The principal difficulties in the solution of the potential flow problem of the submerged body were the singularity behavior of the boundary integral equation and the minimizing of numerical error due to discretization of body. This paper introduced a fully desingularized boundary integral equation in which allows an arbitrary high order Gaussian Quadrature to be applied globally to solve exterior 3-D boundary value problem in potential theory numerically. The Gaussian points were used as the collocation points of the integral equation. Analytical surfaces as well as Non Uniform Rational B-Spline (NURBS) surfaces were employed to represent the body surface of submerged body. The numerical results for submerged ellipsoid demonstrated here indicated the present method was adapted to the potential flow problem.
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