Stokes流问题中的辛本征解方法

A METHOD OF SYMPLECTIC EIGENSOLUTIONS IN STOKES FLOW

通过引入哈密顿体系,将二维Stokes流问题归结为哈密顿体系下的本征值和本征解问题．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的流动,而非零本征值本征解则显示着端部效应影响特点．数值算例给出了辛本征值和本征解的一些规律和具体例子．这些数值例子说明了端部非规则流动的衰减规律．为研究其它问题提供了一条路径．

In this paper, the problem of two dimensional Stokes flow is reduced to the determination of eigenvalues and eigensolutions in a Hamiltonian system. A closed method for the symplectic eigensolution is presented based on the completeness of the space of symplectic eigensolutions. The results show that basic flows can be described by eigensolutions of zero-eigenvalue and the end effects for the Stokes flow by eigensolutions of non-zero-eigenvalues. Numerical results include some examples of symplectic eigenvalues and eigensolutions, which show that the irregular flow at the ends of the pipeline is decayed. At the same time, the method can also be used for other problems.