End Effects of Symplectic Solution to Stokes Flow in a Rectangular Cavity

Abstract

The end effects of symplectic direct solution to Stokes flow in a rectangular cavity are considered. Based on establishing the dual equations for Stokes flow in Hamilton system, the non-zero eigenvalues and their eigensolutions for an anti-symmetric problem were obtained. Expanding the solutions of dual equations by non-zero eigensolutions and determining the expansion coefficients by the end boundary conditions, the decay tendency and interaction mechanism of end effects were discussed and the end boundary errors were investigated. The resultant velocity caused by tangentially driving lid is gradually decayed along the longitudinal direction of cavity. The more number of the expansion items are superposed, the more accurate the solutions are. The smaller the depth-to-width ratios are, the stronger the interference between the end velocities is. The error of ends moving in the same directions is bigger than that in opposite directions.