Staggered schemes for the Navier-Stokes equations with general meshes
The simulation of the Navier-Stokes equations requires accurate and robust numerical methods that
take into account diffusion operators, gradient and convection terms. Operational approaches have
shown their effectiveness on simplexes. However, in some models or codes
(TrioCF, Flica5), it may be useful to improve the accuracy of solutions locally using an
error estimator or to take into account general meshes. We are here interested in staggered schemes.
This means that the pressure is calculated at the centre of the mesh and the velocities on the edges
(or faces) of the mesh. This results in methods that are naturally accurate at low Mach numbers .
New schemes have recently been presented in this context and have shown their
robustness and accuracy. However, these discretisations can be very costly in terms of memory and
computation time compared with MAC schemes on regular meshes
We are interested in the "gradient" type methods. Some of them are based on a
variational formulation with pressure unknowns at the mesh centres and velocity vector unknowns on
the edges (or faces) of the cells. This approach has been shown to be effective, particularly in terms of
robustness. It should also be noted that an algorithm with the same degrees of freedom as the
MAC methods has been proposed and gives promising results.
The idea would therefore be to combine these two approaches, namely the "gradient" method with the same degrees of freedom as MAC methods. Initially, the focus will be on recovering MAC schemes on regular meshes. Fundamental
questions need to be examined in the case of general meshes: stability, consistency, conditioning of
the system to be inverted, numerical locking. An attempt may also be made to recover the gains in
accuracy using the methods presented in for discretising pressure gradients.
During the course of the thesis, time will be taken to settle the basic problems of this method (first and
second years), both on the theoretical aspects and on the computer implementation. It may be carried
out in the Castem, TrioCFD, Trust or POLYMAC development environments. The focus will be on
application cases that are representative of the community.
Electrical impédanceTomography for the Study of Two-Phase Liquid Metal/Gas Flows
As part of the sustainable use of nuclear energy within a carbon-free energy mix in combination with renewable energies, fourth-generation fast neutron reactors are crucial for closing the fuel cycle and controlling uranium resources. Ensuring the safety of such a sodium-cooled reactor relies for a significant part on the early detection of gas voids in their circuits. In these opaque and metallic environments, optical imaging methods are ineffective, making it necessary to develop innovative techniques.
This PhD project is part of the development of Electrical Impedance Tomography (EIT) applied to liquid metals, a non-intrusive approach enabling the imaging of local conductivity distributions within a flow.
The work will focus on the study of electromagnetic phenomena in two-phase metal/gas systems, in particular the skin effect and eddy currents generated by oscillating fields.
Artificial-intelligence approaches, such as Physics-Informed Neural Networks (PINNs), will be explored to combine numerical learning with physical constraints and will be compared with purely numerical simulations.
The objective is to establish refined physical models adapted to metallic environments and to design inversion methods robust against measurement noise.
Experiments on Galinstan will be conducted to validate the models and demonstrate the feasibility of detecting gas inclusions in a liquid metal.
This research, carried out at IRESNE Institute of CEA Cadarache, will open new perspectives in electromagnetic imaging for opaque, highly conductive media.
Towards a new iterative approach for the efficient modeling of mechanical contact
As part of the modeling and simulation of nuclear fuel behavior across different reactor types, the Institute for Research on Nuclear Energy Systems for Low-Carbon Energy Production (IRESNE) at CEA Cadarache, in partnership with various industrial and academic stakeholders, is developing the PLEIADES software platform for fuel behavior simulation. In this context, the interaction between the fuel and its cladding, the first containment barrier, is a key phenomenon for understanding and predicting the behavior of fuel elements.
The modeling and numerical simulation of mechanical contact phenomena represent a major scientific and technological challenge in solid mechanics, due to the intrinsic complexity of the problem, characterized by its highly nonlinear and non-smooth nature.
To overcome the limitations of classical approaches, such as the penalty or Lagrange multiplier methods, new contact resolution strategies based on iterative fixed-point schemes are currently being explored at the CEA. These approaches offer several advantages: they avoid the direct solution of complex and ill-conditioned systems, significantly improve numerical efficiency, and exhibit very low sensitivity to algorithmic parameters, making them particularly well suited for high-performance computing (HPC) environments.
