Fluid–structure interaction and multi-body contact: Application to aortic valves

Abstract

We present a partitioned procedure for fluid-structure interaction problems in which contacts among different deformable bodies can occur. A typical situation is the movement of a thin valve (e.g. the aortic valve) immersed in an incompressible viscous fluid (e.g. the blood). In the proposed strategy the fluid and structure solvers are considered as independent "black-boxes" that exchange forces and displacements; the structure solvers are moreover not supposed to manage contact by themselves. The hypothesis of non-penetration among solid objects defines a non-convex optimization problem. To solve the latter, we use an internal approximation algorithm that is able to directly handle the cases of thin structures and self-contacts. A numerical simulation on an idealized aortic valve is finally realized with the aim of illustrating the proposed scheme. Résumé : Nous présentons un algorithme de couplage partitionné pour des problèmes d'interaction fluide-structure dans lesquels des contacts peuvent se produire entre plusieurs solidesélastiques immergés. La méthode s'applique par exemple aux valves aortiques (qui sont constituées de trois valvules baignées dans un fluide visqueux incompressible). La stratégie proposée considère les solveurs fluide et structure comme des "boites noires" indépendantes. De plus, le solveurs structure n'est pas supposé savoir gérer le contact. La contrainte de non pénétration entre les solides n'est pas convexe. Le problème est résolu de manière itérative en considérant une suite de problèmes avec contrainte convexe. L'algorithme, qui est capable de traiter l'autocontact et les structures minces, est illustré sur une configuration idéalisée de valves aortiques.Mots-clés : interaction fluide-structure, contact, valves cardiaques FSI and multi-body contact. Appliaticon to aortic valves 3

State-Of-The-Art Methods for the Numerical Simulation of Aortic BMHVs

“…Other IB techniques were developed and used by Tai et al (2007), De Tullio et al (2009 and Xia et al (2009). Also, the fictitious domain (FD) method can be used to simulate flexible heart valves (De Hart et al, 2000Diniz dos Santos et al, 2008;Astorino et al, 2009). This fixed grid method uses Lagrange multipliers to impose the kinematic constraints.…”

“…Partitioned simulations of heart valves using the Aitken Δ 2 relaxation method are reported in Borazjani et al (2008), Diniz dos Santos et al (2008), and Astorino et al (2009). More recently, however, a (quasi-Newton) method with a dynamically changing relaxation matrix has been developed Dahl et al, 2010) and subsequently optimized in Annerel et al (2011).…”

A simplified fluid–structure model for arterial flow. Application to retinal hemodynamics

“…In many situations, complex nonlinear models that include large displacements and deformations have to be considered. This is, for example, the case for valve simulation [1, 2,3,4] or in the aorta [5,6,7]. It is well-known that these simulations are very demanding, and in spite of the progress achieved in recent years ( [8,9,10] to name but a few), they remain challenging and the subject of active research.…”

Inverse modelling of an aneurysm’s stiffness using surrogate-based optimization and fluid-structure interaction simulations

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