Towards a Framework for Non-Linear Thermal Models in Shell Domains

Francisco Chinesta (1) , Adrien Leygue (1) , Marianne Béringhier (2) , Linh Tuan Nguyen (2) , Jean-Claude Grandidier (2) , Bernhard Schrefler (3) , Francisco Pasavento (3)

1 Matériaux, Procédés et Technologie des Composites
2 ISAE-ENSMA - École Nationale Supérieure de Mécanique et d’Aérotechnique [Poitiers]
3 Unipd - Università degli Studi di Padova = University of Padua

Purpose: The purpose of this paper is to solve non-linear parametric thermal models defined in degenerated geometries, such as plate and shell geometries.
Design/methodology/approach: The work presented in this paper is based in a combination of the proper generalized decomposition (PGD) that proceeds to a separated representation of the involved fields and advanced non-linear solvers. A particular emphasis is put on the asymptotic numerical method.
Findings: The authors demonstrate that this approach is valid for computing the solution of challenging thermal models and parametric models.
Originality/value: This is the first time that PGD is combined with advanced non-linear solvers in the context of non-linear transient parametric thermal models.

Mots clés: Mathematical modelling; Numerical methods; Model reduction; Proper generalized decomposition; Thermal model; Shell geometries; Asymptotic numerical method

Domaines: Mécanique [physics.med-ph]; Matériaux

Francisco Chinesta, Adrien Leygue, Marianne Béringhier, Linh Tuan Nguyen, Jean-Claude Grandidier, et al.. Towards a Framework for Non-Linear Thermal Models in Shell Domains. International Journal of Numerical Methods for Heat and Fluid Flow, 2013, 23 (1), pp.55-73. ⟨10.1108/09615531311289105⟩. ⟨hal-01007391⟩