Symplectic Analytical Solution for Stokes Flow in an Annular Cavity

This paper addresses a Hamiltonian symplectic analytical method to determine stokes flow in an annular geometry. The dual equations for stokes flow are presented. In the symplectic space the problem can be solved via the method of separation of variables and eigenvector expansion. Using the lateral and two ends boundary conditions to determine the eigenvalue and the coefficients, the analytical solutions can be derived. The results of the examples show that the symplectic method is effective, and our method is applicable to other stokes flow problems in a two-dimensional polar region.