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A monotonically-damping second-order-accurate unconditionally-stable numerical scheme for diffusion

✍ Scribed by Nigel Wood; Michail Diamantakis; Andrew Staniforth

Book ID
104564842
Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
662 KB
Volume
133
Category
Article
ISSN
0035-9009

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✦ Synopsis

Abstract

We present a new two‐step temporal discretization of the diffusion equation, which is formally second‐order‐accurate and unconditionally stable. A novel aspect of the scheme is that it is monotonically damping: the damping rate is a monotonically‐increasing function of the diffusion coefficient, independent of the size of the time step, when the diffusion coefficient is independent of the variable being diffused. Furthermore, the damping rate increases without bound as the diffusion coefficient similarly increases. We discuss the nonlinear behaviour of the scheme when the diffusion coefficient is a function of the diffused variable. The scheme is designed to maintain any steady‐state solution. We present examples of the performance of the scheme. © Crown Copyright 2007. Reproduced with the permission of the Controller of HMSO. Published by John Wiley & Sons, Ltd.

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