A symplectic integrator for dynamic coupling between nonlinear vessel motion with variable cross-section and bottom topography and interior shallow-water sloshing

The coupled motion between shallow-water sloshing in a moving vessel with variable cross-section and bottom topography, and the vessel dynamics is considered, with the vessel dynamics restricted to horizontal motion governed by a nonlinear spring. The coupled fluid and vessel equations in Eulerian coordinates are transformed to the Lagrangian particle path setting which leads to a formulation with nice properties for numerical simulation. In the Lagrangian representation, a simple and fast numerical algorithm based on the Störmer–Verlet method, is implemented. The numerical scheme conserves the total energy in the system, as well as giving the partition of energy between the fluid and vessel. Numerical simulations of the coupled nonlinear dynamics are presented.