Representation of Cross Sections based on the Wavelet Expansion Method, and Development of a Dedicated Solver
The deterministic solution of the neutron transport equation traditionally relies on the use of the multigroup approximation to discretize the energy variable. The energy domain is divided using a one-dimensional mesh, where the volume elements are called "groups" in neutronics. Within each group, all physical quantities (neutron flux, cross sections, reaction rates, etc.) are projected using piecewise constant functions. This homogenization of cross sections, which are the input data of the transport equation, becomes particularly challenging in the presence of resonant nuclei, whose cross sections vary rapidly over several decades. Correcting for this requires computationally expensive on-the-fly treatments to improve the accuracy of the transport solution.
The goal of this thesis is to eliminate the need for the multigroup approximation in the resonant energy range by applying a Galerkin projection of the continuous energy equation onto an orthonormal wavelet basis. The candidate will develop a generic expansion method adapted to mixtures of resonant isotopes, including preprocessing of cross sections, selection of the wavelet basis, and determination of an efficient coefficient truncation strategy. A dedicated neutron transport solver will be developed, with a focus on efficient algorithmic implementation using advanced programming techniques suited to modern architectures (GPU, Kokkos). The results of this thesis research will be valorized through publications in peer-reviewed international journals and presentations at scientific conferences.
Scaling Up Dislocation Dynamics Simulations for the Study of Nuclear Material Aging
Materials used in nuclear energy production systems are subjected to mechanical, thermal, and irradiation condition, leading to a progressive evolution of their mechanical properties. Understanding and modeling the underlying physical mechanisms involved is a significant challenge.
Dislocation Dynamics simulation aims to understand the behavior of the material at the crystal scale by explicitly simulating the interactions between dislocations, microstructure, and crystal defects induced by irradiation. The CEA, CNRS, and INRIA have been developing the NUMODIS calculation code for this purpose since 2007 (Etcheverry 2015, Blanchard 2017, Durocher 2018).
More specific work on zirconium alloys (Drouet 2014, Gaumé 2017, Noirot 2025) has allowed the validation and enhancement of NUMODIS's ability to handle these individual physical mechanisms by directly comparing them with experiments, through in situ tensile tests under a transmission electron microscope. However, these studies are limited by the current inability of the NUMODIS code to handle a sufficiently high and representative number of defects, and thus to obtain the mechanical behavior of the grain (~10 microns).
The objective of the proposed work is to implement new algorithms to extend the functionalities of the code, propose and test new numerical algorithms, parallelize certain parts still processed sequentially, and ultimately demonstrate the code's ability to simulate the deformation channeling mechanism in an irradiated zirconium grain.
The work will focus primarily on algorithms for calculating velocities, junction formation, and time integration, requiring both mastery of dislocation physics and the corresponding numerical methods. Algorithms for integration recently proposed by Stanford University and LLNL will be implemented and tested for this purpose.
Significant work will also be devoted to adapting the current code (hybrid MPI-OpenMP parallelism) to new computing machines that favor GPU processors, through the adoption of the Kokkos programming model.
Building on both previous experimental and numerical work, this study will conclude with the demonstration of NUMODIS's ability to simulate the channeling mechanism in an irradiated zirconium grain and to identify or even model the main physical and mechanical parameters involved.
At the interface between several fields, the candidate must have a good foundation in physics and/or mechanics, while being comfortable with programming and numerical analysis.
References:
1. Etcheverry Arnaud, Simulation de la dynamique des dislocations à très grande échelle, Université Bordeaux I (2015).
2. Blanchard, Pierre, Algorithmes hiérarchiques rapides pour l’approximation de rang faible des matrices, applications à la physique des matériaux, la géostatistique et l’analyse de données, Université Bordeaux I (2017).
3. Durocher, Arnaud, Simulations massives de dynamique des dislocations : fiabilité et performances sur architectures parallèles et distribuées (2018).
4. Drouet, Julie, Étude expérimentale et modélisation numérique du comportement plastique
des alliages de zirconium sous et après irradiation (2014).
5. Gaumé, Marine, Étude des mécanismes de déformation des alliages de zirconium
après et sous irradiation (2017).
6. Noirot, Pascal, Etude expérimentale et simulation numérique, à l'échelle nanométrique et en temps réel, des mécanismes de déformation des alliages de zirconium après irradiation (2025).
