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    Well-Posed Lateral Boundary Conditions for Spectral Semi-Implicit Semi-Lagrangian Schemes: Tests in a One-Dimensional Model

    Source: Monthly Weather Review:;2009:;volume( 137 ):;issue: 001::page 315
    Author:
    Voitus, F.
    ,
    Termonia, P.
    ,
    Bénard, P.
    DOI: 10.1175/2008MWR2539.1
    Publisher: American Meteorological Society
    Abstract: The aim of this paper is to investigate the feasibility of well-posed lateral boundary conditions in a Fourier spectral semi-implicit semi-Lagrangian one-dimensional model. Two aspects are analyzed: (i) the complication of designing well-posed boundary conditions for a spectral semi-implicit scheme and (ii) the implications of such a lateral boundary treatment for the semi-Lagrangian trajectory computations at the lateral boundaries. Straightforwardly imposing boundary conditions in the gridpoint-explicit part of the semi-implicit time-marching scheme leads to numerical instabilities for time steps that are relevant in today?s numerical weather prediction applications. It is shown that an iterative scheme is capable of curing these instabilities. This new iterative boundary treatment has been tested in the framework of the one-dimensional shallow-water equations leading to a significant improvement in terms of stability. As far as the semi-Lagrangian part of the time scheme is concerned, the use of a trajectory truncation scheme has been found to be stable in experimental tests, even for large values of the advective Courant number. It is also demonstrated that a well-posed buffer zone can be successfully applied in this spectral context. A promising (but not easily implemented) alternative to these three above-referenced schemes has been tested and is also presented here.
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      Well-Posed Lateral Boundary Conditions for Spectral Semi-Implicit Semi-Lagrangian Schemes: Tests in a One-Dimensional Model

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    contributor authorVoitus, F.
    contributor authorTermonia, P.
    contributor authorBénard, P.
    date accessioned2017-06-09T16:26:27Z
    date available2017-06-09T16:26:27Z
    date copyright2009/01/01
    date issued2009
    identifier issn0027-0644
    identifier otherams-67914.pdf
    identifier urihttp://onlinelibrary.yabesh.ir/handle/yetl/4209414
    description abstractThe aim of this paper is to investigate the feasibility of well-posed lateral boundary conditions in a Fourier spectral semi-implicit semi-Lagrangian one-dimensional model. Two aspects are analyzed: (i) the complication of designing well-posed boundary conditions for a spectral semi-implicit scheme and (ii) the implications of such a lateral boundary treatment for the semi-Lagrangian trajectory computations at the lateral boundaries. Straightforwardly imposing boundary conditions in the gridpoint-explicit part of the semi-implicit time-marching scheme leads to numerical instabilities for time steps that are relevant in today?s numerical weather prediction applications. It is shown that an iterative scheme is capable of curing these instabilities. This new iterative boundary treatment has been tested in the framework of the one-dimensional shallow-water equations leading to a significant improvement in terms of stability. As far as the semi-Lagrangian part of the time scheme is concerned, the use of a trajectory truncation scheme has been found to be stable in experimental tests, even for large values of the advective Courant number. It is also demonstrated that a well-posed buffer zone can be successfully applied in this spectral context. A promising (but not easily implemented) alternative to these three above-referenced schemes has been tested and is also presented here.
    publisherAmerican Meteorological Society
    titleWell-Posed Lateral Boundary Conditions for Spectral Semi-Implicit Semi-Lagrangian Schemes: Tests in a One-Dimensional Model
    typeJournal Paper
    journal volume137
    journal issue1
    journal titleMonthly Weather Review
    identifier doi10.1175/2008MWR2539.1
    journal fristpage315
    journal lastpage330
    treeMonthly Weather Review:;2009:;volume( 137 ):;issue: 001
    contenttypeFulltext
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