Shape design optimization of stationary fluid-structure interaction problems with large displacements and turbulence

This paper presents general and efficient methods for analysis and gradient based shape optimization of systems characterized as strongly coupled stationary fluid-structure interaction (FSI) problems. The incompressible fluid flow can be laminar or turbulent and is described using the Reynolds-averaged Navier-Stokes equations (RANS) together with the algebraic Baldwin–Lomax turbulence model. The structure may exhibit large displacements due to the interaction with the fluid domain, resulting in geometrically nonlinear structural behaviour and nonlinear interface coupling conditions. The problem is discretized using Galerkin and Streamline-Upwind/Petrov–Galerkin finite element methods, and the resulting nonlinear equations are solved using Newton’s method. Due to the large displacements of the structure, an efficient update algorithm for the fluid mesh must be applied, leading to the use of an approximate Jacobian matrix in the solution routine. Expressions for Design Sensitivity Analysis (DSA) are derived using the direct differentiation approach, and the use of an inexact Jacobian matrix in the analysis leads to an iterative but very efficient scheme for DSA. The potential of gradient based shape optimization of fluid flow and FSI problems is illustrated by several examples.