Issue ESAIM: M2AN Volume 37, Number 4, July-August 2003 Biological and Biomedical Applications Page(s) 601 - 616 DOI 10.1051/m2an:2003050

M2AN, Vol. 37, N°4, pp. 601-616
DOI: 10.1051/m2an:2003050

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

Simone Deparis¹, Miguel Angel Fernández¹ and Luca Formaggia<sup>2

1</sup>  École Polytechnique Fédérale de Lausanne, IMA, 1015 Lausanne, Switzerland. Simone.Deparis@epfl.ch.
²  Politecnico di Milano, MOX, Piazza L. da Vinci 32, 20133 Milano, Italy.

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.

Mathematics Subject Classification. 65M60, 65B99, 74F10.

Key words: Fluid-structure interaction, Block-Gauss-Seidel iterations, transpiration, highly coupled non-linear problems, weak and strong coupling algorithms, partitioned procedures.


© EDP Sciences, SMAI 2003

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