Incremental displacement-correction schemes for incompressible fluid-structure interaction

Abstract

Schémas avec correction de déplacement incrémentale pour l'interaction fluide-structure: stabilité et convergence Résumé : Dans cet article nous introduisons une classe de schémas avec correction de déplacement incrémentale pour le couplage explicite d'une structure mince et d'un fluide incompressible. Ces méthodes imposent un traitement spécifique Robin-Neumann explicite du couplage à l'interface. Nous proposons une analyse générale de stabilité et de convergence, qui traite à la fois les variantes incrémentales et non-incrémentale. Leurs propriétés de stabilité sont indépendants de l'effet de masse ajoutée. La précision supérieure des schémas incrémentaux (par rapport à la variante originale non-incrémentale) est mise en évidence par des estimations d'erreur a priori, puis confirmée par des expériences numériques dans un cas test connu.

Partitioned Simulation of Fluid-Structure Interaction

“…The splitting error depends on the physical parameters of the solid. This explicit scheme corresponds with using a generalized Robin boundary condition to include the structural inertia and damping into the flow equations [70]. As this non-incremental scheme may lack accuracy, Fernandez [67] extended this approach to incremental schemes.…”

Robin-Neumann Schemes for Incompressible Fluid-Structure Interaction

“…The RobinNeumann methods proposed in Fernández [2013], achieve this purpose. The fundamental ingredient in the derivation of these schemes is the interface Robin consistency featured by the continuous problem (1)-(2).…”

“…Theoretical results on the stability and accuracy of Algorithm 2 have been reported in Fernández [2013] and . A fundamental ingredient in the analysis is the fact that Algorithm 2 can be viewed as a fully implicit scheme with the following perturbed kinematic constraint…”

“…In the particular case of an undamped thin-walled solid (i.e., L v = 0), Algorithm 2 with r = 0 yields the splitting scheme reported in Guidoboni et al [2009], which is known to deliver very poor accuracy (see Fernández [2013], and the example below).…”

Simplified Fluid-Structure Interactions for Hemodynamics

“…The problem was addressed by Charles Peskin in the nineties and his team have made impressive simulations since using fictitious domains and immersed boundary techniques [14,13,19,1]. Another approach, taken by Quarteroni et al [6] and the REO project at INRIA [5,4,20] is to discretize the full fluid-structure coupled problem with solvers working in moving domains. In a seminal paper [12], Nobile and Vergana showed that the problem is well posed and conserves energy.…”