Directional agglomeration multigrid techniques for high-Reynolds-number viscous flows

A preconditioned directional-implicit agglomeration multigrid algorithm is developed for solving two- and three-dimensional viscous flows an highly anisotropic unstructured meshes of mixed-element types. The multigrid smoother consists of a preconditioned point- or line-implicit solver that operates on lines constructed in the unstructured mesh using a weighted graph algorithm. Directional coarsening or agglomeration is achieved using a similar weighted graph algorithm. A tight coupling of the line construction and directional agglomeration algorithms enables the use of aggressive coarsening ratios in the multigrid algorithm, which in turn reduces the cost of a multigrid cycle. Convergence rates that ape independent of the degree of grid stretching are demonstrated In both two and three dimensions. Further improvement of the three-dimensional convergence rates through a Generalized Minimum Residual (GMRES) technique is also demonstrated.