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

Lixin Ge, Jun Zhang

Research output: Contribution to journalArticlepeer-review

52 Scopus citations


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.

Original languageEnglish
Pages (from-to)560-578
Number of pages19
JournalJournal of Computational Physics
Issue number2
StatePublished - Aug 10 2001

Bibliographical note

Funding Information:
1This research was supported in part by the U.S. National Science Foundation under Grant CCR-9902022, in part by the University of Kentucky Center for Computational Sciences and by the University of Kentucky College of Engineering. 2Joint appointment with Center for Computational Sciences, University of Kentucky, Lexington, 40506-0045.


  • Boundary layer
  • Convection diffusion equation
  • Grid stretching
  • Grid transformation
  • Multigrid method

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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