A three-dimensional high-order panel method based on Non-Uniform Rational B-Spline (NURBS) for predicting the ship-ship hydrodynamic interaction during meeting and overtaking in shallow water is developed. The NURBS surface is used to precisely represent the hull geometry. The velocity potential on the body surface is described by B-spline after the source density distribution on the boundary surface is determined. A collocation approach is applied to the boundary integral equation discretization, and the velocity potential is being solved at each time step. Under the low-speed assumption, the effect of free surface elevation is neglected in the numerical calculation, and the infinite image method is used to deal with the finite water depth effect. Two tankers in model tests are investigated, and the predicted hydrodynamic interaction forces and moments are compared with experimental measurements to clarify the validity of the proposed numerical method. Calculations are then conducted for different water depths, lateral ship-ship distances and ship speeds, and the detailed results are discussed to demonstrate the effects of these factors.
- high-order panel method
- ship-ship hydrodynamic interaction
- shallow water