Journées scientifiques 2023 du GdR MaNu

Liste des Contributions

1. Mathematical modelling and simulation of corrosion in an underground repository

Claire Chainais (Université Lille 1 Sciences et Technologies)

23/10/2023 14:30

The modelling and the numerical simulation of corrosion take part in the general description of the nuclear waste repository. After a brief introduction of the context of the study, I will introduce in a first part the Diffusion Poisson Coupled Model (Electrochemical Acta 2010) that describes the transport of charges in an oxide layer. I will review the main results obtained for the DPCM and...

2. Mathematical modelling and simulation of corrosion in an underground repository

Claire Chainais (Université Lille 1 Sciences et Technologies)

23/10/2023 16:30

The modelling and the numerical simulation of corrosion take part in the general description of the nuclear waste repository. After a brief introduction of the context of the study, I will introduce in a first part the Diffusion Poisson Coupled Model (Electrochemical Acta 2010) that describes the transport of charges in an oxide layer. I will review the main results obtained for the DPCM and...

22. Session poster

23/10/2023 18:00

3. An advection-diffusion equation within a nonlinear degenerate thermal diffusion in a diffuse interface framework (part I)

Gloria Faccanoni (Université de Toulon)

24/10/2023 09:00

This study is motivated by the modeling of liquid-vapor flows with phase transitions, specifically focusing on the evolution of coolant within a heat exchanger, such as the core of a Pressurized Water Reactor. We investigate an advection-diffusion equation incorporating a degenerate and nonlinear thermal diffusion coefficient. The degeneracy arises from a liquid-vapor mixture at saturation,...

4. An advection-diffusion equation within a nonlinear degenerate thermal diffusion in a diffuse interface framework (part II)

Gloria Faccanoni (Université de Toulon)

24/10/2023 11:00

This study is motivated by the modeling of liquid-vapor flows with phase transitions, specifically focusing on the evolution of coolant within a heat exchanger, such as the core of a Pressurized Water Reactor. We investigate an advection-diffusion equation incorporating a degenerate and nonlinear thermal diffusion coefficient. The degeneracy arises from a liquid-vapor mixture at saturation,...

5. Méthodes de bases réduites pour des problèmes aux valeurs propres non-symmétriques: application à la neutronique

Virginie Ehrlacher (École des Ponts ParisTech)

24/10/2023 14:00

Les calculs de criticité en neutronique ont pour objectif de déterminer si un réacteur nucléaire restera stable étant donné une configuration donnée du coeur du réacteur. D'un point de vue mathématique, ces types de calcul nécessitent de résoudre un problème aux valeurs propres non symmétriques pour des opérateurs vérifiant les hypothèses de théorème de Krein-Rutman. Il est très important...

6. Equation d’advection-convection du titre massique d’une espèce : schémas volumes finis vérifiant le principe du maximum discret sans contrainte sur le pas de temps

Gauthier Lazare (EDF R&D)

24/10/2023 15:00

Dans un écoulement diphasique déséquilibré en vitesse, l’évolution du titre massique vapeur 𝑦 peut être modélisé par une équation d’advection-convection non linéaire avec un débit 𝒒𝒚 = 𝒒 + (1 − 𝑦)𝒒𝒓 où 𝒒 est le débit de mélange et 𝒒𝒓 est le débit relatif. Cette équation peut être complétée par un terme source de retour à l’équilibre 𝑦̅ caractérisé par un temps de relaxation 𝜏.

Après avoir...

7. Staggered finite volumes methods on general meshes

Pierre-Loïc Bacq (CEA)

24/10/2023 16:00

We consider the discretization of incompressible Navier-Stokes equations. It is well known that staggered discretizations such as the MAC scheme are robust in practice [1]. In particular, they mitigate efficiently potential spurious modes that are commonly encountered with collocated meshes. However, such discretizations are restricted to Cartesian meshes which are rather limited in...

8. Relaxation process in an immiscible three-phase flow model

Guillaume Jomée (EDF R&D)

24/10/2023 16:30

This presentation deals with the numerical modeling of immiscible three-phase flows. The main focus here is on the numerical treatment of the source terms of the model. A new scheme based on a more coupled approach than the preexisting fractional step strategy is presented. Properties of this scheme are given. Numerical applications highlight the benefits of this scheme in terms of both...

24. Session poster

24/10/2023 17:00

10. Les SMRs, un nouveau modèle de nucléaire : contexte et enjeux associés

Pierre Gavoille (CEA)

25/10/2023 09:00

Depuis quelques années, les études de nouveaux concepts de réacteurs, les SMRs (Small Modular Reactors), ont pris de l’ampleur, prenant le contrepied de la course à la puissance unitaire des réacteurs constatée jusqu’alors. L’idée sous-jacente est de produire des réacteurs de petite taille unitaire, dont la construction se ferait en série par modules assemblés sur site. Au travers de ce...

