Computational Mechanics

, Volume 51, Issue 2, pp 129–150

# A three dimensional immersed smoothed finite element method (3D IS-FEM) for fluid–structure interaction problems

• Zhi-Qian Zhang
• G. R. Liu
• Boo Cheong Khoo
Original Paper

## Abstract

A three-dimensional immersed smoothed finite element method (3D IS-FEM) using four-node tetrahedral element is proposed to solve 3D fluid–structure interaction (FSI) problems. The 3D IS-FEM is able to determine accurately the physical deformation of the nonlinear solids placed within the incompressible viscous fluid governed by Navier-Stokes equations. The method employs the semi-implicit characteristic-based split scheme to solve the fluid flows and smoothed finite element methods to calculate the transient dynamics responses of the nonlinear solids based on explicit time integration. To impose the FSI conditions, a novel, effective and sufficiently general technique via simple linear interpolation is presented based on Lagrangian fictitious fluid meshes coinciding with the moving and deforming solid meshes. In the comparisons to the referenced works including experiments, it is clear that the proposed 3D IS-FEM ensures stability of the scheme with the second order spatial convergence property; and the IS-FEM is fairly independent of a wide range of mesh size ratio.

## Keywords

Fluid–structure interaction Finite element method Immersed boundary Immersed smoothed finite element method Characteristic-based split Incompressible viscous fluid

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