Solvers for large-displacement fluid-structure interaction problems: Segregated versus monolithic approaches. (English) Zbl 1309.76126

Summary: 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.


76M10 Finite element methods applied to problems in fluid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S05 Finite element methods applied to problems in solid mechanics
Full Text: DOI


[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: 1278–1293 · Zbl 1173.74418
[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: 794–821 · Zbl 1194.74393
[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 19–49 · Zbl 1323.74085
[4] Irons BM, Tuck RC (1969) A version of the Aitken accelerator for computer iteration. Int J Num Methods Eng 1: 275–277 · Zbl 0256.65021
[5] Jensen OE, Heil M (2003) High-frequency self-excited oscillations in a collapsible-channel flow. J Fluid Mech 481: 235–268 · Zbl 1049.76015
[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/\(\sim\)xiaoye/SuperLU/ · Zbl 0931.65022
[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: 1–23 · Zbl 1137.74439
[8] Bertram CD, Tscherry J (2006) The onset of flow-rate limitation and flow-induced oscillations in collapsible tubes. J Fluids Struct 22: 1029–1045
[9] Elman HC, Silvester DJ, Wathen AJ (2006) Finite elements and fast iterative solvers with applications in incompressible fluid dynamics. Oxford University Press, New York
[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 371–385 · Zbl 1323.76049
[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] Trilinos. Sandia National Laboratories. http://trilinos.sandia.gov/
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.