9. Les SMRs : concepts et axes de R&D multiples

André Bergeron (CEA)

25/10/2023 09:45

Depuis quelques années le mot SMR est évoqué de plus en plus souvent dans les médias quand on évoque les développements actuels de l’énergie nucléaire.

Le SMR est un petit réacteur modulaire. Le concept de petit réacteur n’est pas nouveau mais son association en batterie sur un même site, facilitée notamment par la modularité, permet d’adapter la puissance électrique ou la chaleur produite...

11. Réacteurs innovants: le nucléaire en mode “startup"

Antoine Gerschenfeld (CEA & Stellaria)

25/10/2023 11:00

12. Discussion et présentation du futur réseau thématique

Nicolas Seguin (Inria), Olga Mula (TU Eindhoven)

25/10/2023 11:45

13. On classical and modern approximations for neutron transport in a unified framework

Matthias Schlottbom (University of Twente)

26/10/2023 09:00

In this lecture we consider the numerical approximation of the neutron transport equation.
First, we will model the relevant physical processes using integro-partial differential equations.
Next, we discuss classical approximation techniques, such as Legendre expansions or the discrete ordinates method, which have mostly been treated independently. We present a variational framework that...

14. On classical and modern approximations for neutron transport in a unified framework

Matthias Schlottbom (University of Twente)

26/10/2023 11:00

In this lecture we consider the numerical approximation of the neutron transport equation.
First, we will model the relevant physical processes using integro-partial differential equations.
Next, we discuss classical approximation techniques, such as Legendre expansions or the discrete ordinates method, which have mostly been treated independently. We present a variational framework that...

15. The Nuclear Engineering MOdelling (NEMO) group at Politecnico di Torino: a focus on reactor physics studies and research

Sandra Dulla (Politecnico di Torino)

26/10/2023 14:00

The Nuclear Engineering MOdelling (NEMO) group at Politecnico di Torino is working since many years on various modelling aspects of nuclear engineering, covering both fission and fusion applications, thanks to the active participation of its members to a variety of national and international research projects.
In this seminar, a brief overview of the NEMO group activities will be given. Then,...

16. Robust resolution of chemical equilibrium by the methods of parametrization and cartesian representations

Maxime Jonval (Inria)

26/10/2023 15:00

The calculation of chemical equilibrium of a single-phase system amounts to finding the quantities of chemical species that minimize the Gibbs free energy under constant temperature and pressure, with mass conservation and non-negativity constraints. This problem can be expressed as the solution of a nonlinear system of equations that presents many numerical difficulties. In particular,...

17. Convergence of a Finite-Volume scheme for a heat equation with multiplicative noise

Flore Nabet (École polytechnique)

26/10/2023 16:00

In this talk we will focus on the finite volume approximation of the heat equation with a continuous Lipschitz multiplicative noise. The aim is to prove the convergence of the numerical scheme to the unique variational solution of the continuous problem.
To this end, we adapt the method based on Prokhorov's theorem to obtain a first convergence result, then Skorokhod's representation theorem...

18. A new exact and scalable model for multitask gaussian process regression: application to the reconstruction of nuclear data in neutronics codes

Olivier Truffinet (CEA)

26/10/2023 17:00

Multitask gaussian processes are popular tools for learning several correlated outputs, and find applications for instance in medicine, robotics, earth sciences, etc. In this field, the Linear Model of Co-regionalization (LMC) is a very general model, which expressivity and conceptual simplicity are appealing; however, its cubic complexity in both the number of datapoints and number of tasks...

20. An introduction to Uncertainty Quantification: Bayesian inference, rare event estimation and dimension reduction

Olivier Zahm (Inria)

27/10/2023 08:45

In the first part of this lecture, we will introduce the basics of uncertainty quantification (UQ) for complex and multi-dimensional models. Our emphasis will be on addressing Bayesian inverse problems and rare events estimation. In the second part, we will demonstrate how employing gradient-based dimension reduction techniques allows for the effective identification of pertinent subspaces in...

21. An introduction to Uncertainty Quantification: Bayesian inference, rare event estimation and dimension reduction

Olivier Zahm (Inria)

27/10/2023 10:30

In the first part of this lecture, we will introduce the basics of uncertainty quantification (UQ) for complex and multi-dimensional models. Our emphasis will be on addressing Bayesian inverse problems and rare events estimation. In the second part, we will demonstrate how employing gradient-based dimension reduction techniques allows for the effective identification of pertinent subspaces in...

23. Exposé de recherche

19. Research talk