2^nd-order Wave Action On Structure With Corners By Scaled Boundary Finite Element Method

BEM?Boundary Element Method?is recognized as an effective and well-developed method to analyze the interaction between wave and structures.Nevertheless,difficulties still exist.A significant one is the singular solution due to the discontinuity of boundary conditions.This kind of singularity frequently occurs at corners of ocean structures,around which the spatial derivatives of velocity potential change severely with the decline of precision.It is to cause divergence especially when we set about higher order research.To obtain a converged result,the singularity is technically simplified or the computational grid is refined unilaterally.In fact,the singular behavior probably contains important factors and has important impact on nonlinear questions or complicated boundary-value questions.Aimed at the singularity of corners,Scaled Boundary Finite Element Method?SBFEM?is applied in this thesis.Solution of SBFEM consists of the circumferential part and the radial part.The former is numerical,while the latter,named as radial function,is analytically worked out from the transformed PDE.The radial function possesses the feature of analysis,thus it has high precision and fine smoothness.With the radial function applied,explicit formulas of physical quantities on radial boundary are available so that the singular behavior is disclosed.Description of singularity by SBFEM is verified with analytic approaches.On basis of this,researches on the 2^nd-order diffraction and radiation problems of a 2-D box are carried out.According to radial function,the 1st and 2^nd order derivatives of velocity potential and 2^nd-order water pressure on structure are given in explicit formula.Finally,the pressure integration on body surface is implemented analytically in both direct and indirect method to earn the accurate wave forces.In this thesis,most of the results are verified by analytic approaches and compared with those worked out by Higher Order Boundary Element Method?HOBEM?.According to the research,the singular effect of corner has noticeably impact on nonlinear wave force,which is underestimated with traditional numerical method.Result shows that besides precision and efficiency,SBFEM has the superiority in singularity analysis.