• 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.38 no.3
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• pp.31-40
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• 2001

Low-order panel methods are being used to design marine propellers. Since the potential value over each panel for these methods is assumed to be a constant, the accuracy of prediction is known to be limited. Therefore, a higher order boundary element method(HOBEM) has been studied to enhance the accuracy of prediction. In this paper, a HOBEM representing the body boundary surfaces and physical quantities by a 9-node Lagrangian shape function is employed to analyse the flow around marine propellers in steady potential flow. First, the numerical results for a circular wing with thickness variations are compared with Jordan's linear solution. Then, the computational results of two propellers(DTRC 4119 & DTRC 4842 propeller) are compared with the experimental and numerical results published. The pressure distribution on the surface of the propeller is also compared with experimental data.

• Journal of Ocean Engineering and Technology
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• v.14 no.3
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• pp.41-45
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• 2000

In solving the unsteady potential flow problem of the ship in waves with the panel method, in general one can consider the basic flow as the free stream or double body solution. For the double body solution, the body boundary condition has the 2nd derivatives of the velocity potential. Low order panel methods are known to suffer from the significant error in the 2nd derivatives computed at the body surface. This paper analyzes the numerical error in the 2nd derivatives for a 2-D cylinder and a 3-D sphere problem, and an extrapolation method to obtain the correct derivatives on the body surface is suggested.

• Journal of the Society of Naval Architects of Korea
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• v.37 no.2
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• pp.57-69
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• 2000

A higher order panel method based on representation for both the geometry and the velocity potential is developed for the analysis of steady flow around marine propellers. The self-influence functions due to the normal dipole and the source are desingularized through the quadratic transformation, and then the singular part is integrated analytically whereas the non-singular part is integrated using Gaussian quadrature. 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. Numerical experiments indicate that the present method is robust and predicts the pressure distribution around lifting bodies with much fewer panels than existing low order panel methods.

• Journal of the Society of Naval Architects of Korea
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• v.36 no.4
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• pp.9-20
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• 1999

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. The self-influence functions due to the normal dipole and the source are separated into the singular and nonsingular parts, and then the former is integrated analytically whereas the latter is integrated using Gaussian quadrature. 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. Numerical experiments indicate that the present method is robust and predicts the pressure distribution around lifting foils with much fewer panels than existing low order panel methods.

• Journal of the Society of Naval Architects of Korea
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• v.38 no.1
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• pp.43-51
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• 2001

The unsteady problems of ships in waves are analyzed by a low order panel method with Rankine source. Considering the basic flow as the uniform incoming flow(so called Kelvin flow) and also the double body flow. the solutions to satisfy the governing equation with the boundary conditions are obtained, and these two results are compared. The hydrodynamic coefficients for the modified Wigley hull and Series 60($C_B=0.7$) are computed and compared with the experimental data available and also other computational results published. It is shown that the computational results by the double body approximation agree well with the experimental results compared with those by the uniform Kelvin flow approximation.