Numerical evaluation of various levels of singular integrals, arising in BEM and its application in hydrofoil analysis

The sound implementation of the boundary element method (BEM)is highly dependent on an accurate numerical integration of singular integrals. In this paper, a set of various types of singular domain integrals with three-dimensional boundary element discretization is evaluated based on a transformation integration technique. In the BEM, the integration domain (body surface)needs to be discretized into small elements. For each element, the integral I(xp,x)is calculated on the domain dS. Several types of integrals IBa and ICa are numerically and analytically computed and compared with the relative error. The method is extended to evaluate singular integrals which arise in the solution of the three-dimensional Laplace's equation. An example of the elliptic hydrofoil is performed to study the physical accuracy. The results obtained using both numerical and analytical methods are shown in good agreement with the experimental data.