The dynamic response of a fluid in a rolling tank is one of the most important issues for the integrity of LNG tanks and the overall stability of the vessel. When the tanks oscillate near the sloshing resonance frequencies, sloshing phenomena with strong nonlinearity and large free-surface deformations can be observed. For some liquid depths and external forcing characteristics, hydraulic jumps may form, wave component interactions would occur, and severe impacts on the walls would follow. In this paper, the formations of different types of sloshing waves as well as the impact forces on the walls are simulated by an Eulerian-Lagrangian method, which was developed on the past for the horizontal excitation problem and is extended in this paper to a tank subject to roll motions. This approach allows the use of boundary element method (BEM) and fourth-order Runge-Kutta scheme (RK4) to track the particles on the free surface. In the case of rolling excitation, some highly nonlinear waves and thin jets where the wave impacts on the boundaries of the tank are more likely to occur. Therefore these very thin wave jets would be slightly truncated to alleviate the associated numerical instability. Furthermore, the artificial damping effect, which is linearly proportional to the fluid velocity, is introduced in the dynamic boundary condition on the free surface and the impermeable condition of the walls to take the effects of viscosity into account. This has been proven to be effective in improving the numerical accuracy of the method. Correlations of our results with experimental observations and measurements will be presented.

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