Premium
An implicit full Eulerian method for the fluid–structure interaction problem
Author(s) -
Ii S.,
Sugiyama K.,
Takeuchi S.,
Takagi S.,
Matsumoto Y.
Publication year - 2010
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2460
Subject(s) - hyperelastic material , mathematics , eulerian path , tensor (intrinsic definition) , constitutive equation , cauchy stress tensor , nonlinear system , mathematical analysis , mechanics , geometry , finite element method , physics , quantum mechanics , lagrangian , thermodynamics
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. Copyright © 2010 John Wiley & Sons, Ltd.