An immersed-boundary/isogeometric method for fluid–structure interaction involving thin shells

A computational framework is designed to accurately predict the elastic response of thin shells undergoing large displacements induced by local hydrodynamic forces, as well as to resolve the complex fluid pattern arising from its interaction with an incompressible fluid. Within the context of partitioned algorithms, two different approaches are employed for the fluid and structural domain. The fluid motion is resolved with a pressure projection method on a Cartesian structured grid. The immersed shell is modeled by means of a NURBS surface, and the elastic response is obtained from a displacement-based isogeometric analysis relying on the Kirchhoff–Love theory. The two solvers exchange data through a direct-forcing immersed-boundary approach, where the interpolation/spreading of the variables between Lagrangian and Eulerian grids is implemented with a Moving Least Squares approximation, which has proven to be very effective for moving boundaries. In this scenario, the isoparametric paradigm is exploited to perform an adaptive collocation of the Lagrangian markers, decoupling the local grid density of fluid and shell domains and reducing the computational expense. The accuracy of the method is verified by refinement analyses, segregating the Eulerian/Lagrangian refinement, which confirm the expected scheme accuracy in space and time. The effectiveness of the method is then validated against different test-cases of engineering and biologic inspiration, involving fundamentally different physical and numerical conditions, namely: (i) a flapping flag, (ii) an inverted flag, (iii) a clamped plate, (iv) a buoyant seaweed in a free stream. Both strong and loose coupling approaches are implemented to handle different fluid-to-structure density ratios, providing accurate results.