8 research outputs found
An alternative view on the Bateman-Luke variational principle
A new derivation of the Bernoulli equation for water waves in
three-dimensional rotating and translating coordinate systems is given. An
alternative view on the Bateman-Luke variational principle is presented. The
variational principle recovers the boundary value problem governing the motion
of potential water waves in a container undergoing prescribed rigid-body motion
in three dimensions. A mathematical theory is presented for the problem of
three-dimensional interactions between potential surface waves and a floating
structure with interior potential fluid sloshing. The complete set of equations
of motion for the exterior gravity-driven water waves, and the exact nonlinear
hydrodynamic equations of motion for the linear momentum and angular momentum
of the floating structure containing fluid, are derived from a second
variational principle
Rigid-body motion with interior shallow-water sloshing
EThOS - Electronic Theses Online ServiceGBUnited Kingdo
Adaptation of f-wave finite volume methods to the Boonkasame–Milewski non-Boussinesq two-layer shallow interfacial sloshing equations coupled to the vessel motion
Shallow-water sloshing in a moving vessel with variable cross-section and wetting-drying using an extension of George's well-balanced finite volume solver
A class of augmented approximate Riemann solvers due to George (2008) [12] is extended to solve the shallow-water equations in a moving vessel with variable bottom topography and variable cross-section with wetting and drying. A class of Roe-type upwind solvers for the system of balance laws is derived which respects the steady-state solutions. The numerical solutions of the new adapted augmented f-wave solvers are validated against the Roe-type solvers. The theory is extended to solve the shallow-water flows in moving vessels with arbitrary cross-section with influx–efflux boundary conditions motivated by the shallow-water sloshing in the ocean wave energy converter (WEC) proposed by Offshore Wave Energy Ltd. (OWEL) [1]. A fractional step approach is used to handle the time-dependent forcing functions. The numerical solutions are compared to an extended new Roe-type solver for the system of balance laws with a time-dependent source function. The shallow-water sloshing finite volume solver can be coupled to a Runge–Kutta integrator for the vessel motion