Development and Calibration of an Hyperbolic Phase-Field Model for Explicit Dynamic Fracture Simulation
The numerical simulation of the mechanical behavior of structures subjected to dynamic loads is a major challenge in the design and safety assessment of industrial systems. In the nuclear industry, this issue is particularly critical for the analysis of severe accident scenarios in Pressurized Water Reactors (PWRs) such as the Loss of Coolant Accident (LOCA), during which the rapid depressurization of the primary circuit can lead to pipe rupture. Developing physically representative models and robust, efficient numerical methods to simulate such phenomena with high fidelity remains an active area of research.
Among the existing non-local approaches, phase-field methods have emerged as a interesting framework for simulating crack initiation and propagation. However, most current studies are limited to quasi-static or low-rate dynamic problems, where wave propagation effects can be neglected. In contrast, high-rate dynamic regimes - relevant to accidental loads - require explicit time integration schemes for the mechanical equations, which are sensitive to the stability condition. The classical elliptic formulation of the damage evolution equation is therefore not ideally suited to this context. To address these limitations, recent works have proposed and assessed hyperbolic phase-field formulations, which are naturally more compatible with explicit dynamics and allow better control of crack propagation kinetics.
The objective of this PhD thesis is to advance this emerging modeling strategy through three main research directions:
- Extend the theoretical framework of the hyperbolic phase-field formulation for damage within the context of generalized standard materials, which is suitable for ductile fracture;
- Propose solutions to the negative impact of damage evolution on the critical time step;
- Rely on an dynamic fracture experimental test campaign to calibrate simulations, with a focus on the identification of damage-related parameters
This research is to be conducted in collaboration between CEA Paris-Saclay, ONERA Lille, and Sorbonne Université, with CEA as the main host institution.
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.
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.
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.
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.
Design of asynchronous algorithms for solving the neutron transport equation on massively parallel and heterogeneous architectures
This PhD thesis work aims at designing an efficient solver for the solution to the neutron transport equation in Cartesian and hexagonal geometries for heterogeneous and massively parallel architectures. This goal can be achieved with the design of optimal algorithms with parallel and asynchronous programming models.
The industrial framework for this work is in solving the Boltzmann equation associated to the transportof neutrons in a nuclear reactor core. At present, more and more modern simulation codes employ an upwind discontinuous Galerkin finite element scheme for Cartesian and hexagonal meshes of the required domain.This work extends previous research which have been carried out recently to explore the solving step ondistributed computing architectures which we have not yet tackled in our context. It will require the cou-pling of algorithmic and numerical strategies along with programming model which allows an asynchronousparallelism framework to solve the transport equation efficiently.
This research work will be part of the numerical simulation of nuclear reactors. These multiphysics computations are very expensive as they require time-dependent neutron transport calculations for the severe power excursions for instance. The strategy proposed in this research endeavour will decrease thecomputational burden and time for a given accuracy, and coupled to a massively parallel and asynchronousmodel, may define an efficient neutronic solver for multiphysics applications.
Through this PhD research work, the candidate will be able to apply for research vacancies in highperformance numerical simulation for complex physical problems.
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.