Geodesic
The Immersed Boundary Method for Fluid-Structure Interactions: Mathematical Formulation and Numerical
Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 3, pp. 711-724

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

The Immersed Boundary Method (IBM) has been introduced by Peskin in the 70's in order to model and approximate fluid-structure interaction problems related to the blood flow in the heart. The original scheme makes use of finite differences for the discretization of the Navier-Stokes equations. Recently, a finite element formulation has been introduced which has the advantage of handling the presence of the solid (modeled via a Dirac delta function) in a more natural way. In this paper we review the finite element formulation of the IBM focusing, in particular, on the choice of the finite element spaces in order to guarantee a suitable mass conservation. Moreover, we present some links with the fictitious domain method. 
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     author = {Boffi, Daniele},
     title = {The {Immersed} {Boundary} {Method} for {Fluid-Structure} {Interactions:} {Mathematical} {Formulation} and {Numerical}},
     journal = {Bollettino della Unione matematica italiana},
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     year = {2012},
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     mrnumber = {3051741},
     language = {en},
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Boffi, Daniele. The Immersed Boundary Method for Fluid-Structure Interactions: Mathematical Formulation and Numerical. Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 3, pp. 711-724. http://geodesic.mathdoc.fr/item/BUMI_2012_9_5_3_a9/