The Immersed Boundary Method for Fluid-Structure Interactions: Mathematical Formulation and Numerical

Daniele Boffi

Bollettino dell'Unione Matematica Italiana (2012)

  • Volume: 5, Issue: 3, page 711-724
  • ISSN: 0392-4041

Abstract

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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.

How to cite

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Boffi, Daniele. "The Immersed Boundary Method for Fluid-Structure Interactions: Mathematical Formulation and Numerical." Bollettino dell'Unione Matematica Italiana 5.3 (2012): 711-724. <http://eudml.org/doc/290882>.

@article{Boffi2012,
abstract = {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.},
author = {Boffi, Daniele},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {711-724},
publisher = {Unione Matematica Italiana},
title = {The Immersed Boundary Method for Fluid-Structure Interactions: Mathematical Formulation and Numerical},
url = {http://eudml.org/doc/290882},
volume = {5},
year = {2012},
}

TY - JOUR
AU - Boffi, Daniele
TI - The Immersed Boundary Method for Fluid-Structure Interactions: Mathematical Formulation and Numerical
JO - Bollettino dell'Unione Matematica Italiana
DA - 2012/10//
PB - Unione Matematica Italiana
VL - 5
IS - 3
SP - 711
EP - 724
AB - 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.
LA - eng
UR - http://eudml.org/doc/290882
ER -

References

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