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Baroclinic stability for a family of two‐level, semi‐implicit numerical methods for the 3D shallow water equations
Author(s) -
Rueda Francisco J.,
SanmiguelRojas Enrique,
Hodges Ben R.
Publication year - 2006
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.1391
Subject(s) - baroclinity , barotropic fluid , inviscid flow , shallow water equations , euler equations , primitive equations , mathematics , hydrostatic equilibrium , limit (mathematics) , discretization , dissipative system , froude number , stability (learning theory) , mathematical analysis , mechanics , geometry , physics , flow (mathematics) , computer science , thermodynamics , partial differential equation , quantum mechanics , numerical partial differential equations , machine learning
The baroclinic stability of a family of two time‐level, semi‐implicit schemes for the 3D hydrostatic, Boussinesq Navier–Stokes equations (i.e. the shallow water equations), which originate from the TRIM model of Casulli and Cheng ( Int. J. Numer. Methods Fluids 1992; 15 :629–648), is examined in a simple 2D horizontal–vertical domain. It is demonstrated that existing mass‐conservative low‐dissipation semi‐implicit methods, which are unconditionally stable in the inviscid limit for barotropic flows, are unstable in the same limit for baroclinic flows. Such methods can be made baroclinically stable when the integrated continuity equation is discretized with a barotropically dissipative backwards Euler scheme. A general family of two‐step predictor‐corrector schemes is proposed that have better theoretical characteristics than existing single‐step schemes. Copyright © 2006 John Wiley & Sons, Ltd.