Numerical model of sloshing in rectangular tank based on Boussinesq-type equations

The highly accurate Boussinesq-type equations in terms of velocity potential are adopted for the simulation of sloshing phenomena in a two-dimensional rectangular tank. The fully nonlinear free surface conditions are used and linearized energy dissipation term is added into the dynamic free surface condition. The total velocity potential is divided into two parts: the particular solution and the rest which is calculated by the Boussinesq-type model. Different filling levels of liquid in the tank are considered for the validation of the numerical model, including shallow water, intermediate water depth and finite water depth cases. The linear theory based on the superposition of eigen-modes corresponding to natural sloshing frequencies is introduced. Compared with results calculated by linear theory and results from literatures, the numerical model based on Boussinesq-type equations presents good performances in predicting the sloshing motions in rectangular tank with small excitation amplitude.