PTEBEM for wave drift forces based on hydrodynamic pressure integration

Abstract

Taylor Expansion Boundary Element Method(TEBEM) is an accurate numerical scheme for solving waves and floating bodies related potential problems, especially the induced velocity at the sharp corner. However, the TEBEM method introduces too many unknowns, resulting in a decrease in the computational efficiency. In this paper, a less time consuming method with similar numerical accuracy named Partial Taylor Expansion Boundary Element Method(PTEBEM) is proposed. Firstly, research shows that the singular property at sharp corner panels is stronger than others. Therefore, retain the Taylor expansion related coefficient and the partial derivatives corresponding to the panels only can form a smaller algebraic system. After solving all the velocity potential and the partial derivatives at sharp corner panels, the partial derivatives at smooth boundary panels can be obtained by constant panel method. From the results of KVLCC2, coupled with Extended Boundary Integral Method(EBIM), the irregular frequency is eliminated. And the irregular frequency mainly comes from the water line integral term and the square of velocity term. Applying the Taylor expansion at sharp corner panels only can retain the numerical accuracy of TEBEM, and the computational efficiency is improved.