Glowinski-Pironneau method for the 3D ω-ψequations

Glowinski-Pironneau method for solving the 2D Stokes problem as two uncoupled scalar Poisson equations for the vorticity and the stream Function is extended to the three-dimensional problem. The determination of the two tangential components of vorticity over the boundary is achieved by solving an auxiliary boundary problem characterized by a symmetric definite positive linear operator. In the discrete case, tile explicit determination of the corresponding matrix and/or its solution involves the computation of solenoidal fields for the vorticity and the stream vector which are solution to Poisson equations supplemented by both essential and natural boundary conditions, the latter implying a coupling between the three Cartesian components of each vector unknown.