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    Stability of Leapfrog Constant-Coefficients Semi-Implicit Schemes for the Fully Elastic System of Euler Equations: Case with Orography

    Source: Monthly Weather Review:;2005:;volume( 133 ):;issue: 005::page 1065
    Author:
    Bénard, P.
    ,
    Mašek, J.
    ,
    Smolíková, P.
    DOI: 10.1175/MWR2907.1
    Publisher: American Meteorological Society
    Abstract: The stability of constant-coefficients semi-implicit schemes for the hydrostatic primitive equations and the fully elastic Euler equations in the presence of explicitly treated thermal residuals has been theoretically examined in the earlier literature, but only for the case of a flat terrain. This paper extends these analyses to a case in which an orography is present, in the shape of a uniform slope. It is shown, with mass-based coordinates, that for the Euler equations, the presence of a slope reduces furthermore the set of the prognostic variables that can be used in the vertical momentum equation to maintain the robustness of the scheme, compared to the case of a flat terrain. The situation appears to be similar for systems cast in mass-based and height-based vertical coordinates. Still for mass-based vertical coordinates, an optimal prognostic variable is proposed and is shown to result in a robustness similar to the one observed for the hydrostatic primitive equations system. The prognostic variables that lead to robust semi-implicit schemes share the property of having cumbersome evolution equations, and an alternative time treatment of some terms is then required to keep the evolution equation reasonably simple. This treatment is shown not to modify substantially the stability of the time scheme. This study finally indicates that with a pertinent choice for the prognostic variables, mass-based vertical coordinates are equally suitable as height-based coordinates for efficiently solving the compressible Euler equations system.
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      Stability of Leapfrog Constant-Coefficients Semi-Implicit Schemes for the Fully Elastic System of Euler Equations: Case with Orography

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    http://yetl.yabesh.ir/yetl1/handle/yetl/4228903
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    contributor authorBénard, P.
    contributor authorMašek, J.
    contributor authorSmolíková, P.
    date accessioned2017-06-09T17:26:51Z
    date available2017-06-09T17:26:51Z
    date copyright2005/05/01
    date issued2005
    identifier issn0027-0644
    identifier otherams-85454.pdf
    identifier urihttp://onlinelibrary.yabesh.ir/handle/yetl/4228903
    description abstractThe stability of constant-coefficients semi-implicit schemes for the hydrostatic primitive equations and the fully elastic Euler equations in the presence of explicitly treated thermal residuals has been theoretically examined in the earlier literature, but only for the case of a flat terrain. This paper extends these analyses to a case in which an orography is present, in the shape of a uniform slope. It is shown, with mass-based coordinates, that for the Euler equations, the presence of a slope reduces furthermore the set of the prognostic variables that can be used in the vertical momentum equation to maintain the robustness of the scheme, compared to the case of a flat terrain. The situation appears to be similar for systems cast in mass-based and height-based vertical coordinates. Still for mass-based vertical coordinates, an optimal prognostic variable is proposed and is shown to result in a robustness similar to the one observed for the hydrostatic primitive equations system. The prognostic variables that lead to robust semi-implicit schemes share the property of having cumbersome evolution equations, and an alternative time treatment of some terms is then required to keep the evolution equation reasonably simple. This treatment is shown not to modify substantially the stability of the time scheme. This study finally indicates that with a pertinent choice for the prognostic variables, mass-based vertical coordinates are equally suitable as height-based coordinates for efficiently solving the compressible Euler equations system.
    publisherAmerican Meteorological Society
    titleStability of Leapfrog Constant-Coefficients Semi-Implicit Schemes for the Fully Elastic System of Euler Equations: Case with Orography
    typeJournal Paper
    journal volume133
    journal issue5
    journal titleMonthly Weather Review
    identifier doi10.1175/MWR2907.1
    journal fristpage1065
    journal lastpage1075
    treeMonthly Weather Review:;2005:;volume( 133 ):;issue: 005
    contenttypeFulltext
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