Numerical modeling of fluid-structure interaction (FSI): time-consistent pressure computation, rigid bodies contact and coupled particle-mesh methods.

This thesis is devoted to developing efficient computational solutions based on meshless particle-based methods for complex fluid-structure interaction (FSI) in free-surface flow from two different ways, namely, the truly incompressible and weakly-compressible approaches. Overall, the main contributions of this thesis can be summarized into three distinct parts: I. Proposal of a new approach from the viewpoint of the momentum conservation regarding particle-level collisions to derive new source terms of pressure Poisson equation (PPE) of the moving particle semi-implicit (MPS) method. The new source terms depend directly on the spatial discretization and are independent to the time step, i.e., a direct consequence is the time-consistent computation of the pressure. The effectiveness of the proposed approach, namely time-scale correction of particle-level impulses (TCPI), is demonstrated through the simulations of hydrostatic and hydrodynamic problems. II. A numerical solid contact model adopting a penalty-based method, that uses a nonlinear spring and dashpot concept, is proposed for the incompressible MPS. To address some geometrical anomalies such as non-smooth modeling of a plane, which may occur when using particles to represent the shell of the rigid bodies, an approach based on the faces of the bodies and contact force computed taken into account the normal vectors of solid walls is derived. The improvements on stability and accuracy computations are investigated by problems involving free-surface flow interacting with multiple bodies. III. Development of a 3D coupled particle-mesh model. An improved weakly-compressible moving particle semi-implicit (WC-MPS) to solve transient violent free-surface flows is coupled with a geometrically exact shell model for nonlinear structural dynamic. Besides enhancements on the stability and accuracy of WC-MPS, a stable repulsive Lennard-Jone force, discrete divergence operators with proper modifications, and a simple technique to avoid false interaction between particles placed at opposite sides of thin shell are introduced in the explicitly represented polygon (ERP) wall boundary model. Hydroelastic simulations are conducted to verify the robustness and accuracy of the coupled model.