An extension of shape sensitivity analysis to an immersed boundary method based on Cartesian grids

Gradient-based shape optimization processes of mechanical components require the gradients (sensitivity) of the magnitudes of interest to be calculated with sufficient accuracy. The aim of this study was to develop algorithms for the calculation of shape sensitivities considering geometric representation by parametric surfaces (i.e. NURBS or T-splines) using 3D Cartesian h-adapted meshes independent of geometry. A formulation of shape sensitivities was developed for an environment based on Cartesian meshes independent of geometry, which implies, for instance, the need to take into account the special treatment of boundary conditions imposed in non body-fitted meshes. The immersed boundary framework required to implement new methods of velocity field generation, which have a primary role in the integration of both the theoretical concepts and the discretization tools in shape design optimization. Examples of elastic problems with three-dimensional components are given to demonstrate the efficiency of the algorithms.