Numerical methods for partitioned Arbitrary Lagrangian-Eulerian fluid–structure interaction and multiphase flow with applications to lightweight structures

In recent decades, enhancements of numerical simulation tools have substantially contributed to the industry shift towards more computationally driven design and have reduced reliance on extensive experimental campaigns, with the overarching goal of lowering development costs and accelerating innovation. In particular, applications involving the interaction between fluids and structures, usually referred to as fluid–structure interaction, are central to a wide range of engineering fields. This dissertation presents an advanced numerical framework to simulate three-dimensional fluid–structure interaction phenomena. The fluid problem, described by incompressible Navier--Stokes equations, is solved with a finite element Arbitrary Lagrangian-Eulerian approach. In this context, a novel remeshing algorithm based on connectivity manipulation and local refinement has been implemented to reduce element distortion in fluid mesh, therefore increasing the overall accuracy of the fluid solution. Conversely, the solid domain is addressed using the classical finite element method. Here, an innovative surface splitting procedure enables the treatment of lightweight structures, which are commonly parameterised in a lower-dimensional space and discretised using structural elements such as membranes and shells. In the fluid domain, the two split surfaces occupy the same geometric location, while their outward normals point in opposite directions. Consequently, the fluid tractions on the two sides are evaluated independently. The second part of this thesis extends the approach to multiphase flow, where the presence of moving internal interfaces and discontinuous material properties introduces additional modelling and numerical challenges. In this context, an advanced numerical method for simulating three-dimensional, immiscible, two-phase flows is introduced, where the interface surface is well-defined and surface tension is neglected, in order to focus on the discontinuity of physical properties across the interface. The incompressible Navier–Stokes equations are expressed in a one-fluid formulation, whereas the interface is tracked using Lagrangian nodes. Moreover, physical properties are assigned elementwise, assuming a sharp interface between the two distinct fluids. To capture pressure jump discontinuities, an auxiliary pressure variable is introduced, which is continuous throughout the entire domain. The real pressure field is then reconstructed by evaluating the boundary conditions at the interface. Several analytical and numerical benchmarks are presented to assess the accuracy and reliability of the proposed numerical framework. At the same time, extensive case studies in biomimetics, i.e. Micro Air Vehicles, and marine engineering, i.e. hydrofoils and sails, are carried out to demonstrate its robustness and predictive capability in application-driven scenarios.