Detailed Numerical investigations on highly-concentrated bubbly flows
To assess the safety of industrial facilities, the CEA develops, validates, and uses thermohydraulic simulation tools. Its research focuses on modelling two-phase flows using various approaches, from the most detailed to the largest system-scale. In order to better understand two-phase flows, Service of Thermal-hydraulic and Fluid Mechanics (STMF) is working on implementing a multi-scale approach in which high-fidelity simulations (DNS, Direct Numerical Simulation of two-phase flows) are used as “numerical experiments” to produce reference data. This data is then averaged to be compared with models used on a larger scale. This approach is applied to high-pressure flows where the bubbly flow regime is maintained even at very high void fractions. The Laboratory of Development at Local Scales (LDEL) belonging to STMF has developed a DNS method (Front-Tracking) implemented in its open-source thermo-hydraulics code: TRUST/TrioCFD [1] (object-oriented code, C++). In several PhDs, it has been used to perform massively parallel simulations to describe interfaces in detail without resorting to models, for example in groups of bubbles (called swarms) [2][3][4].
Currently applied to low-concentration two-phase bubbly flows (volume fraction less than 12%), the objective of this thesis will be to evaluate and use the method at higher void fractions. Reference HPC simulations of bubble swarms will be conducted on national supercomputers up to gas fractions of 40%. The quality of the results will be evaluated before extracting physical models of bubble interactions under these conditions. The objective of these models is to recover the overall dynamics of the bubble swarm at much lower resolutions, thereby enabling the study of larger systems in disequilibrium (external forcing of imposed turbulence generation, imposed average velocity gradient, etc.).
This work is funded by the French ANR, in collaboration with IMFT and LMFL, in parallel with two other theses with which there will be strong interactions. It will be performed at CEA-Saclay, in the STMF/LDEL laboratory. It includes numerical aspects (validation), computer developments (C++), and a physical analysis of the flows obtained.
study of radon diffusion in natural barriers as a function of their water saturation rate, aging levels, and heterogeneity
Radium-226 is one of the main radionuclides remaining in uranium mining residues. However, its direct descendant, radon-222, is a noble gas with a half-life of 3.8 days, which is potentially dangerous to humans if inhaled. In order to minimize the release of this element into the air, mining residues are placed under barriers that limit the diffusive transport of Rn-222 to the surface. The design of these barriers (thickness, materials, water saturation, etc.) should be based on experimental data that quantitatively describe the mobility of radon within them. However, due to the many experimental difficulties associated with studying this radioactive gas, this type of data is rare and often specific to a particular study site, making it difficult to generalize (Fournier et al., 2005; Furhman et al., 2023). However, new investigation techniques have recently emerged that should enable us to deepen our understanding of the diffusive behavior of radon. For example, new devices have been developed to study the diffusion of radionuclides through materials that are partially saturated with water (Savoye et al., 2018; 2024). In addition, spectroscopic autoradiography has recently made it possible to quantify and map alpha emitters present in materials, particularly those in the 238U decay chain and therefore 222Rn (Lefeuvre et al., 2024).
The objective of this doctoral project is therefore to combine these two new approaches to investigate how the diffusion of radon through materials considered as barriers (laterites, bentonite, etc.) can be impacted by the key parameters used to design barriers, namely their degree of water saturation, their level of aging, and their intrinsic heterogeneity.
GPU-ACCELERATED CHARACTERISTICS METHOD FOR 3D NEUTRON TRANSPORT COMBINING THE LINEAR-SURFACE METHOD AND THE AXIAL POLYNOMIAL EXPANSION
This thesis falls within the framework of advancing numerical computation techniques for reactor physics. Specifically, it focuses on the implementation of methods that incorporate higher-order spatial expansions for neutron flux and cross-sections. The primary objective is to accelerate both existing algorithms and those that will be developed through GPU programming. By harnessing the computational power of GPUs, this research aims to enhance the efficiency and accuracy of simulations in reactor physics, thereby contributing to the broader field of nuclear engineering and safety.
Simulation of nuclear glass gels at the mesoscopic scale using a quaternary system.
This research work is part of studies conducted on the long-term behavior of nuclear glass used to immobilize radioactive waste and potentially intended for geological disposal. The challenge lies in understanding the mechanisms of alteration and gel formation (a passivating layer that can slow down the rate of glass alteration) by water and in predicting the kinetics of radionuclide release over the long term.
The proposed simulation approach aims to predict, at a mesoscopic scale, the maturation process of the gel formed during the alteration of glass by water using a ternary “phase field model” composed of silicon, boron, and water (leachate), to which aluminum will be added.
The underlying quaternary mathematical model will consists of a set of coupled nonlinear partial differential equations. These are based on Allen-Cahn and transport equations. The numerical solution of the associated equations is performed using the Lattice Boltzmann Method (LBM) programmed in C++ in the massively parallel LBM_saclay calculation code, which runs on several HPC architectures, both multi-CPUs and multi-GPUs.
The proposed research requires a solid foundation in applied mathematics and programming in order to develop the algorithms necessary for the correct resolution of the new system of strongly coupled equations.
