We present an explicit fourth-order compact ยฎnite dierence scheme for approximating the threedimensional convectionยฑdiusion equation with variable coecients. This 19-point formula is deยฎned on a uniform cubic grid. We compare the advantages and implementation costs of the new scheme with the standar
A second-order ADI scheme for three-dimensional parabolic differential equations
โ Scribed by W. Dai; R. Nassar
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 324 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0749-159X
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โฆ Synopsis
A second-order unconditionally stable ADI scheme has been developed for solving three-dimensional parabolic equations. This scheme reduces three-dimensional problems to a succession of one-dimensional problems. Further, the scheme is suitable for simulating fast transient phenomena. Numerical examples show that the scheme gives an accurate solution for the parabolic equation and converges rapidly to the steady state solution.
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