Numerical Investigation of Three-Dimensional Shallow-Water Sloshing Based on High Accuracy Boussinesq Equations

Abstract

Highly accurate Boussinesq-type equations in terms of velocity potential are used for the simulation of shallow-water sloshing in a three-dimensional tank under the framework of the potential flow theory. The total velocity potential is separated into two parts: one part is a particular solution which satisfies the Laplace equation in the fluid domain and the no-flow condition on the walls while the other part is solved by the Boussinesq-type model. In the process of numerical calculation, the finite difference method is used for spatial derivative discretization and the 4th Runge-kutta method is used for time iteration. To verify the numerical model, the aspect ratio of the tank is set to be much less than 1 for simulation of 2D cases and is compared with the results published. In the 3D cases, four different sloshing motion forms are observed at each external excitation frequency, and a corresponding number of traveling waves are observed on the free surface. Moreover, the effects of external excitation frequency and coupling excitation on the sloshing motion in the tank are discussed.

Keywords

• boussinesq equations
• finite difference method
• potential flow theory
• sloshing
• shallow-water