treated by "explicit" time integrators.

The final objective of the proposed thesis is to carry out a nominal regime calculation followed by a transient calculation in a context of fluid/immersed-structure interaction. The transient phase of the calculation is necessarily based on "explicit" time integration and involves the MBM fluid/structure interaction technique. In order to minimize numerical disturbances during the transition between nominal and transient regimes, the calculation of the nominal regime should be based on the same numerical model as the transient calculation, and therefore also rely on an adaptation of the MBM method.

Recent work defined an efficient and robust strategy for calculating steady states for compressible flows, based on "implicit" time integration. However, although generic, this approach has so far only been tested in the case of perfect gases, and in the absence of viscosity.

On the basis of this initial work, the main technical challenges of this thesis are 1) to validate and possibly adapt the methodology for more complex fluids (in particular water), 2) to introduce and adapt the MBM method for fluid-structure interaction in this steady-state calculation strategy, 3) to introduce fluid viscosity, in particular within the framework of the MBM method initially developed for non-viscous fluids. At the end of this work, implicit/explicit transition demonstration calculations with fluid-structure interaction will be implemented and analyzed.

An internship can be arranged in preparation for thesis work, depending on the candidate's wishes.

[1] Jamond, O., & Beccantini, A. (2019). An embedded boundary method for an inviscid compressible flow coupled to deformable thin structures: The mediating body method. International Journal for Numerical Methods in Engineering, 119(5), 305-333.

Steam generators are essential components of nuclear reactors whose main function is heat exchange. The chemical species present in steam generators are the cause of many parasitic phenomena (clogging, fouling, sludge deposition, etc.). Numerical simulation of species transport, taking into account the migration of chemical species and exchanges between species, both intra- and inter-phase, will allow a better understanding and better management of these problems. Numerical resolution of species transport systems presents real difficulties, in particular the management of the appearance and total disappearance of certain species, high void rates, as well as rapidly excessive calculation times.

While relying on the new code for nuclear components developed at STMF, the thesis will address the following three main scientific issues:
• Upstream, the analysis of numerical methods allowing in particular the management of evanescence, as mentioned above, and thermo-hydraulic modeling at high void rates. For this, we will rely on the PolyMAC and PolyVEF numerical schemes, already implemented in the component code.
• The physical modeling of a steam generator in the new component code, via the addition (in C++) of correlations specific to steam generators, the completion of the state laws already available, etc..
• The determination of the major chemical species to be transported, in order to be able to take into account both thermo-hydraulics and chemistry. The algorithmic coupling between thermo-hydraulics and chemistry, taking into account feedback, being the long-term objective.

While benefiting from the existing parallelization of the component code, the thermo-hydraulic and chemical modeling will be done taking into account the constraints on computation times.

This thesis aims to explore the application of machine learning techniques to improve turbulence modeling and numerical simulations in fluid mechanics. More specifically, we are interested in the application of artificial neural networks (ANNs) for large eddy simulation. The latter is a modeling approach that focuses on the direct resolution of large turbulent structures, while modeling small scales by a subgrid-scale model. It requires a certain ratio of total kinetic energy to be resolved. However, this ratio may be difficult to achieve for industrial simulations due to the high computational cost, leading to under-resolved simulations. We aim to improve the latter by focusing work along two main axes: 1) Using ANNs to build generic sub-mesh models that outperform analytical models and compensate for coarse spatial discretization; 2) Training ANNs to learn wall models. One of the main challenges is the ability of the new models to generalize correctly in configurations different from those used during training. Thus, taking into account the different sources and quantification of uncertainties plays a vital role in improving the reliability and robustness of machine-learned models.

Many industrial systems involve structures immersed in dense fluids. Examples include the submarine industry, or, more specifically, certain 4th generation nuclear reactors using coolant fluids such as sodium or salt mixtures. The effect of the interaction of the surrounding fluid on the contact forces between structures is a phenomenon of primary importance, particularly during accidental transient scenarios that can generate large displacements of structures whose residual integrity must be demonstrated for safety purposes.

In the context of this thesis, we are particularly interested in modeling the rapid impact of a structural fragment immersed in a fluid against a wall, resulting, for example, from an explosive phenomenon in a nuclear reactor vessel cooled by sodium. In this context, the sodium, modeled as a compressible fluid, is treated numerically using a volume-finite approach. The reactor's internal structures are treated using a finite-element approach. In order to deal with large structural displacements and possible fracturing, “immersed boundary” techniques are used for fluid-structure interaction.

The aim of this thesis is to define an innovative numerical method to better simulate the fluid film between two structures that come into contact in this context. Initially, we will focus on identifying the physical characteristics of the flow at the level of the fluid film (compressibility, viscosity, etc.) that have the greatest influence on the kinematics of the structures. Secondly, the main challenge of this thesis will be to improve current numerical methods in order to represent the flow characteristics of the fluid film as accurately as possible.

The proposed thesis will be carried out at CEA Saclay, in close collaboration with the EM2C laboratory at CentraleSupélec, within the environment of the Université Paris-Saclay. The PhD student will be immersed in a team with recognized expertise in transient simulations of fluid-structure interaction.