Author(s)

S. ´Etienne, D. Pelletier, D. Tremblay & A. Garon

Abstract

We present several aspects of a general monolithic formulation for the steady-state interaction of a viscous incompressible flow with an elastic structure undergoing large displacements. The problem is solved in a direct fully-coupled manner by a Newton–Raphson adaptive finite element method. A pseudo-solid formulation is used to manage the deformations of the fluid domain. The formulation uses fluid velocity, pressure, and pseudo-solid displacements as unknowns in the flow domain and displacements in the structural components. The adaptive formulation is verified on a problem with a closed form solution. Its capabilities are then demonstrated on different fluid-structure configurations ranging from aeronautical to biomedical fields. Keywords: monolithic, finite-elements, adaptivity, pseudo-solid, fluid, structure. 1 Introduction In many instances, interaction between fluids and solids is achieved through weak or loose coupling of specialized softwares. This is very cost-effective because it requires little changes to analysis modules and takes advantage of expertise accumulated in each discipline. Hydrodynamic loads obtained by CFD are transferred to the structure model to predict solid displacements which are then transferred back to the fluidmodule to reflect changes in the geometry. This process is repeated until convergence.However weak coupling does not always converge to a solution. For example, if the fluid added mass is much larger than that of the structure, a weak coupling treatment will result in failure of the solution procedure. In decoupled approaches equilibrium of interface forces is approximately satisfied. This error may be amplified in sensitivity analysis or gradient-based optimization. To avoid such difficulties we consider monolithic formulations of

Keywords

monolithic, finite-elements, adaptivity, pseudo-solid, fluid, structure.