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A monotonically‐damping second‐order‐accurate unconditionally‐stable numerical scheme for diffusion
Author(s) -
Wood Nigel,
Diamantakis Michail,
Staniforth Andrew
Publication year - 2007
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.116
Subject(s) - monotonic function , discretization , diffusion , variable (mathematics) , function (biology) , variable coefficient , mathematics , nonlinear system , mathematical analysis , physics , thermodynamics , quantum mechanics , evolutionary biology , biology
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.