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

波-结构相互作用的非线性匹配特征函数表达式配置法

基本信息

批准号：
02650364
负责人：
YOSHIDA Akinori
金额：
$ 0.83万
依托单位：
Kyushu University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1990
资助国家：
日本
起止时间：
1990 至 1991
项目状态：
已结题

项目摘要

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.

首先提出了一种求解波结构相互作用边值问题的匹配特征函数展开的新方法。当划分子域的解在公共边界上匹配时，该方法具有点向收敛性，而不是传统方法的平均相干性。理论公式和计算机编程变得极其简单，因为不需要对与特征函数相关的积分进行繁琐的计算。基于两种方法的数值计算表明，新方法比传统方法更简单、更准确。利用匹配特征函数展开的配点法，提出了一种研究stokes -二阶波与结构相互作用的数值方法。该方法有两个显著特点：(1)物理量的微分是理论上得到的；避免了边界元法、有限元法等离散化方法中不可避免的数值微分误差。(2)采用匹配特征函数展开法中的搭配匹配，而不是传统的匹配；因此，通常比线性相互作用问题复杂得多的理论表述和计算机编程变得极其简单。数值计算结果与实验结果吻合较好。最后将匹配特征函数展开的配点法推广到三维、线性、波-结构相互作用问题，从而发展了求解三维非线性相互作用问题的数值方法。