High-order fluid-structure interaction in 2D and 3D. Application to blood flow in arteries

Vincent Chabannes (1) , Gonçalo Pena (2) , Christophe Prud'Homme (3, 1)

1 EDP - Equations aux Dérivées Partielles
2 CMUC - Center for Mathematics [Coimbra]
3 IRMA - Institut de Recherche Mathématique Avancée

This paper addresses the numerical approximation of Fluid Structure Interaction (FSI) problems through the Arbitrary Lagrangian Eulerian (ALE) framework, high order methods and a Dirichlet-Newmann approach for the coupling. The paper is divided in two main parts. The first part concerns the discretization method for the FSI problem. We introduce an improved ALE map, capable of handling curved geometries in 2D and 3D in an unified manner, that is based on a local differential operator. We also propose a minimal CIP stabilization term for the fluid discretization that accounts for a smaller computational effort, while stabilizing the flow regime. The second part is dedicated to validate our numerical strategy through a benchmark and some applications to blood flow in arteries.

Mots clés: Arbitrary Lagrangian Eulerian transformation; Fluid-Structure Interaction; High order methods

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

Vincent Chabannes, Gonçalo Pena, Christophe Prud'Homme. High-order fluid-structure interaction in 2D and 3D. Application to blood flow in arteries. Journal of Computational and Applied Mathematics, 2013, 246, pp.1-9. ⟨10.1016/j.cam.2012.10.006⟩. ⟨hal-00657622v2⟩