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Title

A stability analysis of finite-volume advection schemes permitting long time steps

Abstract

Finite-volume schemes developed in the meteorological community that permit long time steps are considered. These include Eulerian flux-form schemes as well as fully two-dimensional and cascade cell-integrated semi-Lagrangian (CISL) schemes. A one- and two-dimensional Von Neumann stability analysis of these finite-volume advection schemes is given. Contrary to previous analysis, no simplifications in terms of reducing the formal order of the schemes, which makes the analysis mathematically less complex, have been applied. An interscheme comparison of both dissipation and dispersion properties is given. The main finding is that the dissipation and dispersion properties of Eulerian flux-form schemes are sensitive to the choice of inner and outer operators applied in the scheme that can lead to increased numerical damping for large Courant numbers. This spurious dependence on the integer value of the Courant number disappears if the inner and outer operators are identical, in which case, under the assumptions used in the stability analysis, the Eulerian flux-form scheme becomes identical to the cascade scheme. To explain these properties a conceptual interpretation of the flux-based Eulerian schemes is provided. Of the two CISL schemes, the cascade scheme has superior stability properties.

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document

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http://n2t.net/ark:/85065/d700028j

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eng

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geoscientificInformation

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publication

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2016-01-01T00:00:00Z

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publication

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2007-07-01T00:00:00Z

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Copyright 2007American Meteorological Society (AMS). Permission to use figures, tables, and brief excerpts from this work in scientific and educational works is hereby granted provided that the source is acknowledged. Any use of material in this work that is determined to be "fair use" under Section 107 or that satisfies the conditions specified in Section 108 of the U.S. Copyright Law (17 USC, as revised by P.L. 94-553) does not require the Society's permission. Republication, systematic reproduction, posting in electronic form on servers, or other uses of this material, except as exempted by the above statements, requires written permission or license from the AMS. Additional details are provided in the AMS Copyright Policies, available from the AMS at 617-227-2425 or amspubs@ametsoc.org. Permission to place a copy of this work on this server has been provided by the AMS. The AMS does not guarantee that the copy provided here is an accurate copy of the published work.

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OpenSky Support

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UCAR/NCAR - Library

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PO Box 3000

Boulder

80307-3000

email address

opensky@ucar.edu

web address

http://opensky.ucar.edu/

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