Second-order Taylor expansion boundary element method for the second-order wave radiation problem

• The second-order Taylor Expansion Boundary Element Method (the 2nd order TEBEM) is developed in this paper. It can give accurate solution of the second-order velocity potential and sum-frequency wave loads for the floating bodies with sharp corners.
• The radiation condition is enforced by a hybrid method of the multi-transmitting formula and damping zone.

A novel Boundary Element Method (BEM) named the second-order Taylor Expansion Boundary Element Method (the 2nd order TEBEM) is developed for the solution of the second-order wave radiation velocity potential and sum-frequency wave loads for floating bodies. The radiation condition is enforced by a hybrid method of the multi-transmitting formula and damping zone. For the interior domain problem of a cube and a sphere, numerical results demonstrate that the 2nd order TEBEM can accurately solve the first and second-order gradients of velocity potential on the no-smoothed and smoothed boundary compared to the low-order BEM. The double frequency forces acting on the truncated cylinder are calculated under finite water depth. The agreement between the 2nd order TEBEM and others' numerical results is good. Moreover, all of the singular integrals in the 2nd order TEBEM can be solved analytically, so its implementation is much easier compared to the high-order BEM.