Empirical Natural Closure Relation for Short Fiber Suspension Models

Etienne Prulière (1) , Amine Ammar (1) , Francisco Chinesta (2)

1 LR - Laboratoire de rhéologie
2 LMSP - Laboratoire de Mécanique des Systèmes et des Procédés

This work focuses on the resolution of the Fokker-Planck equation that governs the evolution of the fibers orientation distribution. To reduce the computing time, that equation is solved along some flow trajectories in order to extract the significant information of the solution from the application of the Karhunen-Loève decomposition. Now, from this information one could solve the Fokker-Planck equation everywhere in the flow domain or simply adjust a closure relation that becomes optimal for such flow, solving the evolution of some orientation moments which require a less amount of computation. This paper focuses on this last strategy. For this purpose we start introducing the Karhunen-Loève decomposition that is applied later to automatically extract the main solution characteristics for adjusting empirically a natural closure relation.

Mots clés: Short fiber suspensions; Closure relations; Numerical modeling; Model reduction; Karhunen-Loève decomposition

Domaines: Intelligence artificielle [cs.AI]; Mécanique [physics.med-ph]

Etienne Prulière, Amine Ammar, Francisco Chinesta. Empirical Natural Closure Relation for Short Fiber Suspension Models. International Journal of Forming Processes, 2007, 10/3, pp.361-385. ⟨10.3166/ijfp.10.361-385⟩. ⟨hal-00742450⟩