An iterative solver for the Navier-Stokes equations in Velocity-Vorticity-Helicity form

We study a variant of augmented Lagrangian (AL)-based block triangular preconditioners to accelerate the convergence of GMRES when solving linear algebraic systems arising from finite element discretizations of the 3D Navier-Stokes equations in VelocityVorticity-Helicity form. This recently proposed formulation couples a velocity-pressure system with a vorticity-helicity system, providing a numerical scheme with enhanced accuracy and superior conservation properties. We find that the resulting discrete systems can be solved efficiently by using AL preconditioning technique, together with the inner-outer FGMRES method for solving the sub-problems. Two numerical experiments are given which illustrate the effectiveness of the proposed method.