An immersed finite-discrete element method (IFDEM) framework for water entry with fracture dynamics

Water entry is a current but challenging topic with numerous applications in engineering. However, little work has been devoted to water entry problems involving contact and fracture dynamics of solid systems. This work presents a complete immersed finite-discrete element method (IFDEM) framework that contains multiphase fluid dynamics, elastodynamics and a fracture model for crack initiation and propagation, fragmentation, collision and the resultant random distribution of solid debris. The fluid domain governed by the Navier-Stokes equations is discretized by fixed Cartesian grid, while the immersed violently evolved fluid-solid interfaces are tracked by a set of Lagrangian points efficiently through the improved direct forcing immersed boundary method (IBM). The formulation of the bidirectional interaction between multiphase fluid and breakable bodies is derived from the exact velocity boundary condition, and the physical law, i.e., the true divergence-free condition could be satisfied. In addition to capturing the free water surface by the conservative level set (CLS) method that has been widely applied in multiphase flow, the surface normal correction is carried out by a signed distance function so that both the conservation and accuracy could be ensured. The finite-discrete element method (FDEM) is developed to handle the elastic deformation, fragmentation and contact mechanism of solid bodies that are divided into finite elements with zero-thickness joint elements embedded in each pair of adjacent elements. Therefore, this complete approach could cope with the entire continuous-discontinuous evolution process of complex solid systems during water entry, and the strong coupling is enhanced through a stagger iterative technique by solving the fluid and solid domain repeatedly until they converge. The present solver is then tested against a number of benchmark problems, which demonstrate the physical accuracy and reliability. Additional investigations are complemented to showcase the capability of the advanced framework to model water entry phenomena across a variety of scenarios involving dynamic fracture, multi-body contact and the resultant large displacement, which also indicate its significant application potential in engineering.