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Forward‐in‐time upwind‐weighted methods in ocean modelling
Author(s) -
Hecht Matthew W.
Publication year - 2005
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1136
Subject(s) - discretization , scalar (mathematics) , upwind scheme , context (archaeology) , ocean current , meteorology , magnitude (astronomy) , momentum (technical analysis) , computational fluid dynamics , ocean dynamics , mathematics , computer science , geology , mechanics , climatology , physics , mathematical analysis , geometry , paleontology , finance , astronomy , economics
The World Ocean presents a remarkably wide range of spatial and temporal scales within complicated domains. At larger scales, beyond a few tens of meters, the ocean circulation can be seen to separate into quasi‐horizontal and vertical directions, with the magnitude of mixing differing by many orders of magnitude between the two. It is within this context, and with additional constraints of flux‐conservation when used for coupled climate simulation, that transport schemes are placed within ocean general circulation models. Forward‐in‐time upwind‐weighted methods have made gradual, steady inroads into the field. We review this evolution from centred‐in‐time centred‐in‐space schemes, first discussing temporally hybrid models (centred discretization of the momentum equations with forward‐in‐time treatment of the scalar transport equations), then fully forward‐in‐time models, touching on a number of test problems and analyses that have provided guidance to these model development efforts and discussing selected results. Copyright © 2005 John Wiley & Sons, Ltd.