接触表面中多场耦合方程的边界层特征解  

Boundary-Layer Eigen Solutions for Multi-Field Coupled Equations in the Contact Interface

作　　者：侯磊[1,2] 李涵灵[1] 张家健[1] 林德志[1] 仇璘[2,3] 

机构地区：[1]上海大学数学系,上海200444 [2]上海高校计算科学E-研究院SJTU研究所,上海200240 [3]上海交通大学数学系,上海200240

出　　处：《应用数学和力学》2010年第6期690-702,共13页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10871225);上海市浦江人才计划资助项目(D)(06PJ14416)

摘　　要：介绍由约束场和受重力影响的对流扰动耦合而成的衰减平衡向量场动力学方程的渐近求解.为分析实验室内微观与自然界中宏观现象的正则和奇异扰动问题.运用复合尺度方法进行Fourier调和分析、尺度变化,并引进新的参数,将一个复杂的三维约束耦合动力学方程降维投影并转化成复空间里一维的边界层问题.通过渐近摄动分析,给出多场耦合中扰动问题的特征函数边界层解法,在例2中对流场扰动问题分析,得出从指数振荡解过渡到代数解的转点.进一步分析计算非线性特征值问题并做了渐近摄动分析,最后给出多场耦合中扰动问题的特征值边界层解法.最后,特征关系式的各参数表明其在接触表面中对动力衰变的关键影响.The dissipative equilibrium dynamics studied the law of fluid motion under constraints in the contact interface of the coupling system. It needed to examine how constraints act upon the fluid movement, while the fluid movement reacted to the constraint field. It also needed to examine the coupling fluid field and media within the contact interface, and to use the multi-scale analysis to solve the regular and singular perturbation problems in micro-phe- nomena of laboratories and macro-phenomena of nature. The field affected by the gravity constraints was described. Applying the multi-scale analysis to the complex Fourier harmonic analysis, scale changes, and the introduction of new parameters, the complex three-dimensional coupling dynamic equations were transformed into a boundary layer problem in the one-dimensional complex space. Asymptotic analysis was carried out for inter and outer solutions to the perturbation characteristic function of the boundary layer equations in multi-field coupling. Examples were given for disturbance analysis in the flow field, showing the turning point from the index oscillation solution to the algebraic solution. With further analysis and calculation on non- linear eigenfunctions of the contact interface dynamic problems by the eigenvalue relation, an asymptotic perturbation solution was obtained. Finally, a boundary layer solution to multi-field coupling problems in the contact interface was obtained by asymptotic estimates of eigenvalues for the G-N mode in the large flow limit. Characteristic parameters in the final form of the eigenvalue relation are key factors of the dissipative dynamics in the contact interface.

关 键 词：耦合动力学方程 边界层问题 特征值 渐近摄动分析 转点 

分 类 号：O242.1[理学—计算数学]