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A semi‐implicit method conserving mass and potential vorticity for the shallow water equations on the sphere
Author(s) -
Bonaventura Luca,
Kornblueh Luis,
Heinze Thomas,
Ripodas Pilar
Publication year - 2004
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.857
Subject(s) - discretization , vorticity , shallow water equations , advection , mathematics , vorticity equation , geopotential , mathematical analysis , divergence (linguistics) , classical mechanics , mechanics , physics , vortex , geophysics , linguistics , philosophy , thermodynamics
A semi‐implicit discretization for the shallow water equations is discussed, which uses triangular Delaunay cells on the sphere as control volumes and conserves mass and potential vorticity. The geopotential gradient, the Coriolis force terms and the divergence of the velocity field are discretized implicitly, while an explicit time discretization is used for the non‐linear advection terms. The results obtained with a preliminary implementation on some idealized test cases are presented, showing that the main features of large scale atmospheric flows are well represented by the proposed method. Copyright © 2004 John Wiley & Sons, Ltd.