A linear‐stability analysis of the semi‐implicit semi‐Lagrangian discretization of the fully‐compressible equations | Zendy

Payne T. J. | Zendy

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A linear‐stability analysis of the semi‐implicit semi‐Lagrangian discretization of the fully‐compressible equations

Author(s) -

Payne T. J.

Publication year - 2008

Publication title -

quarterly journal of the royal meteorological society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.744

H-Index - 143

eISSN - 1477-870X

pISSN - 0035-9009

DOI - 10.1002/qj.227

Subject(s) - discretization , hydrostatic equilibrium , mathematics , stability (learning theory) , adiabatic process , compressibility , isothermal process , work (physics) , mathematical analysis , computer science , physics , mechanics , thermodynamics , quantum mechanics , machine learning

We give a linear‐stability analysis of the two‐time‐level semi‐implicit discretization of the adiabatic fully‐compressible equations on an f ‐plane. Previous work has shown that the scheme is stable with respect to perturbations to a hydrostatic and isothermal basic state if the same time‐implicit weight is used throughout and is greater than ½. In this note, we generalize this result to the case where different time weights are used for different terms. © Crown Copyright 2008. Reproduced with the permission of the Controller of HMSO and the Queen's Printer for Scotland. Published by John Wiley & Sons, Ltd.

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