Computational Mechanics

, Volume 43, Issue 1, pp 91–101 | Cite as

Solvers for large-displacement fluid–structure interaction problems: segregated versus monolithic approaches

Original Paper

Abstract

We compare the relative performance of monolithic and segregated (partitioned) solvers for large- displacement fluid–structure interaction (FSI) problems within the framework of oomph-lib, the object-oriented multi-physics finite-element library, available as open-source software at http://www.oomph-lib.org. Monolithic solvers are widely acknowledged to be more robust than their segregated counterparts, but are believed to be too expensive for use in large-scale problems. We demonstrate that monolithic solvers are competitive even for problems in which the fluid–solid coupling is weak and, hence, the segregated solvers converge within a moderate number of iterations. The efficient monolithic solution of large-scale FSI problems requires the development of preconditioners for the iterative solution of the linear systems that arise during the solution of the monolithically coupled fluid and solid equations by Newton’s method. We demonstrate that recent improvements to oomph-lib’s FSI preconditioner result in mesh-independent convergence rates under uniform and non-uniform (adaptive) mesh refinement, and explore its performance in a number of two- and three-dimensional test problems involving the interaction of finite-Reynolds-number flows with shell and beam structures, as well as finite-thickness solids.

Keywords

Fluid-structure interaction Monolithic solvers Preconditioning 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Förster C, Wall W, Ramm E (2007) Artificial mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows. Comput Methods Appl Mech Eng 196: 1278–1293CrossRefGoogle Scholar
  2. 2.
    Fernandez MA, Gerbeau J-F, Grandmont C (2007) A projection semi-implicit scheme for the coupling of an elastic structure with an incompressible fluid. Int J Numer Methods Eng 69: 794–821CrossRefMathSciNetGoogle Scholar
  3. 3.
    Heil M, Hazel AL (2006) oomph-lib—An object-oriented multi-physics finite-element library. In: Schafer M, Bungartz H-J (eds) Fluid–structure interaction. Springer (Lecture Notes on Computational Science and Engineering), pp 19–49Google Scholar
  4. 4.
    Irons BM, Tuck RC (1969) A version of the Aitken accelerator for computer iteration. Int J Num Methods Eng 1: 275–277MATHCrossRefGoogle Scholar
  5. 5.
    Jensen OE, Heil M (2003) High-frequency self-excited oscillations in a collapsible-channel flow. J Fluid Mech 481: 235–268MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Demmel JW, Eisenstat SC, Gilbert JR, Li XS, Liu JWH (1999) A supernodal approach to sparse partial pivoting. SIAM J. Matrix analysis and applications 20:720-755. http://crd.lbl.gov/~xiaoye/SuperLU/ Google Scholar
  7. 7.
    Heil M (2004) An efficient solver for the fully coupled solution of large-displacement fluid-structure interaction problems. Comput Methods Appl Mech Eng 193: 1–23MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Bertram CD, Tscherry J (2006) The onset of flow-rate limitation and flow-induced oscillations in collapsible tubes. J Fluids Struct 22: 1029–1045CrossRefGoogle Scholar
  9. 9.
    Elman HC, Silvester DJ, Wathen AJ (2006) Finite elements and fast iterative solvers with applications in incompressible fluid dynamics. Oxford University Press, New YorkGoogle Scholar
  10. 10.
    Turek S, Hron J, (2007) Proposal for numerical benchmarking of fluid–structure interaction between an elastic object and laminar incompressible flow. In: Schafer M, Bungartz H-J (eds) Fluid–structure interaction. Lecture Notes on Computational Science and Engineering. Springer, Heidelberg. pp 371–385Google Scholar
  11. 11.
    hypre—High performance preconditioning library. Center for Applied Scientific Computing at Lawrence Livermore National Laboratory. http://www.llnl.gov/CASC/hypre/software.html
  12. 12.
    Trilinos. Sandia National Laboratories. http://trilinos.sandia.gov/

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Matthias Heil
    • 1
  • Andrew L. Hazel
    • 1
  • Jonathan Boyle
    • 1
  1. 1.School of MathematicsUniversity of ManchesterManchesterUK

Personalised recommendations