Two-dimensional solutions for the two-sided lid-driven cavity problem are c
alculated in a wide parameter range using finite volumes. By a tracking met
hod we find multiple flow states which either preserve or break the symmetr
y of the governing equations when the boundary conditions are symmetric. Al
l solution have been traced for non-symmetric boundary conditions to explor
e the connection of the different solution branches. The solution manifold
is illustrated by two- and three-dimensional cuts through the catastrophe s
pace.