多重極ポテンシャルの浅水表示に現れる特異積分の効率的評価法 : 半無限区間主値積分の計算と漸近表示

概要

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This paper presents a simple, stable and accurate algorithm for evaluating the following semi-infinite principal integrals efficiently for all relevant values of V, above all for small V, which appear in some expressions of velocity potentials due to pulsating multipoles in water of finite depth. [numerical formula] m=0,1,2,… where V=Kh(h: water depth, K: wave number for h→∞). The asymptotic expressions to the above principal integrals for V〜0 are also derived analytically and are compared with the results by the above scheme numerically. Excellent coincidence is found between the numerical results and the asymptotic ones for V〜0 as well as the existing ones for larger V. High computational accuracy and stability of the present numerical scheme is thus illustrated and, conversely, the validity of the asymptotic expressions derived are proved at the same time. Accordingly, the velocity potentials due to pulsating multipoles, including sources, in shallow water can be calculated very efficiently. A great reduction of computer time and cost can then be achieved in the three-dimensional boundary element computations of shallow water waves of radiation and diffraction, which are known as much more time-consuming than the deep water counterpart. It will also allow the practicing engineers to do such computations on workstations and personal computers easily and freely.
社団法人日本船舶海洋工学会の論文
1992-03-29