Stokes流问题的环向辛对偶求解方法

基于极坐标下Stokes流的基本方程,将环向坐标模拟为时间坐标,采用由流速和应力组成的全状态向量来描述控制方程,得到哈密顿正则对偶方程组,说明Stokes流具有哈密顿结构。在Ham ilton体系下,通过对偶方程组的分离变量法,根据侧边边界条件求出问题的本征值及本征向量,并通过辛正交系、展开求解等手段可以求出问题的通解,然后根据端部边界条件确定本征向量系数后得到具体问题的辛解析解。本文给出了不同边界条件扇形域问题的实际算例,其结果说明了本文方法的有效性。

Symplectic Solution in Circumferential Direction for Stokes Flow Problems in an Annular Cavity

This paper presents a Symplectic method in circumferential direction to determine the Stokes flow in an annular cavity.The flow is drawn across the radial direction with constant velocities.Taking velocities and their dual variables as the basic variables,the Hamilton formulation can be introduced into Stokes flow problems.Then the non-zero eigenvalues and their eigenvectors for the Symplectic eigenvalue problem in circumferential direction are obtained.Using the two ends boundary conditions to determine the coefficients,the method of eigenvector expansion can be used.The results of the examples show that the Symplectic method is effective.