A general approach to sensitivity analysis of fluid-structure interactions

This paper presents a general monolithic formulation for sensitivity analysis of the steady-state interaction of a viscous incompressible flow with an elastic structure undergoing large displacements (geometric nonlinearities). The problem is solved in a direct implicit manner using 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. It is then applied to sensitivity analysis of an elastic cylinder placed in a uniform flow. Sensitivities are used for fast evaluation of nearby problems (i.e. for nearby values of the parameters) and for cascading uncertainty through the Computational Fluid Dynamics/Computational Structural Dynamics code to yield uncertainty estimates of the cylinder shape.