Directional agglomeration multigrid techniques for high-Reynolds-number viscous flows
Dimitri J. Mavriplis · AIAA Journal · 1999
A preconditioned directional-implicit agglomeration algorithm is developed for solving twoand three-dimensional viscous flows on highly anisotropic unstructured meshes of mixed-element types.The multigrid smoother consists of a pre-conditioned point-or line-implicit solver which 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 thc 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 which are 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 GMRES technique is also demonstrated.