Unsteady hydrodynamic interaction between two cylindroids in shallow water based on high-order panel method

A NURBS-based high-order panel method is developed for predicting the hydrodynamic interaction of two bodies moving along parallel courses in shallow water. Source and dipole are distributed on the body surfaces, while dipole is distributed on the wake surfaces; the singularity strengths are determined by satisfying the boundary condition on the body surfaces and the Kutta condition at the trailing edges. The wave-making effect is neglected under the low speed assumption; the image method is used to deal with the effects of finite water depth and undisturbed free surface. The time-stepping method is used to update the velocity potential and the position of each body. Firstly, calculations are carried out for a cylindroid passing a stationary cylindroid and two cylindroids moving in the same direction with the same speed. Detailed convergence study with respect to panel size, time step and truncated mirrored images is carried out. On the basis of convergence study, numerical results are compared with experimental measurements to validate the numerical method. Then, calculations are conducted for two cylindroids during passing, meeting and overtaking under different lateral distances between cylindroids, different water depths and different cylindroid geometry. Numerical results are presented to demonstrate the effects of these factors.