A Nonlinear Solution of Wave-Structure Interactions with Collocation Method of Matched Eigenfunction Expressions

点击翻译按钮获取中文摘要

A new method for the matched eigenfunction expansions on the boundary-value problem of wavestructure interactions is presented first. When the solution of divided subdomains are matched on the common boundaries, pointwise convergence is specified in the new method instead of mean coherence in the conventional one. Theoretical formulation and computer programing become extremely simple because no tedious evaluations of the integrals related to the eigenfunctions are needed. Numerical calculations based on both the methods show the new method is more simple and accurate than the conventional one.Using the new method (Collocation method of matched eigenfunction expansions), a numeric method for the study of interaction between Stokes-second-order waves and structures is developed. The method has two distinctive features : (1) the differentiations of the physical quantities are obtained theoretically ; thus it is free from errors caused by numerical differentiations which is unavoidable in other methods using discretaization technique such as Boundary Element Method and Finite Element Method, (2) the collocation matching instead of the conventional matching in the method of matched eigenfunction expansions is used ; thus the theoretical formulation and the computer programing, which are usually far more complicated than linear interaction problems become extremely simple. Comparisons of the numerical results with experimental ones show good agreements.The collocation method of matched eigenfunction expansions is lastly extended to threedimensional, linear, wave-structure interaction problems for the purpose of developing the numerical method to solve three-dimensional nonlinear interaction problems.