Numerical Simulation of Water Sloshing in Rectangular Tank Using Virtual Source Method

Résumé

This paper examines the two-dimensional sloshing in a stationary rectangular tank induced by a tilt-and-release free surface, analyzed using the VSM. The inviscid, irrotational formulation enhances the potential in a rectangular eigenvalues including a closed-form vertical kernel, while a minor least-squares system progresses the modal coefficients from the free-surface conditions. The approach shows clean fourth-order temporal convergence of the free-surface elevation and of the relative errors in total energy and volume throughout a range of tilt amplitudes, and this was checked against a high-resolution reference. Long-term runs are still stable and safe: the volume stays close to round-off, and the energy drift is tiny, limited, and not secular. The results show that energy and volume clearly converge in space in the second order until a temporal plateau is attained.