深海域における定常波動問題の近似解析法

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タイトル別名
  • A Finite Element Approach to Steady Water Wave Problems in Deep Sea
  • シンカイイキ ニ オケル テイジョウ ハドウ モンダイ ノ キンジ カイセキホ

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抄録

Finite element formulations have been proposed by several authors for water waves caused by harmonic motions of a body. In any case, the water field is divided into two parts, the outer and inner domains, by a fictitious surface which surrounds the body under consideration. The solution in the outer domain, which will be called the outer solution, can be determined analytically within a number of unknown parameters, and it can be expressed by the eigenfunction expansion or the linear combination of Green's function and its derivatives. The solution in the inner domain, which will be called the inner solution, can be obtained by a numerical method such as the finite element method, and the unknown parameters in the outer solution are determined by the continuity condition for both solutions on the fictitious surface.<BR>In the case of shallow water, the formulation with the eigenfunction expansion in the vertical direction can be applied efficiently. In the case of deep water, however, Green's function has to be used as an analytical solution for the outer domain, which is inconvenient for treatments because of its complexity.<BR>In the present paper, a method of superposition of analytical and numerical solutions, which is proposed by Seto and the senior author1).2) for water wave problems, is modified for easy treatments of infinite or deep water field. The progressing part of the outer solution is determined for the actual depth of water, and the standing part is approximately determined by the eigenfunction expansion for a water depth restricted properly. The validity of this approximation for the outer solution can be acertained by the fact that the standing part decreases rapidly with the increase of depth. This analytical solution thus obtained does not necessarily satisfy the condition of continuity everywhere ; this difficulty can be solved by modifying the continuity condition properly on the fictitious surface.<BR>By this method, the inner domain is reduced to a great deal, and numerical computations can be performed efficiently. Example calculations by this method for two-dimensional or three-dimensional axi-symmetric wave propagation problems are performed by the aid of an input generator prepared, and the results obtained show good agreement with the previous authors'.

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