Sloshing waves in a three dimensional tank are simulated in potential theory based on a fully nonlinear numerical wave tank (NWT) model. The model is developed by using a time-domain higher-order boundary element method (HOBEM) including a mixed Eulerian-Lagrangian technique and a 4th-order Runge-Kutta scheme as a time marching process. By using an auxiliary velocity potential relating with the original one and the translational velocity of tank (Wu et al 1998), the tank can be fixed in the solving process. Thus the image Green function (Newman, 1992) can be used in the whole fluid domain so that the integrations on the lateral walls and bottom are excluded. It means that only free surface is descritized in the whole calculation domain and the corresponding computational cost and storage are saved. The numerical model is validated against the analytical solutions, experimental data and other published data for 2D and 3D liquid sloshing.
The sloshing phenomenon is of great theoretical and practical importance in coastal and offshore engineering. They exist in many engineering problems, such as liquid oscillations in large storage tanks by earthquakes, the motions of liquid fuel in aircraft and spacecraft, the liquid motions in containers and the water flow on the deck of ships. Due to such sloshing motions inside a partially filled container, the safety of engineering structures may be damaged, especially when the excitation is large or when the excitation is near to the natural frequencies. It is urged the need for further research on accurate sloshing flows predictions. For example, Faltinsen (1978) derived the linear analytical solution of a horizontally excitation tank in 2D. Frandsen (2004) obtained the linear and second-order analytical solutions of a fixed tank with initial free surface being cosine curve. Faltinsen et al. (2005) performed sloshing experiments in a square-base tank.
