“…Roughly speaking, multigrid becomes more effective in these methods because the defect equation is solved by a Krylov-accelerated AMG, that is, by a Krylov method with AMG preconditioning (with a variable number of iterations), instead of being approximated by a recursive application of the multigrid method alone. This adaptive, recursive scheme is referred as the k-cycle AMG.For simulations of weakly compressible flows (with symmetric positive definite matrix of the pressure-correction equation), the performance of this new method is not significantly better than that of the conventional algorithms, see Emans [11,12]. In the present paper, we will examine k-cycle methods for other important classes of flow problems.The treatment of incompressible flows with SIMPLE leads to systems with semi-definite matrices.…”