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

Published online by Cambridge University Press:  15 November 2003

Simone Deparis ,
Miguel Angel Fernández  and
Luca Formaggia
Simone Deparis
Affiliation:
École Polytechnique Fédérale de Lausanne, IMA, 1015 Lausanne, Switzerland. Simone.Deparis@epfl.ch.
Miguel Angel Fernández
Affiliation:
École Polytechnique Fédérale de Lausanne, IMA, 1015 Lausanne, Switzerland. Simone.Deparis@epfl.ch.
Luca Formaggia
Affiliation:
Politecnico di Milano, MOX, Piazza L. da Vinci 32, 20133 Milano, Italy.
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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.

Keywords

Fluid-structure interactionBlock-Gauss-Seideliterationstranspirationhighly coupled non-linear problemsweak and strong coupling algorithmspartitioned procedures.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 4: Special issue on Biological and Biomedical Applications , July 2003 , pp. 601 - 616
Copyright
© EDP Sciences, SMAI, 2003

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