This work presents a partitioned solution procedure to compute shape gradients in fluid–structure interaction (FSI) using black-box adjoint solvers. Special attention is paid to project the gradients onto the undeformed configuration due to the mixed Lagrangian–Eulerian formulation of large-deformation FSI in this work. The adjoint FSI problem is partitioned as an assembly of well-known adjoint fluid and structural problems. The sub-adjoint problems are coupled with each other by augmenting the target functions with auxiliary functions, independent of the concrete choice of the underlying adjoint formulations. The auxiliary functions are linear force-based or displacement-based functionals which are readily available in well-established single-disciplinary adjoint solvers. Adjoint structural displacements, adjoint fluid displacements, and domain-based adjoint sensitivities of the fluid are the coupling fields to be exchanged between the adjoint solvers. A reduced formulation is also derived for the case of boundary-based adjoint shape sensitivity analysis for fluids. Numerical studies show that the complete formulation computes accurate shape gradients whereas inaccuracies appear in the reduced gradients. Mapping techniques including nearest element interpolation and the mortar method are studied in computational adjoint FSI. It is numerically shown that the mortar method does not introduce spurious oscillations in primal and sensitivity fields along non-matching interfaces.

这项工作提出了一种分区解决方案程序，该程序使用黑盒伴随解算器计算流体-结构相互作用（FSI）中的形状梯度。由于这项工作中大变形FSI的混合拉格朗日-欧拉公式，应特别注意将梯度投影到未变形的构型上。伴随FSI问题被划分为众所周知的伴随流体和结构问题的集合。通过使用辅助功能扩展目标功能，可以独立于子伴随问题而相互耦合，而不必依赖于基础伴随表达式的具体选择。辅助功能是基于线性力或基于位移的功能，这些功能可以在完善的单学科伴随求解器中轻松使用。伴随结构位移，伴随流体位移，流体的基于域的伴随灵敏度是伴随求解器之间要交换的耦合场。对于基于边界的流体伴随形状敏感性分析，还可以得出简化的公式。数值研究表明，完整的配方可以计算出准确的形状梯度，而减少的梯度中会出现不准确的现象。在计算伴随FSI中研究了包括最近单元插值和灰浆法在内的制图技术。数值显示，砂浆法不会在非匹配界面的原始场和敏感场中引入杂散振荡。对于基于边界的流体伴随形状敏感性分析，还可以得出简化的公式。数值研究表明，完整的配方可以计算出准确的形状梯度，而减少的梯度中会出现不准确的现象。在计算伴随FSI中研究了包括最近元素插值和灰浆法在内的制图技术。数值表明，砂浆法不会沿非匹配界面在原始场和灵敏度场中引入杂散振荡。对于基于边界的流体伴随形状敏感性分析，还可以得出简化的公式。数值研究表明，完整的配方可以计算出准确的形状梯度，而减少的梯度中会出现不准确的现象。在计算伴随FSI中研究了包括最近元素插值和灰浆法在内的制图技术。数值显示，砂浆法不会在非匹配界面的原始场和敏感场中引入杂散振荡。