Nonlinear fluid-structure interaction problem. Part I: implicit partitioned algorithm, nonlinear stability proof and validation examples

Christophe Kassiotis (1) , Adnan Ibrahimbegovic (2) , Rainer Niekamp (3) , Hermann G. Matthies (3)

1 Saint-Venant - Laboratoire d'Hydraulique Saint-Venant / Saint-Venant Laboratory for Hydraulics
2 LMT - Laboratoire de Mécanique et Technologie
3 WiRe - Institut für Wissenschaftliches Rechnen

In this work we consider the fluid-structure interaction in fully nonlinear setting, where different space discretization can be used. The model problem considers finite elements for structure and finite volume for fluid. The computations for such interaction problem are performed by implicit schemes, and the partitioned algorithm separating fluid from structural iterations. The formal proof is given to find the condition for convergence of this iterative procedure in the fully nonlinear setting. Several validation examples are shown to confirm the proposed convergence criteria of partitioned algorithm. The proposed strategy provides a very suitable basics for code-coupling implementation as discussed in Part II.

Mots clés: fluid-structure interaction; partitioned iterations; nonlinear stability proof

Domaines: Sciences de l'ingénieur [physics]; Mécanique [physics.med-ph]; Mécanique des structures [physics.class-ph]; Physique [physics]; Mécanique [physics]; Mécanique des structures [physics.class-ph]; Sciences de l'ingénieur [physics]; Mécanique [physics.med-ph]; Mécanique des fluides [physics.class-ph]; Physique [physics]; Mécanique [physics]; Mécanique des fluides [physics.class-ph]

Christophe Kassiotis, Adnan Ibrahimbegovic, Rainer Niekamp, Hermann G. Matthies. Nonlinear fluid-structure interaction problem. Part I: implicit partitioned algorithm, nonlinear stability proof and validation examples. Computational Mechanics, 2011, 47, pp.305-323. ⟨10.1007/s00466-010-0545-6⟩. ⟨hal-00601366⟩