Acceleration of a fixed point algorithm for fluid-structure interaction using transpiration conditions
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 37 (2003) no. 4, p. 601-616

In this work, we address the numerical solution of fluid-structure interaction problems. This issue is particularly difficulty to tackle when the fluid and the solid densities are of the same order, for instance as it happens in hemodynamic applications, since fully implicit coupling schemes are required to ensure stability of the resulting method. Thus, at each time step, we have to solve a highly non-linear coupled system, since the fluid domain depends on the unknown displacement of the structure. Standard strategies for solving this non-linear problems, are fixed point based methods such as Block-Gauss-Seidel (BGS) iterations. Unfortunately, these methods are very CPU time consuming and usually show slow convergence. We propose a modified fixed-point algorithm which combines the standard BGS iterations with a transpiration formulation. Numerical experiments show the great improvement in computing time with respect to the standard BGS method.

DOI : https://doi.org/10.1051/m2an:2003050
Classification:  65M60,  65B99,  74F10
Keywords: fluid-structure interaction, Block-Gauss-Seidel iterations, transpiration, highly coupled non-linear problems, weak and strong coupling algorithms, partitioned procedures
@article{M2AN_2003__37_4_601_0,
author = {Deparis, Simone and Fern\'andez, Miguel Angel and Formaggia, Luca},
title = {Acceleration of a fixed point algorithm for fluid-structure interaction using transpiration conditions},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {37},
number = {4},
year = {2003},
pages = {601-616},
doi = {10.1051/m2an:2003050},
zbl = {1118.74315},
mrnumber = {2018432},
language = {en},
url = {http://www.numdam.org/item/M2AN_2003__37_4_601_0}
}

Deparis, Simone; Fernández, Miguel Angel; Formaggia, Luca. Acceleration of a fixed point algorithm for fluid-structure interaction using transpiration conditions. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 37 (2003) no. 4, pp. 601-616. doi : 10.1051/m2an:2003050. http://www.numdam.org/item/M2AN_2003__37_4_601_0/

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