Fully coupled flow-induced vibration of structures under small deformation with GMRES method

Li-xiang Zhang, Yakun Guo, Hong-ming Zhang

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4 Citations (Scopus)


Lagrangian-Eulerian formulations based on a generalized variational principle
of fluid-solid coupling dynamics are established to describe flow-induced vibration of a structure under small deformation in an incompressible viscous fluid flow. The spatial discretization of the formulations is based on the multi-linear interpolating functions by using the finite element method for both the fluid and solid structures. The generalized trapezoidal rule is used to obtain apparently non-symmetric linear equations in an incremental form for the variables of the flow and vibration. The nonlinear convective term and time factors are contained in the non-symmetric coefficient matrix of the equations. The generalized minimum residual (GMRES) method is used to solve the incremental equations. A new stable algorithm of GMRES-Hughes-Newmark is developed to deal with the flow-induced vibration with dynamical fluid-structure interaction in complex geometries. Good agreement between the simulations and laboratory measurements of the pressure and blade vibration accelerations in a hydro turbine passage was obtained, indicating that the GMRES-Hughes-Newmark algorithm presented in this paper is suitable for dealing with the flow-induced vibration of structures under small deformation.
Original languageEnglish
Pages (from-to)87-96
Number of pages10
JournalApplied Mathematics and Mechanics
Issue number1
Publication statusPublished - Jan 2010


  • flow-induced vibration
  • fluid-structure interaction
  • generalized variational principle
  • numerical methods
  • generalized minumum residual (GMRES) method


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