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.