Immersed borders approach for fluid-structure interaction

In this paper, a formulation using the Generalized Finite Element Method (GFEM) in conjunction with Lagrange Multipliers is proposed to impose the boundary condition on the interface of the Fluid-Structure Interaction (FSI) problem. The objective of this work is the development of an efficient and robust computational code for solving problems of Fluid Mechanics and FSI. We chose a formulation of Immersed Borders to allow simulations of problems involving complex movements and transformations of the structure. In problems with these characteristics, classical ALE approaches tend to lose robustness because of the need for fluid mesh reconstruction to avoid excessive distortion of the elements. Examples of future applications are biomechanics, aeroelasticity of civil works and aerospace and multiphysical structures. The numerical examples solved proved that the formulation and implementation in finite elements developed in this work are capable to solve problems of 2D flow of fluids described by the Navier-Stokes equation for incompressible flows, even in regimes with dominant convection; and, to simulate the fluid problems with mobile interfaces using the concept of boundaries immersed in two dimensions. © 2017 Lavoisier.