Mathematical and Numerical Analysis of some fluid-structure interaction problems

Céline Grandmont (1, 2) , Sárka Necasová (3) , Maria Lukacova-Medvid'Ova (4)

1 REO - Numerical simulation of biological flows
2 LJLL - Laboratoire Jacques-Louis Lions
3 Mathematical Institute [Praha] - Academy of Sciences
4 Technical University Hamburg Harburg [Hamburg]

In this chapter we deal with some specific existence and numerical results applied to a 2D/1D fluid-structure coupled model, for an incompressible fluid and a thin elastic structure. We will try to underline some of the mathematical and numeri- cal difficulties that one may face when studying this kind of problems such as the geometrical nonlinearities or the added mass effect. In particular we will try to underline the link between the strategies of proof of weak or strong solutions and the possible algorithms to discretize these type of coupled problems

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Biomécanique [physics.med-ph]; Biomécanique [physics.med-ph]

Céline Grandmont, Sárka Necasová, Maria Lukacova-Medvid'Ova. Mathematical and Numerical Analysis of some fluid-structure interaction problems. Bodnár, Tomáš and Galdi, Giovanni P. and Nečasová, Šárka. Fluid-Structure interaction and biomedical applications, Springer, 2014, Advances in Mathematical Fluid Mechanics, 978-3-0348-0821-7. ⟨hal-00917363⟩