Hamilton体系下环扇形域的Stokes流动问题

基于极坐标下Stokes流的基本方程,将径向坐标模拟为时间坐标,推导了Hamilton体系下Stokes流动问题的对偶方程,采用本征向量展开法对环扇形域Stokes流动问题进行了分析,并给出了相应的实际算例,其结果说明了本文方法的有效性。

The Hamiltonian analytical method for Stokes flow problems in an annular cavity

This paper presents a Hamiltonian analytical method to determine the Stokes flow in an annular cavity.The flow is induced by a rotation of the curved walls with prescribed constant unit velocities.Taking velocity and its dual variables as the basic variable,the Hamiltonian formulation can be introduced into Stokes flow problems.In the Symplectic space the problem can be solved by using the method of separation of variables,and the original problem is reduced to finding zero eigenvalue eigen-solutions and non-zero eigenvalue eigen-solutions.Based on the adjoint Symplectic orthogonality relationship between eigenvectors of Hamiltonian matrix,the solutions of equation can be obtained by eigenvectors expansion.Substituting them into the of boundary conditions two ends and determining the related constants,the analytical solutions can be derived.Finally,two examples are given to illustrate the Symplectic method.The results of the examples show that the Symplectic method is effective,and our method is applicable to other Stokesflow in a two-dimensional polar region,thus widening the application of the Hamiltonian system.