• Journal of the Society of Naval Architects of Korea
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• v.39 no.1
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• pp.8-15
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• 2002

A two-dimensional higher order panel method using B-splines has been developed to overcome the disadvantages of the low order panel method and to obtain more accurate solution. The sources and the normal dipoles are distributed on both the body and the free surface. Instead of applying the upwind finite difference schemes to satisfy the linearized free surface and the radiation condition, the derivatives of the basis functions of the B-splines are directly applied to the linearized free surface condition. Numerical damping in the Dawson's method are avoided in the Present computations. In order to validate the present method, numerical computations are carried out for a submerged cylinder and a two-dimensional hydrofoil steadily moving beneath a free surface. The numerical results show that fast convergence and better accuracies have been achieved by the present method.

• Journal of the Society of Naval Architects of Korea
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• v.37 no.3
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• pp.27-36
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• 2000

A higher order panel method based on B-spline representation for both the geometry and the velocity potential is developed for the solution of the flow around two-dimensional lifting bodies. Unlike Lee/Kerwin, who placed multiple control points on each panel and solved the overdetermined system of equation by the least square approach, the present method places only as many number of control points as required by the unknowns of the problem. Especially, a null pressure jump Kutta condition at the trailing edge is found to be effective in stabilizing the solution process and in predicting the correct solution. The new approach, is validated to be accurate through comparison with the analytic solution for a 2-D airfoil and to be less time-consuming due to fewer number of panels required than that used in Lee/Kerwin.