Continuous Sensitivity Analysis of Fluid-Structure Interaction Problems Using Least-Squares Finite Elements

Abstract

A least-squares continuous sensitivity analysis method is developed for fluid-structure interaction problems to support computationally efficient analysis and optimization of aeroelastic design problems. The continuous sensitivity system equations and sensitivity boundary conditions are derived and the problem is posed in first-order form. A leastsquares finite element solution of the coupled fluid-structure physics is then used to determine the sensitivity boundary conditions. The least-squares finite element method permits a simultaneous solution of the fluid-structure system and the mesh deformation problem within a single numerical framework. A least-squares finite element solution of the linear continuous sensitivity equations is then used to produce computationally efficient design parameter gradient calculations without needing to derive and code the problematic mesh sensitivities. An example nonlinear fluid-structure interaction problem is solved. Continuous sensitivity results for both the local and total material derivatives are presented and compared to gradients obtained by finite-difference methods.