Abstract
This contribution focuses on partitioned solution approaches in fluid-structure interaction problems. Depending on certain physical parameters of fluid and structure, the fixed-point iteration that is mostly used to strongly couple the different solvers in each time step is susceptible to deceleration. We present a method that is able to overcome this effect by a specific preconditioning of the fixed-point iteration. Thus, the full convergence order of the underlying time-discretisation schemes is preserved. As computational example, a benchmark problem from hemodynamics is considered where this effect has a particularly strong influence. It turns out that, though a single step of the preconditioned iteration is more expensive, the overall gain in efficiency can be significant.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Badia, S., Quaini, A., Quarteroni, A.: Modular vs. non-modular preconditioners for fluid-structure systems with large added-mass effect. Comput. Meth. Appl. Mech. Eng. 197, pp. 4216–4232 (2008)
Bazilevs, Y., Calo, V. M., Zhang, Y., Hughes, T.J.R.: Isogeometric Fluid-structure interaction analysis with applications to arterial blood flow. Comput. Mech. 38, pp. 310–322 (2006)
Bungartz, H.J., Schäfer, M.: Fluid-Structure Interaction, Modelling, Simulation, Optimisation. In: Lecture Notes in Computational Science and Engineering, Vol. 53, Springer (2006)
Ciarlet, P.G.: Mathematical Elasticity - Volume 1: Three-Dimensional Elasticity, North-Holland (1988)
Dörfel, M.R.: Fluid-Structure Interaction: A Differential-Algebraic Approach and Acceleration Techniques for Strong Coupling, In: Fortschritt-Berichte VDI Reihe 20, No. 436, VDI Verlag (2011)
Dörfel, M.R., Simeon, B.: Analysis and acceleration of a fluid-structure interaction coupling scheme. In: Kreiss, G. et al. (Eds.) Numerical Mathematics and Advanced Applications 2009, pp. 307–316. Springer (2010)
Fernndez, M.A., Gerbeau, J.-F., Grandmont, C.: A projection semi-implicit scheme for the coupling of an elastic structure with an incompressible fluid. Technical Report INRIA Rocquencourt 5700, pp.1–31 (2005)
Förster, C., Wall, W.A., Ramm, E.: Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows. Comput. Meth. Appl. Mech. Eng. 196, pp. 1278–1293 (2007)
Irons, B., Tuck, R.C.: A version of the Aitken accelerator for computer implementation. Int. J. Numer. Meth. Eng. 1, pp. 275–277 (1969)
Küttler, U., Wall, W.A.: Fixed-point fluid-structure interaction solvers with dynamic relaxation. Comput. Mech. 43, pp. 61–72 (2008)
Acknowledgements
The first author was supported by Deutsche Forschungsgemeinschaft (DFG) through the TUM International Graduate School of Science and Engineering (IGSSE) within Project 2-11. This support is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dörfel, M.R., Simeon, B. (2013). Fluid-Structure Interaction: Acceleration of Strong Coupling by Preconditioning of the Fixed-Point Iteration. In: Cangiani, A., Davidchack, R., Georgoulis, E., Gorban, A., Levesley, J., Tretyakov, M. (eds) Numerical Mathematics and Advanced Applications 2011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33134-3_78
Download citation
DOI: https://doi.org/10.1007/978-3-642-33134-3_78
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33133-6
Online ISBN: 978-3-642-33134-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)