The objective of this PhD work is to extend these strategies to more complex and realistic situations, by taking into account nonlinear material behaviors and incorporating more sophisticated contact laws, such as friction. Depending on the progress of the work, the final phase will focus on transferring the developments to a high-performance computing (HPC) environment, using a parallel finite element solver.
The project will benefit from internationally recognized expertise in mechanics, applied mathematics, and nuclear fuel simulation, with supervision from CEA researchers and additional academic collaborations (CNRS).
[1] P. Wriggers, "Computational Contact Mechanics", Springer, 2006. doi:10.1007/978-3-540-32609-0.
[2] V. Yastrebov, "Numerical Methods in Contact Mechanics", ISTE Ltd and John Wiley & Sons, 2013. doi: 10.1002/9781118647974
[3] I. Ramière and T. Helfer, “Iterative residual-based vector methods to accelerate fixed point iterations”, Computers & Mathematics with Applications, vol. 70, no. 9, pp. 2210–2226, 2015. doi: 10.1016/j.camwa.2015.08.025.
Investigation of Fuel Damage under Reactivity-Initiated Accident Conditions Using Laser Heating: Correlation with Fission Gas Release
High-power laser heating is an experimental technique developed within the Fuel Study Department that allows the induction of thermal transients on nuclear ceramic samples. It notably makes it possible to reproduce, at the laboratory scale, the thermomechanical conditions representative of an incidental or accidental sequence, in order to study fundamental mechanisms such as fuel cracking or fragmentation.
Indeed, in certain situations, such as a thermal transient of the Reactivity-Initiated Accident (RIA) type, fuel fragmentation (or over-fragmentation) can lead to the release of fission gases and ultimately result in the rupture of the fuel rod cladding.
This type of transient is particularly characterized by a complex spatiotemporal evolution of temperature within the fuel, which is difficult to reproduce at the laboratory scale. To date, only high-power laser heating techniques make it possible to replicate the heating rates reached during such transients and to reproduce the thermomechanical conditions of an RIA at the scale of a manipulable sample in the laboratory.
In this context, the PhD project aims to provide experimental data related to fuel fragmentation and over-fragmentation under Reactivity-Initiated Accident conditions. To achieve this, the student will be required to improve and develop the existing experimental setup and perform experiments aimed at reproducing the thermomechanical conditions leading to fuel fragmentation. A combined experimental/modeling approach will be necessary to optimally design and interpret the experiments. The data obtained will be used to validate the fragmentation models developed at CEA and should also allow projections for integrating these experimental techniques into shielded cells.
The PhD will be conducted within a collaborative framework (CHAIRE MATLASE) between LAMIR (Laboratory for the Analysis of Radionuclide Migration) within the Institute for Research on Nuclear Systems for Low-Carbon Energy Production (IRESNE) at CEA Cadarache, and the ILM team (Laser-Matter Interaction) at the Institut Fresnel in Marseille. The latter will provide expertise in high-power laser/material interactions and optical instrumentation for the development of the system and complex optical diagnostics.
This environment will allow the doctoral student to work in a stimulating scientific setting and to disseminate their research both in France and internationally, through conferences and publications in peer-reviewed journals.
[1]M. Reymond, J. Sercombe, L. Gallais, T. Doualle, and Y. Pontillon, ‘Thermo-mechanical simulations of laser heating experiments on UO2’, Journal of Nuclear Materials, vol. 557, 2021, doi: 10.1016/J.JNUCMAT.2021.153220.
[2]M. Reymond et al., ‘High power laser heating of nuclear ceramics for the generation of controlled spatiotemporal gradients’, J Appl Phys, vol. 134, no. 3, p. 33101, Jul. 2023, doi: 10.1063/5.0146541.
