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Unconditionally Stable Explicit Algorithms for Nonlinear Fluid Dynamics Problems

โœ Scribed by John L. Richardson; Robert C. Ferrell; Lyle N. Long

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
225 KB
Volume
104
Category
Article
ISSN
0021-9991

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โœฆ Synopsis

This paper describes novel explicit algorithms that are unconditionally stable. The algorithms are applied to some 1D convection and diffusion problems, including nonlinear problems. Algorithms such as these are of particular interest for massively parallel computers, where one is trying to minimize communications while at the same time maintain the stability properties normally associated with implicit schemes. It is shown how these stable algorithms can be applied in higher spatial dimensions and how they can be extended to problems defined on unstructured meshes. (c) 1993 Academic Press. Inc.

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## Abstract It has been shown that both ADIโ€FDTD and CNโ€FDTD are unconditionally stable. While the ADI is a secondโ€order approximation, CN is only in the first order. However, analytical expressions reveal that the CNโ€FDTD has much smaller truncation errors and is more accurate than the ADIโ€FDTD. N