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Errors arising from irregular boundaries in ADI solutions of the shallow‐water equations
Author(s) -
Weare T. J.
Publication year - 1979
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620140611
Subject(s) - shallow water equations , boundary (topology) , mathematics , operator (biology) , truncation (statistics) , scheme (mathematics) , boundary value problem , mathematical analysis , truncation error , waves and shallow water , geology , biochemistry , chemistry , statistics , oceanography , repressor , transcription factor , gene
Truncation errors introduced by operator splittingtechniques, such as the ADI scheme, are discussed in the contextof the two‐dimensional shallow‐water equations. Numericalexamples of flow along a uniform channel, with and withoutfriction, illustrate the practical significance of these errors when the boundary is not aligned with the computational gridaxes. With irregular boundaries the maximum time step aceptable ismore severely restricted than has been realized hitherto. The problem, which is shown to stem from the treatment of the boundary conditons, is inherent in any splitting scheme and is difficult to circumvent.