In this paper, the local singular behavior of Stokes flow is solved near the salient and re-entrant corners by the matching eigenfunction method. The flow in a rectangular and an L-shaped cavity are considered as a model for the flow generated by the motion of the upper lid. The solutions of the Stokes equation in polar coordinates are matched with a velocity vector components obtained by analytic or numerical solution for the streamfunction developed for any values of the heights of the rectangular and an L-shaped cavity. Streamline patterns near the corner are simulated for a different aspect ratio A. The techniques are tested on a flow problem undergoing Stokes or Navier–Stokes equations in a square cavity. It is seen that the method appears to be cheaper and more accurate than the numerical and analytical methods. It is expected that the study will lead to useful insights into the understanding of the flow topology near a re-entrant corner from a combined analytical-numerical method. Attention is then focused on the topological behavior near the re-entrant corner of the L-shaped cavity. Careful analysis of the streamlines of streamfunction near the re-entrant corner by using wall shear stress allows us to give a possible flow bifurcation of dividing streamline.

The two-dimensional (2D) steady, incompressible, Stokes flow is considered in a T-shaped cavity which has the upper-lid moving in horizontal directions. A Galerkin finite element method is used to investigate a new eddy generation and flow bifurcation. The flow in a cavity is controlled by two parameters  and  which are associated with the heights of the T-shaped domain. By varying  and , the second eddy formation mechanism and the  control space diagram are obtained.

Flow development and eddy structure in an L‐shaped cavity with lids moving in the same directions have been investigated using both tools from topological and numerical methods. In particular, structural bifurcation near a nonsimple degenerate point is investigated by making a local analysis of the velocity field based on a Taylor series expansion. The streamlines of a Hamiltonian vector field system are simplified by using the homotopy invariance of the index theory. A series of bifurcation curves are constructed to determine the sequence of flow structures by which eddies are generated in the L‐shaped cavity.

The magnetohydrodynamic flow of an incompressible, steady and electrically conducting fluid is considered in double lid-driven square cavity under an inclined magnetic field. The non-dimensional governing equations are solved numerically using a radial basis function (RBF) approximation meshless method in order to obtain the flow patterns. Hartmann number [Formula: see text] and the inclination angle of magnetic field [Formula: see text] are taken as a problem variables that produce various flow transformations by their variation for [Formula: see text]. Streamlines are examined topologically, and it has been observed that the inclination angle and strength of magnetic field have different influence on the bifurcation of flow structures.