From Domain Decomposition to Model Reduction for Large Nonlinear Structures

Bertrand Leturcq; Patrick Le Tallec

doi:10.5802/crmeca.168

From Domain Decomposition to Model Reduction for Large Nonlinear Structures
[De la décomposition de domaine à la réduction de modèle pour les grandes structures non linéaires]

Bertrand Leturcq ¹ ; Patrick Le Tallec ²

¹ Université Paris-Saclay, CEA, Service d’études mécaniques et thermiques, 91191 Gif-sur-Yvette, France
² M3DISIM/LMS, École Polytechnique, CNRS, Institut Polytechnique de Paris, 91128 Palaiseau, France

Comptes Rendus. Mécanique, Online first (2023), pp. 1-17.

Résumé
Abstract

La simulation numérique de problèmes multi-échelles et multi-physiques nécessite des outils performants de localisation spatiale et de réduction de modèle. Une stratégie générale combinant la décomposition de domaine et l’analyse de champ de transformation non uniforme (NTFA) est proposée ici pour la simulation d’assemblages de combustible nucléaire à l’échelle d’un réacteur nucléaire complet. Le modèle au niveau du sous-domaine résout le problème élastique complet mais avec un chargement non linéaire réduit, basé sur des conditions aux limites simplifiées, des règles d’écoulement de fluage réduites, des conditions de contact préservant le signe projeté et une loi de frottement réduit de type NTFA pour obtenir l’évolution de chaque mode de glissement. Avec cette réduction de chargement, la solution locale peut être obtenue explicitement à partir d’un petit ensemble de solutions élastiques élémentaires précalculées. Les tests numériques indiquent qu’une réduction considérable des coûts (un facteur de 50 à 1000) peut être obtenue tout en préservant la précision du calcul.

The numerical simulation of multiscale and multiphysics problems requires efficient tools for spatial localization and model reduction. A general strategy combining Domain Decomposition and Nonuniform Transformation Field Analysis (NTFA) is proposed herein for the simulation of nuclear fuel assemblies at the scale of a full nuclear reactor. The model at subdomain level solves the full elastic problem but with a reduced nonlinear loading, based on simplified boundary conditions, reduced creep flow rules, projected sign preserving contact conditions, and a NTFA like reduced friction law to get the evolution of each slipping mode. With this loading reduction, the local solution can be explicitly obtained from a small set of precomputed elementary elastic solutions. The numerical tests indicate that considerable cost reduction (a factor of 50 to 1000) can be achieved while preserving engineering accuracy.

Reçu le : 2022-12-21
Accepté le : 2023-01-02
Première publication : 2023-05-15

DOI : 10.5802/crmeca.168

Keywords: Model reduction, Domain decomposition, Nuclear fuel assemblies, creep, contact
Mot clés : Réduction de modèle, Décomposition de domaines, Assemblage de combustible, fluage, contact

Affiliations des auteurs :

Bertrand Leturcq ¹ ; Patrick Le Tallec ²

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Bertrand Leturcq and Patrick Le Tallec},
     title = {From {Domain} {Decomposition} to {Model} {Reduction} for {Large} {Nonlinear} {Structures}},
     journal = {Comptes Rendus. M\'ecanique},
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     year = {2023},
     doi = {10.5802/crmeca.168},
     language = {en},
     note = {Online first},
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Bertrand Leturcq; Patrick Le Tallec. From Domain Decomposition to Model Reduction for Large Nonlinear Structures. Comptes Rendus. Mécanique, Online first (2023), pp. 1-17. doi : 10.5802/crmeca.168.

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