We propose a quasi-Newton algorithm for solving fluid-structure interaction problems. The basic idea of the method is to build an approximate tangent operator which is cost effective and which takes into account the so-called added mass effect. Various test cases show that the method allows a significant reduction of the computational effort compared to relaxed fixed point algorithms. We present 2D and 3D fluid-structure simulations performed either with a simple 1D structure model or with shells in large displacements.
Mots-clés : fluid-structure interaction, quasi-Newton algorithm, added mass effect, blood flows
@article{M2AN_2003__37_4_631_0,
author = {Gerbeau, Jean-Fr\'ed\'eric and Vidrascu, Marina},
title = {A {quasi-Newton} algorithm based on a reduced model for fluid-structure interaction problems in blood flows},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {631--647},
publisher = {EDP-Sciences},
volume = {37},
number = {4},
year = {2003},
doi = {10.1051/m2an:2003049},
mrnumber = {2018434},
zbl = {1070.74047},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2003049/}
}
TY - JOUR AU - Gerbeau, Jean-Frédéric AU - Vidrascu, Marina TI - A quasi-Newton algorithm based on a reduced model for fluid-structure interaction problems in blood flows JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2003 SP - 631 EP - 647 VL - 37 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2003049/ DO - 10.1051/m2an:2003049 LA - en ID - M2AN_2003__37_4_631_0 ER -
%0 Journal Article %A Gerbeau, Jean-Frédéric %A Vidrascu, Marina %T A quasi-Newton algorithm based on a reduced model for fluid-structure interaction problems in blood flows %J ESAIM: Modélisation mathématique et analyse numérique %D 2003 %P 631-647 %V 37 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2003049/ %R 10.1051/m2an:2003049 %G en %F M2AN_2003__37_4_631_0
Gerbeau, Jean-Frédéric; Vidrascu, Marina. A quasi-Newton algorithm based on a reduced model for fluid-structure interaction problems in blood flows. ESAIM: Modélisation mathématique et analyse numérique, Special issue on Biological and Biomedical Applications, Tome 37 (2003) no. 4, pp. 631-647. doi : 10.1051/m2an:2003049. http://www.numdam.org/articles/10.1051/m2an:2003049/
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