Non Incremental Transient Solution of the Rayleigh-Bénard Convection Model Using the PGD

Mohammad Saeid Aghighi (1) , Amine Ammar (1) , Christel Metivier (2) , Magdeleine Normandin (2) , Francisco Chinesta (3)

1 LAMPA - Laboratoire Angevin de Mécanique, Procédés et InnovAtion
2 LR - Laboratoire de rhéologie
3 Matériaux, Procédés et Technologie des Composites

This paper focuses on the non-incremental solution of transient coupled non-linear models, in particular the one related to the Rayleigh-Benard flow problem that models natural thermal convection. For this purpose we are applying the so-called Proper Generalized Decomposition that proceeds by performing space-time separated representations of the different unknown fields involved by the flow model. This non-incremental solution strategy allows significant computational time savings and opens-new perspectives for introducing some flow and/or fluid parameters as extra-coordinates.

Mots clés: Rayleigh–Bénard model; Power-law fluids; Model reduction; Non-incremental solution; Proper Generalized Decomposition

Domaines: Mécanique des fluides [physics.class-ph]; Matériaux

Mohammad Saeid Aghighi, Amine Ammar, Christel Metivier, Magdeleine Normandin, Francisco Chinesta. Non Incremental Transient Solution of the Rayleigh-Bénard Convection Model Using the PGD. Journal of Non-Newtonian Fluid Mechanics, 2013, 200, pp.65-78. ⟨10.1016/j.jnnfm.2012.11.007⟩. ⟨hal-01007106⟩