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An Investigation of Directional-Coarsening and Line-Implicit Smoothing Applied to Agglomeration Multigrid

The convergence rates of explicit agglomeration multigrid algorithms for turbulent flow problems are significantly worse than for inviscid flow problems. Two techniques for reducing numerical stiffness are investigated and compared. Directional coarsening, controlled by the parameter β, alters the agglomeration algorithm to generate coarse grids that reduce localized cell stretching. Line-implicit smoothing, controlled by the parameter α, adds implicit terms to the preconditioner along one-dimensional lines constructed on the mesh. Optimal values of β and α are presented for structured and hybrid unstructured meshes. A factor of two improvement in asymptotic convergence rates has been demonstrated. Substantial improvements in CPU time can be obtained for a five-order residual reduction.