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    A Generalized Family of Schemes that Eliminate the Spurious Resonant Response of Semi-Lagrangian Schemes to Orographic Forcing

    Source: Monthly Weather Review:;1995:;volume( 123 ):;issue: 012::page 3605
    Author:
    Côté, Jean
    ,
    Gravel, Sylvie
    ,
    Staniforth, Andrew
    DOI: 10.1175/1520-0493(1995)123<3605:AGFOST>2.0.CO;2
    Publisher: American Meteorological Society
    Abstract: The one-parameter three-time-level family of O(?t2)-accurate schemes, introduced in Rivest et al. to address the problem of the spurious resonant response of semi-implicit semi-Lagrangian schemes at large Courant number, has been generalized to a two-parameter family by introducing the possibility of evaluating total derivatives using an additional time level. The merits of different members of this family based on both theory and results are assessed. The additional degree of freedom might be expected a priori to permit a reduction of the time truncation errors while still maintaining stability and avoiding spurious resonance. Resonance, stability, and truncation error analyses for the proposed generalized family of schemes are given. The subfamily that is formally O(?t3)-accurate is unfortunately unstable for gravity modes. Sample integrations for various members of the generalized family are shown. Results are consistent with theory, and stable nonresonant forecasts at large Courant number are possible for a range of values of the two free parameters. Of the two methods proposed in Rivest et al. for computing trajectories, the one using a piecewise-defined trajectory is to be preferred to that using a single great-circle arc since it is more accurate at a large time step for some members of the generalized family.
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      A Generalized Family of Schemes that Eliminate the Spurious Resonant Response of Semi-Lagrangian Schemes to Orographic Forcing

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    http://yetl.yabesh.ir/yetl1/handle/yetl/4203566
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    contributor authorCôté, Jean
    contributor authorGravel, Sylvie
    contributor authorStaniforth, Andrew
    date accessioned2017-06-09T16:10:36Z
    date available2017-06-09T16:10:36Z
    date copyright1995/12/01
    date issued1995
    identifier issn0027-0644
    identifier otherams-62651.pdf
    identifier urihttp://onlinelibrary.yabesh.ir/handle/yetl/4203566
    description abstractThe one-parameter three-time-level family of O(?t2)-accurate schemes, introduced in Rivest et al. to address the problem of the spurious resonant response of semi-implicit semi-Lagrangian schemes at large Courant number, has been generalized to a two-parameter family by introducing the possibility of evaluating total derivatives using an additional time level. The merits of different members of this family based on both theory and results are assessed. The additional degree of freedom might be expected a priori to permit a reduction of the time truncation errors while still maintaining stability and avoiding spurious resonance. Resonance, stability, and truncation error analyses for the proposed generalized family of schemes are given. The subfamily that is formally O(?t3)-accurate is unfortunately unstable for gravity modes. Sample integrations for various members of the generalized family are shown. Results are consistent with theory, and stable nonresonant forecasts at large Courant number are possible for a range of values of the two free parameters. Of the two methods proposed in Rivest et al. for computing trajectories, the one using a piecewise-defined trajectory is to be preferred to that using a single great-circle arc since it is more accurate at a large time step for some members of the generalized family.
    publisherAmerican Meteorological Society
    titleA Generalized Family of Schemes that Eliminate the Spurious Resonant Response of Semi-Lagrangian Schemes to Orographic Forcing
    typeJournal Paper
    journal volume123
    journal issue12
    journal titleMonthly Weather Review
    identifier doi10.1175/1520-0493(1995)123<3605:AGFOST>2.0.CO;2
    journal fristpage3605
    journal lastpage3613
    treeMonthly Weather Review:;1995:;volume( 123 ):;issue: 012
    contenttypeFulltext
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