9 th International Conference on Hydrodynamics October 11-15, 2010 Shanghai, China 509 2010, 22(5), supplement :526-531 DOI: 10.1016/S1001-6058(09)60247-X Pressure distribution computed by wave-interaction theory for adjacent multiple bodies Masashi Kashiwagi 1* , Qi-qi Shi 2 1 Dept of Naval Arch & Ocean Eng, Osaka University, Osaka, Japan 2 Dept of Naval Arch & Ocean Eng, Shanghai Jiao Tong University, Shanghai, China * E-mail: kashi@naoe.eng.osaka-u.ac.jp ABSTRACT: In spite of a mathematical limitation that each interacting body must be far enough apart from the other bodies, the wave interaction theory has been used successfully even for a case where the separation distance between the bodies is vir- tually zero. Numerical investigation is made in this paper on the practical applicability of the wave interaction theory by considering four identical box-shaped bodies as a simplified example and comparing computed results with correct ones obtained by the higher-order boundary element method. It is shown that the wave force in the horizontal direction can be obtained favorably by the interaction theory even if the separa- tion distance between the bodies is very small. To make rea- sons of this somewhat peculiar phenomenon clear, not only the integrated hydrodynamic force but also the pressure distribu- tion on the body surface is calculated and compared with the results by the higher-order boundary element method. Discus- sion is made on whether the pressure is correctly obtained on the regions very close to adjacent bodies and fortuitous cancel- lation in the integration of the pressure occurs between the two vertical planes in close proximity. KEY WORDS: Wave-body interaction; multiple floating bod- ies; higher-order boundary element method; pressure distribu- tion; integrated hydrodynamic force. 1 INTRODUCTION For the problems on multiple floating bodies, hydro- dynamic interactions among bodies are of great im- portance, especially for small separation distance. When the number of bodies is not so large, a direct panel method can be used for the computation. How- ever, as the number of bodies increases, this method becomes formidable due to extremely large number of unknowns. In this circumstance, the wave interaction theory can be effectively applied. In the wave interaction theory, the velocity potentials are expanded with fundamental harmonic functions in the cylindrical coordinate system, and the generalized diffraction problems for each of the bodies are solved by taking into consideration the effects of wave scat- tering by other bodies. This theory was applied first by Ohkusu [1] to water-wave problems and extended by Kagemoto & Yue [2] and others. There is a mathe- matical limitation when applying this theory. The bod- ies must be far enough apart so that the circles cir- cumscribing the bodies will not overlap each other, otherwise this theory will be incorrect. In spite of this limitation, Murai et al. [3] applied the wave interaction theory to hydroelastic problems of VLFS where the structure is divided into a large number of substruc- tures. In this case, the separation distance between two close sub-structures is virtually zero, which obviously violates the mathematical limitation. However, this theory was claimed to work well, and computed re- sults of the elastic deformation of VLFS showed good agreement with measured ones. Thus, it should be fur- ther investigated whether the wave interaction theory can be practically used even for a case when the mathematical limitation is not satisfied. This paper mainly investigates the relations between the accuracy in computed results by the wave inter- action theory and the separation distance between two bodies in proximity, to verify the range of separation distance in which the wave interaction theory can be practically used. For a square arrangement of 4 identi- cal box-shaped bodies floating in finite water depth, numerical computations are performed by both wave interaction theory and higher-order boundary element method (HOBEM). Computed results of the pressure distribution and integrated force on body surfaces by these two methods are compared with each other, be- cause the results by HOBEM are confirmed to be ac- curate irrespective of the separation distance between bodies. It is shown that the pressure distribution and integrated force on one surface by the wave interac-