Global force and moment in rectangular tanks through a modal method for wave sloshing

Basing on a modal description of the sloshing phenomenon, formulas for the global force and moment acting on two-dimensional rectangular tanks are proposed. These are extensively validated through comparison with experimental data for roll motions at different angles of excitement. Moreover, to extend the applicability of the modal method to the most violent breaking cases, a diffusive variant of the scheme is proposed. This relies on the use of a proper diffusive term in the continuity equation and allows for the overcoming of some numerical issues related to the sloshing dynamics in very shallow waters. Finally, a qualitative description of the interaction between diffusion, dispersion and nonlinearities has been proposed for the present modal scheme, along with a physical interpretation of the diffusive term.