Acceleration of a fixed point algorithm for fluid-structure interaction using transpiration conditions

Simone Deparis; Miguel Angel Fernández; Luca Formaggia[1]

  • [1] Politecnico di Milano, MOX, Piazza L. da Vinci 32, 20133 Milano, Italy.

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2003)

  • Volume: 37, Issue: 4, page 601-616
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Deparis, Simone, Fernández, Miguel Angel, and 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 37.4 (2003): 601-616. <http://eudml.org/doc/244984>.

@article{Deparis2003,
abstract = {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.},
affiliation = {Politecnico di Milano, MOX, Piazza L. da Vinci 32, 20133 Milano, Italy.},
author = {Deparis, Simone, Fernández, Miguel Angel, Formaggia, Luca},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {fluid-structure interaction; Block-Gauss-Seidel iterations; transpiration; highly coupled non-linear problems; weak and strong coupling algorithms; partitioned procedures; Fluid-structure interaction; highly coupled nonlinear problems},
language = {eng},
number = {4},
pages = {601-616},
publisher = {EDP-Sciences},
title = {Acceleration of a fixed point algorithm for fluid-structure interaction using transpiration conditions},
url = {http://eudml.org/doc/244984},
volume = {37},
year = {2003},
}

TY - JOUR
AU - Deparis, Simone
AU - Fernández, Miguel Angel
AU - Formaggia, Luca
TI - Acceleration of a fixed point algorithm for fluid-structure interaction using transpiration conditions
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2003
PB - EDP-Sciences
VL - 37
IS - 4
SP - 601
EP - 616
AB - 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.
LA - eng
KW - fluid-structure interaction; Block-Gauss-Seidel iterations; transpiration; highly coupled non-linear problems; weak and strong coupling algorithms; partitioned procedures; Fluid-structure interaction; highly coupled nonlinear problems
UR - http://eudml.org/doc/244984
ER -

References

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