Deflated preconditioned conjugate gradient solvers for the Pressure–Poisson equation

A deflated preconditioned conjugate gradient technique has been developed for the solution of the Pressure–Poisson equation within an incompressible flow solver. The deflation is done using a region-based decomposition of the unknowns, making it extremely simple to implement. The procedure has shown a considerable reduction in the number of iterations. For grids with large graph-depth the savings exceed an order of magnitude. Furthermore, the technique has shown a remarkable insensitivity to the number of groups/regions chosen, and to the way the groups are formed.