Modal analysis of liquid sloshing with different contact line boundary conditions using FEM

A finite element method (FEM) for liquid sloshing modal analysis is established. Surface tension and three kinds of contact line boundary conditions, namely, free-end, pin-end and wetting boundary conditions, are taken into account. Sloshing damping caused by energy dissipation at the wall, in the interior fluid and at the contact line is calculated. Numerical results are compared with the analytical values and measurements. For the pin-end and free-end boundary conditions the differences between numerical value and analytical value are small, and for the wetting boundary condition, because approximation is used, the differences are more significant.