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High Accuracy Iterative Solution of Convection Diffusion Equation with Boundary Layers on Nonuniform Grids

✍ Scribed by Lixin Ge; Jun Zhang

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 297 KB
Volume: 171
Category: Article
ISSN: 0021-9991
DOI: 10.1006/jcph.2001.6794

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✦ Synopsis

A fourth-order compact finite difference scheme and a multigrid method are employed to solve the two-dimensional convection diffusion equations with boundary layers. The computational domain is first discretized on a nonuniform (stretched) grid to resolve the boundary layers. A grid transformation technique is used to map the nonuniform grid to a uniform one. The fourth-order compact scheme is applied to the transformed uniform grid. A multigrid method is used to solve the resulting linear system. Numerical experiments are used to show that a graded mesh and a grid transformation are necessary to compute high accuracy solutions for the convection diffusion problems with boundary layers and dicretized by the fourth-order compact scheme.

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