Article Type:
Research Article

Numerical Stability of the Combined Advection-DiffusionEquation with Nonuniform Spatial Grid

Philip S. Brown Jr. The Center for the Environment and Man, Inc., Hartford, CT 06120

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Joseph P. Pandolfo The Center for the Environment and Man, Inc., Hartford, CT 06120

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Print Publication:
01 Aug 1979
DOI:
https://doi.org/10.1175/1520-0493(1979)107<0959:NSOTCA>2.0.CO;2
Page(s):
959–962
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Abstract

The advection-diffusion equation is often solved by implicit finite-difference schemes that are unconditionally stable when the grid interval is uniform. When such schemes are generalized to account for nonuniform grid spacing, instability can result. The cause of this difficulty is identified and a procedure given to reclaim stability. An example is provided to show that similar computational problems can be encountered in the use of explicit differencing schemes.

Abstract

The advection-diffusion equation is often solved by implicit finite-difference schemes that are unconditionally stable when the grid interval is uniform. When such schemes are generalized to account for nonuniform grid spacing, instability can result. The cause of this difficulty is identified and a procedure given to reclaim stability. An example is provided to show that similar computational problems can be encountered in the use of explicit differencing schemes.

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