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On the discretization of gradient and curl in atmospheric models using height‐based terrain‐following coordinates
Author(s) -
Thuburn J.
Publication year - 2011
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.2247
Subject(s) - curl (programming language) , discretization , terrain , grid , mathematics , coordinate system , curvilinear coordinates , scalar (mathematics) , mathematical analysis , geometry , geology , computer science , geography , cartography , programming language
Different discretizations of the gradient and curl operators are considered for a staggered grid in a height‐based terrain‐following coordinate system. A combination of discrete operators is identified that guarantees the mimetic property that the curl of the gradient of any scalar vanishes identically. The result is illustrated with some numerical examples. Copyright © 2010 John Wiley & Sons, Ltd.