A Stable Multigrid Strategy for Convection-Diffusion Using High Order Compact Discretization

William F. Spotz

NCAR, SCD
P. O. Box 3000
Boulder, CO 80307


Abstract

Multigrid schemes based on high order compact discretization are developed for convection-diffusion problems which circumvent numerical oscillations and instability, while also yielding higher accuracy. These instabilities are typically exacerbated by the coarser grids in multigrid calculations. Our approach incorporates a 4th order compact formulation for the discretization, while also constructing a consistent multigrid restriction scheme to preserve the accuracy of the fine-to-coarse grid projections. Numerical results demonstrating the higher accuracy and robustness of this approach are presented for representative 2D convection-diffusion problems. These calculations also confirm that our numerical algorithms exhibit the typical multigrid efficiency and mesh-independent convergence properties.