Adjoint sensitivity method applied to industrial modeling of nuclear reactor cores
The objective of this thesis is to lay the foundations for applying the adjoint sensitivity method to industrial modeling of solid fuel nuclear reactor cores. The main topic will be the consideration of the coupling between neutronics, thermohydraulics, heat diffusion in fuel rods, and evolution.
Ductile fracture of irradiated materials under cyclic loadings : Experimental characterization, modelling and numerical simulation
Metal alloys used in industrial applications most often have a ductile fracture mode involving nucleation, growth, and coalescence of internal cavities. The cavities appear as a result of the rupture of inclusions and grow under mechanical loading until they join together, leading to the failure of the structure. Resistance to crack initiation and propagation results from this mechanism. The prediction of toughness therefore requires the modeling of the plasticity of porous materials. The behavior of porous materials has been extensively studied from an experimental, theoretical, and numerical point of view in the case of monotonic mechanical loading under large deformations, leading to constitutive equations that can be used to simulate ductile fracture of structures. The case of cyclic mechanical loading and / or involving low levels of deformation / low number of cycles has been comparatively little studied, even though this type of loading is of interest in industrial applications, for example in the case of earthquakes. In this thesis, the effect of oligocyclic loading on ductile fracture properties will be investigated systematically from an experimental, theoretical, and
numerical point of view. Test campaigns will be carried out on various materials used in nuclear applications and under different mechanical stress conditions in order to quantify the effect of oligocyclic loading on fracture deformation and toughness. At the same time, numerical simulations will be performed to obtain an extensive database on the plastic behavior of porous materials under cyclic loading, with a particular focus on the effects of elasticity, porosity, mechanical loading, and spatial distribution of cavities. These numerical simulations will be used to validate analytical models developed during the thesis to predict the evolution of porosity and yield stress. Finally, the models will be implemented in the form of constitutive equations and used to simulate experimental tests.
Interfacial friction modelling for rod bundle geometry in thermohydraulic system code CATHARE
The thermohydraulic system code CATHARE, developed in CEA with EDF, Framatome and ASNR, permits to simulate normal and accidental behaviours of the hydraulic circuit of a Pressured Water Reactor (PWR). This code is used as a reference in France for transient simulation in nuclear reactor, and is especially used as a support for licensing by EDF and Framatome.
Former studies show the need to improve the validity of the interfacial friction modelling for rod bundle geometry at low pressure or for high hydraulic diameter conditions. Moreover, the current interfacial friction modelling for rod bundle geometry is based on numerous simplifications and a calibration against some steam-water at high temperature experimental data. A new interfacial friction model for Cathare could nowadays be developed using more comprehensive models found in the literature and be calibrated against a larger experimental database
This doctorate aims to improve the interfacial friction modelling for rod bundle geometry by studying the physical phenomena associated with this problem. This work will help implement a more comprehensive model in the CATHARE code following the thesis, thus extending the code's validity conditions to new applications.
Modeling of Wall Condensation Phenomena and Liquid Film Interactions
In this thesis, we focus on modeling mass and energy transfer associated with wall condensation in a turbulent flow of a vapor–noncondensable gas mixture. The flow is two-phase and turbulent, where forced, mixed, and natural convection modes may occur. The framework of this work relies on the RANS approach applied to the compressible Navier–Stokes equations, in which wall condensation is described using semi-analytical wall functions developed in a previous doctoral study cite{iziquel2023}. These functions account for the different convection modes as well as suction and species interdiffusion effects, but neglect the presence of a liquid film.
In the literature, the influence of film formation and flow on mass and heat transfer is often neglected, since it is generally assumed that, in the presence of noncondensable gases, the resistance of the gaseous layer to vapor diffusion is much greater than the thermal resistance of the liquid film.
The objective of this thesis is to improve the prediction of heat and mass transfer by investigating, beyond the thermal resistance of the condensate, the dynamic effect of the liquid and its interaction with the gaseous diffusion layer during wall condensation. The study will first consider laminar film flow, and then attempt to extend the analysis to the turbulent regime.
In the gas phase, the wall-function model developed in cite{iziquel2023} for a binary mixture of vapor and a single noncondensable gas will be extended to mixtures of vapor and $n>1$ noncondensable gases (N2, H2, …), in order to address hydrogen risk issues.
The validation of the implemented models will be carried out using results from separate-effect (SET) and coupled-effect (CET) experiments available in the literature (Huhtiniemi cite{huhti89}, COPAIN, ISP47-MISTRA, ISP47-TOSQAN, RIVA). Comparisons at the CFD scale, using wall functions for condensation neglecting the film, will be performed on benchmark cases from the literature and condensation experiments (COPAIN) to assess the impact of this assumption as well as the improvement provided by the new model in terms of accuracy and computational cost.