Volume 6, pp. 211-223, 1997.

A stable multigrid strategy for convection-diffusion using high order compact discretization

Anand L. Pardhanani, William F. Spotz, and Graham F. Carey

Abstract

Multigrid schemes based on high order compact discretization are developed for convection-diffusion problems. These multigrid schemes 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.

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Key words

convection-diffusion, high-order compact discretizations, multigrid.

AMS subject classifications

65F10,65N06,65N22,65N55.

ETNA articles which cite this article

Vol. 39 (2012), pp. 32-45 T. V. S. Sekhar, R. Sivakumar, S. Vimala, and Y. V. S. S. Sanyasiraju: A combined fourth-order compact scheme with an accelerated multigrid method for the energy equation in spherical polar coordinates

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