[3]Hugo Fuentes et al., ‘Numerical and experimental simulation of nuclear fuel fragmentation via laser heating of ceramics’, TopFuel 2024. Accessed: Oct. 02, 2025. [Online]. Available: https://www.researchgate.net/publication/386167297_Numerical and experimental simulation of nuclear fuel via laser heating of ceramics
Mechanical behavior of fourth-generation Li-Ion cells, study at the microstructure scale
Competition to increase the energy density of Li-Ion batteries is leading to the consideration of batteries with solid rather than liquid electrolytes. In this regard, sulfur-based electrolytes such as argyrodites are of great interest due to their high ionic conductivity and mechanical properties allowing a simpler manufacturing. Under the effect of lithiation/delithiation cycles, the silicium active particles embedded within this solid electrolyte cause volume variations that can damage the electrode and reduced its lifetime. This is why batteries with solid sulfide electrolytes only cycle properly when kept under pressure. The objective of this thesis is therefore to model these charge-discharge phases pf the battery at the microstructure scale representative of these new solid electrolyte electrodes. At the silicon particle scale, the work will consist of formulating a lithiation-delithiation model based on previous theoretical work and by comparison with available experimental data. Then, 3D models of electrode microstructures consisting of an argyrodite-type solid electrolyte and silicon particles will be established based on existing characterizations (SEM images). Finally, the microscopic mechanical model of lithiation-delithiation will be integrated on these microstructure models, studying in particular the effects of external mechanical loading on the intensity of mechanical interactions at the microstructure scale and the potential locations of damage. These simulation results will be compared with available measurements (macroscopic and local deformation measurements).
These studies will be carried out at CEA Cadarache within the Institute for Research on Nuclear Systems for Low-Carbon Energy Production (IRESNE), in close collaboration with the teams of the Laboratory for Innovation in New Energy Technologies and Nanomaterials (LITEN) at CEA Grenoble.
This framework will allow the PhD student to evolve in a stimulating scientific environment and to promote their research work both in France and abroad through conferences and publications in peer-reviewed journals.
Multi-physics modelling of a light water nuclear reactor operating under natural convection: study of innovative solutions for startup and power control
Among the most recent designs of water-moderated Small Modular Reactors (SMR), several concepts are characterized by natural convection in the primary circuit during normal and abnormal operation, with the aim of increasing the inherent safety of the design. The absence of primary pumps in this type of SMRs significantly complicates the start-up and power increase ramps. This requires the development of specific start-up procedures to heat up the primary water circuit and enable the reactor to reach its nominal conditions, in accordance with safety requirements. These kinds of procedures rely on simulations using validated models to understand the reactor behavior during these phases and define the accessible parameters domain.
The goal of this PhD project is to develop a numerical model capable of simulating the startup of an SMR operating in natural convection, and to contribute to the validation of this model. The PhD study also aims at developing a methodology for reactor control systems optimization, to attain a fast startup while remaining within the prescribed safety criteria.
The analysis of the reactor startup procedure entails two disciplines: thermal-hydraulics and neutronics, which requires the development of multi-physics coupled simulation tools. Three scientific calculation tools in particular will be coupled in the framework of the PhD study: CATHARE3 (reactor system thermal-hydraulics), FLICA5 (core thermal-hydraulics) and APOLLO3 (neutronics).
The PhD student will work in a team of neutron physicists and thermohydraulic engineers at the IRESNE Institute (CEA Cadarache). He/she will develop skills in nuclear reactor physics and modeling.
Development of a transport chemistry model for spent fuel in deep geological disposal under radiolysis of water
The direct storage of spent fuel (SF) represents a potential alternative to reprocessing as a means of managing nuclear waste. The direct storage of spent fuel in a deep geological environment presents a number of scientific challenges, primarily related to the necessity of developing a comprehensive understanding of the processes involved in the dissolution and release of radionuclides. The objective of this thesis is to develop a comprehensive scientific model that can accurately describe the intricate physico-chemical processes involved, such as the radiolysis of water and the interaction between irradiated fuel and its surrounding environment. The objective is to propose an accurate reactive transport model to enhance long-term predictions of storage performance. This thesis employs a back-and-forth process between modeling and experimentation, with the goal of refining the understanding of alteration mechanisms and validating hypotheses with experimental data. Based on existing models, such as the operational radiolytic model, the work will propose improvements to reduce the current simplifying assumptions. The candidate will contribute to major industrial and societal issues related to nuclear waste management and will help to provide solutions to the associated safety issues.
Simulation of crack initiation and propagation in random heterogeneous materials
This PhD thesis is concerned with cracking in nuclear fuels at the microstructure level, a phenomenon that is essential to understand in order to model the behavior of materials under irradiation. Indeed, crack initiation and propagation can lead to the release of fission gases and the formation of fragments inducing fissile matter displacement. Current industrials models are based on simplified representations of the porous microstructure and empirical fracture criteria, which limits their physical accuracy and validation by separate effects.
