Steady Stokes flow in a rectangular cavity

This paper addresses a general analytical method for investigating the two-dimensional creeping flow field set up in a rectangular cavity by velocities applied along its top and bottom walls in any arbitrary manner. The main goal is to prove the advantages of that approach when studying a local stream function behaviour near the corner points. The values of amplitudes of the so-called corner eddies were established based on the solution of the finite system of linear algebraic equations. The method is illustrated by several numerical examples. The rapidity of convergence and the accuracy of results are investigated. The streamline patterns for some typical distribution of velocities are shown graphically.