Article (Scientific journals)
Analytical linear numerical stability conditions for an anisotropic 3 D advection-diffusion equation
Beckers, Jean-Marie
1992In SIAM Journal on Numerical Analysis, 29 (3), p. 701-713
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Keywords :
Anisotropic 3D advection diffusion; Numerical Stability
Abstract :
[en] A one-timestep scheme for advective-diffusive problems in three dimensions is analysed from a numerical stability point of view. Choosing a realizable general seven-point centred discretization scheme, the amplification factor of the von Neumann method is calculated, and necessary and sufficient stability conditions for the general one-dimensional problem are retrieved. A similar analysis then leads to necessary conditions for the three-dimensional case. It is proved that the conditions obtained are also sufficient for an explicit N-dimensional case. Generalization is made to uncentered schemes and some classical results are recovered or corrected. For practical use, some miminum implicit factors necessary for stability are calculated and it is shown that the inspection of one-dimensional problems to get stability conditions can be tricky.
Disciplines :
Mathematics
Author, co-author :
Beckers, Jean-Marie  ;  Université de Liège - ULiège > Département d'astrophys., géophysique et océanographie (AGO) > Océanographie physique
Language :
English
Title :
Analytical linear numerical stability conditions for an anisotropic 3 D advection-diffusion equation
Publication date :
1992
Journal title :
SIAM Journal on Numerical Analysis
ISSN :
0036-1429
eISSN :
1095-7170
Publisher :
Society for Industrial & Applied Mathematics
Volume :
29
Issue :
3
Pages :
701-713
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 26 January 2009

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