To overcome these limitations, the proposed thesis work consists of using multi-scale approaches and high-performance computing (HPC) finite element simulations. The main objectives are to define a Representative Volume Element (RVE) for crack initiation in materials with random porosity, improve the failure criteria used in legacy codes and define their uncertainties, and finally establish the domain of validity for analyzing crack propagation in the RVE.
The first line of research consists of rigorously defining the size of the RVE based on local physical variables such as the maximum principal stress. Variance reduction methods will be used to optimize the number of calculations required and estimate the associated errors.
In a second step, simulations performed to determine the RVE size will be used to improve industrial models. The approach will seek to separate the mechanical effects of an isolated bubble from those resulting from interactions between neighboring bubbles. Machine learning techniques may be used to develop this new model. Validation will be based on indirect measurements of cracking, such as gas release observed during thermal annealing, particularly for high burn-up structure (HBS) fuels, where legacy models fail to predict the kinetics of cracking.
Finally, crack propagation within the RVE will be studied using 3D phase field simulations, which allow for detailed representation of the various stages after the crack initiation. The influence of boundary conditions on the RVE will be examined by comparison with simulations on larger domains.
The thesis will be carried out at the Institute for Research on Nuclear Systems for Low-Carbon Energy Production (IRESNE) of the CEA Cadarache, within the PLEIADES platform development team, which is specialized in fuel behavior simulation and multiscale numerical methods. It will be conducted in collaboration with the CNRS/LMA as part of the MISTRAL joint laboratory, notably on aspects relating to the analysis of random medium representativeness and micromechanical simulation of crack propagation.
Study and Modelling of Tritium Speciation from the Outgassing of Tritiated Waste
Tritium, the radioactive isotope of hydrogen, is used as fuel for nuclear fusion, particularly in the ITER research reactor currently under construction in Cadarache (France). Its small size allows it to easily diffuse into materials, which will lead to the production of waste containing tritium after the operational phase of ITER.
To optimize the management of this tritiated waste, the CEA is developing technological solutions aimed at extracting and recycling tritium, as well as limiting its migration to the environment. The effectiveness of these solutions largely depends on the chemical form in which tritium is released. Experience from the outgassing of tritium from various types of waste indicates that it is released in two main chemical forms: tritiated hydrogen (HT) and tritiated water vapor (HTO), in varying proportions.
However, the mechanisms determining the distribution of tritium between these two species are not well understood. Several factors, such as oxygen and water concentrations, the nature and surface state of the waste, and the concentration of tritium, can influence this speciation.
The objectives of this thesis are as follows:
- To identify the phenomena affecting the speciation of tritium during the outgassing of tritiated waste.
- To conduct an experimental study to verify the proposed hypotheses.
- To develop a numerical model to predict the proportions of HT and HTO released, in order to optimize the management of this waste.
The thesis will be conducted within the IRESNE Institute (Institute for Research on Nuclear Systems for Low Carbon Energy Production) at the CEA site in Cadarache, in a laboratory specialised in tritium studies. The PhD candidate will work in a stimulating scientific environment and will have the opportunity to showcase their research work. The candidate must hold an engineering degree or a master’s degree in Chemical Engineering, Process Engineering, or Chemistry.
One-sided communication mechanisms for data decomposition in Monte Carlo particle transport applications
In the context of a Monte Carlo calculation for the evolution of a PWR (pressurized water reactor) core, it is necessary to compute a very large number of neutron-nucleus reaction rates, involving a data volume that can exceed the memory capacity of a compute node on current supercomputers. Within the Tripoli-5 framework, distributed memory architectures have been identified as targets for high-performance computing deployment. To leverage such architectures, data decomposition approaches must be used, particularly for reaction rates. However, with a classical parallelization method, processes have no particular affinity for the rates they host locally; on the contrary, each rate receives contributions uniformly from all processes. Access to decomposed data can be costly when it requires intensive use of communications. Nevertheless, one-sided communication mechanisms, such as MPI RMA (Message Passing Interface, Remote Memory Access), make these accesses easier both in terms of expression and performance.
The objective of this thesis is to propose a method for partial data decomposition relying on one-sided communication mechanisms to access remotely stored data, such as reaction rates. Such an approach will significantly reduce the volume of data stored in memory on each compute node without causing a significant degradation in performance.