Second-order Taylor Expansion Boundary Element Method for the second-order wave diffraction problem

Abstract

A new Boundary Element Method (BEM) is developed for the solution of the induced velocity at the sharp corners in the context of potential flow. This method is based on the framework of low-order direct BEM to solve the Boundary Integral Equation (BIE), which mainly applies the Taylor expansion to the dipole strength in the BIE, reserves the first-order, second-order and mixed derivatives, and finally solves the corresponding tangential derivatives with respect to the field point in the BIE to form the closed equations. So the method is named the second-order Taylor Expansion Boundary Element Method (the 2nd order TEBEM), which can accurately solve the induced velocity on the non-smooth boundary, compared with the low-order BEM (Constant panel method), and all of the singular integrals in 2nd order TEBEM can be solved analytically. Its implementation is quite easy compared with high-order BEM. The characteristics of 2nd order TEBEM are studied by various wave diffraction problems, and the results of 2nd order TEBEM are compared with the analytical solutions and other numerical results, which show satisfactory agreements.