  The paper discusses a reuse of matrix factorization as a building block in
the Augmented Lagrangian (AL) and modified AL preconditioners for a
non-symmetric saddle point linear algebraic systems. The strategy is applied to
solve two-dimensional incompressible fluid problems with efficiency rates
independent of the Reynolds number. The solver is then tested to simulate a
motion of surface fluids, an example of 2D flows motivated by an interest in
lateral fluidity of inextensible viscous membranes. Numerical examples include
the Kelvin-Helmholtz instability problem posed on the sphere and on the torus.
