A CaNS-based approach for fluid-structure interaction with peridynamics and the Immersed Boundary Method

This thesis presents a numerical framework for the simulation of fluid-structure interaction (FSI) problems based on the coupling between a high-fidelity fluid solver and a non-local structural model. The fluid phase is resolved using the open-source solver CaNS, which performs Direct Numerical Simulation (DNS) of the incompressible Navier-Stokes equations on a structured Eulerian grid. The solid phase is modeled through bond-based peridynamics, a non-local continuum theory particularly suited for capturing discontinuities such as crack initiation and propagation. The interaction between the fluid and the deformable structure is handled via a multi-direct Immersed Boundary Method (IBM), which enforces no-slip and no-penetration conditions at the interface without requiring body-fitted meshes. A moving-least-squares (MLS) interpolation scheme is adopted to accurately transfer information between the Eulerian and Lagrangian grids. The structural solver is advanced in time using an implicit Generalized-alpha method, improving numerical stability and enabling the simulation of more realistic material responses. The developed framework is validated against the classical benchmark of Turek and Hron, showing good agreement with reference results. Furthermore, the solver is applied to the study of flexible structures immersed in homogeneous isotropic turbulence, highlighting its capability to capture complex coupled dynamics. The present work lays the foundation for future investigations on fracture and damage in fluid-loaded structures, with potential applications in engineering and environmental flows.