二维矩形域内Stokes流问题的辛解析和数值方法  

Analytical and Numerical Method of Symplectic System for Stokes Flow in the Two-Dimensional Rectangular Domain

作　　者：徐新生[1] 王尕平[1] 孙发明[1] 

机构地区：[1]大连理工大学工程力学系；工业装备结构分析国家重点实验室,辽宁大连116024

出　　处：《应用数学和力学》2008年第6期639-648,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10672031);博士学科点基金资助项目(20060141008)

摘　　要：给出了一种新的解析求解二维矩形域中的Stokes流动问题的方法——辛体系方法(Hamil-ton体系方法).在辛体系下,基本问题归结为本征值和本征解的问题.由于辛本征解之间存在辛正交共轭关系,问题的解和边界条件均可以由本征解描述和表示.利用辛本征解空间的完备性,建立一套封闭的求解问题方法.研究结果表明零本征值本征解描述了基本流动,而非零本征值本征解则表示问题的局部效应.数值结果给出了几种有代表性的流动情况,显示了该求解方法对求解许多问题的有效性.同时,这种方法也为研究其他问题提供了一条思路.A new analytical method of symplectic system, Hamiltonian system, was introduced for solving the problem of the Stokes flow in two-dimensional rectangular domain. In the system, the fundamental problem was reduced to eigenvalue and eigensolution problem, and the solution and boundary conditions can be expanded by eigensolutions employing adjoint relationships of the symplectic ortho-normalization between the eigensolutions. The dose method of the symplectic enginsolution was presented based on the completeness of the symplectic eigensolution space. The results explain that fundamental flows can be described by zero eigenvalue eigensolutions and local effects by nonzero eigenvalue eigensolutions. Numerical examples give various flows in rectangular domain and show the effectiveness of the method for solving a variety of problems. Meanwhile, the method is a path for solving other problems.

关 键 词：HAMILTON体系 辛本征值 辛本征解 STOKES流 矩形域 

分 类 号：O357.1[理学—流体力学]