ALE Finite Element Formulation for Fluid-Structure Problems

Based on the arbitrary Lagrange-Euler description the prediction–correction algorithm is presented for analyzing the fluid–structure interaction problems. The Galerkin/Least squares finite element method in ALE form is employed to simulate the incompressible viscous flow with large boundary motions, and the pseudo–elasticity method on the basis of the updated Lagrangian formulation is proposed to calculate the mesh motion. The coupling condition is established by applying Dirichlet and Neumann boundary conditions to the fluid and solid domains, respectively. Then the coupling process of a cantilever beam perpendicular to the flow in a channel is analyzed numerically, and the numerical results demonstrate the validity of the method proposed.