• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.11
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• pp.2773-2781
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• 1993

Laplace's equation is, perhaps, the most important equation, which governs various kinds of physical phenomena. Due to its importance, there have been several numerical techniques such as the finite element method, the finite difference method, and the boundary element method. However, these techniques do not appear very effective as they require a substantial amount of numerical calculation. In this paper, we develop a new most efficient technique based on analytic solutions for Laplace's equation in some convex polygons. Although a similar approach was used for the same problem, the present technique is unique as it solves directly Laplace's equation with the utilization of analytical solutions.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.9
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• pp.2322-2330
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• 1994

The torsion problem in a cylindrical rod is usually formulated in terms of either the warping function or the Prandtl stress function. In a rod whose cross-section is bounded by circles and rectangles, we develop an analytic solution approach based on the warping function, which satisfies Laplace's equation. The present formulation employs polynomials and The Fourier series-type solutions, both of which satisfy exactly the governing differential equation. Using the present method, the maximum shear stress and torsional rigidity are efficiently and accurately calculated and the present results are compared with those by other methods. The specific numerical examples include the case with eccentric holes which was investigated earlier. The finite element results are also compared with the present results.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.20 no.6
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• pp.477-483
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• 1987

We constructed the tidal chart of $M_2$ tide in the East Sea (Japan Sea) by an objective method. The sea level elevations at coastal stations are specified as Dirichlet boundary conditions, and the tidal constants inside of the East Sea basin are determined by the solution of the complex partial differential equation for the sea surface elevation. We studied the influences of the bottom topography and the tidal friction on the distribution of tidal chart inside of the basin. Using the results of basin-wide tidal model, we constructed a detailed tidal chart of the Ma tide off east of Korea.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• v.1
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• pp.51-56
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• 2006

부유식 해상공항과 같은 초대형 부체 구조물(VLFS)의 연안역 설치 후 발생할 수 있는 배후의 해빈변형을 예측하기 위한 토대를 마련하기 위한 기초 연구를 수행하였다. 이를 위해 일정 사면을 가진 천해역에서의 실험 결과를 통하여 비교적 수심이 깊은 곳에 설치된 매립식 구조물 배후에서의 파랑 및 해빈류를 개관하였으며, 매립식 및 부유식 해상 구조물 설치 시 주변 해역의 파랑 및 해빈류장을 계산하였다. 파랑장에 있어서 라프라스 방정식 토대로 유한요소법을 도입한 3차원 파랑 변형 계산을 수행함으로써 매립식 및 부유식 구조물 모두에 대해 적용 가능하였으며, 해상 구조물의 설치 형식이 매립식 및 부유식 경우에 대해 파랑, 해빈류 분포의 변화를 관찰할 수 있었다.

• Journal of the Society of Naval Architects of Korea
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• v.37 no.1
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• pp.67-81
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• 2000

An accurate and efficient numerical method for two-dimensional nonlinear radiation problem has been developed. The wave motion due to a moving body is described by the assumption of ideal fluid flow, and the governing Laplace equation can be effectively solved by the higher-order boundary element method with the help of the GMRES (Generalized Minimal RESidual) algorithm. The intersection or corner problem is resolved by utilizing the so-called discontinuous elements. The implicit trapezoidal rule is used in updating solutions at new time steps by considering stability and accuracy. Traveling waves caused by the oscillating body are absorbed downstream by the damping zone technique. It is demonstrated that the present method for time marching and radiation condition works efficiently for nonlinear radiation problem. To avoid the numerical instability enhanced by the local gathering of grid points, the regriding technique is employed so that all the grids on the free surface may be distributed with an equal distance. This makes it possible to reduce time interval and improve numerical stability. Special attention is paid to the local flow around the body during time integration. The nonlinear radiation force is calculated by the "acceleration potential technique". Present results show good agreement with other numerical computations and experiments.