An implicit full Eulerian method for the fluid-structure interaction problem

S. Ii, K. Sugiyama, S. Takeuchi, S. Takagi, Yoichiro Matsumoto

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21 Citations (Scopus)


A numerical method, which relaxes limitation of small time increment in fluid-structure interaction (FSI) simulations with hard solid, is developed based on a full Eulerian FSI model (Sugiyama et al. Comput. Mech. 2010; 46(1):147-157). In this model, the solid volume fraction is applied for describing the multicomponent material, and the left Cauchy-Green deformation tensor is introduced to describe the deformation of the hyperelastic body. The transport equations for them are solved by finite difference formulation on a fixed Cartesian coordinate grid. In this paper, a simple implicit formulation is proposed for the elastic stress to avoid restriction and instability due to high stiffness. Both linear and nonlinear hyperelastic materials are treated by a unified formulation by introducing a fourth-order Jacobian tensor to overcome the difficulty associated with the difference between the constitutive laws of solid and fluid. The numerical examples are carried out in two dimensions, and the proposed method is confirmed to work well for hard Mooney-Rivlin materials. It is also applied to 2D wall-bounded flows involving biconcave particles, and the effects of the solid stiffness on the shape and distribution of the particles, and the overall flow rate are discussed.

Original languageEnglish
Pages (from-to)150-165
Number of pages16
JournalInternational Journal for Numerical Methods in Fluids
Issue number1-3
Publication statusPublished - 1 Jan 2011



  • Eulerian approach
  • Fluid-structure interaction
  • Implicit formulation
  • Incompressible flow
  • Multiple elastic particles
  • Volume-of-fluid

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