Recycling augmented Lagrangian preconditioner in an incompressible fluid solver

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.

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