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    The Forward–in-Time Upstream Advection Scheme: Extension to Higher Orders

    Source: Monthly Weather Review:;1987:;volume( 115 ):;issue: 002::page 540
    Author:
    Tremback, Craig J.
    ,
    Powell, James
    ,
    Cotton, William R.
    ,
    Pielke, Roger A.
    DOI: 10.1175/1520-0493(1987)115<0540:TFTUAS>2.0.CO;2
    Publisher: American Meteorological Society
    Abstract: A generalized forward-in-time upstream advective operator following the methodology of Crowley is developed and advective schemes of orders 1 through 10 are tested analytically and numerically. Flux forms of these schemes are also derived with Crowley?s methodology. It is shown that thew flux forms do not reduce to the advective form with constant velocity and grid spacing for schemes of order 3 and higher and they are not as accurate as the advective form. A new flux form is derived which does reduce to the advective form under the conditions of constant velocity and grid spacing. The schemes were tested in two dimensions using time splitting. In the rotating cone test, the advective and new flux forms performed identically, while the other flux form had larger dissipation and dispersion errors. In the deformational flow field test, the advective forms were unstable for both time steps tested. Use flux forms were less unstable for the higher Courant number and the domain as a whole was stable for the lower Courant number. With respect to order of the various forms, the schemes performed consistent with the linear stability analysis; errors decrease as the order of the scheme becomes greater. The sixth-order schemes appear to be the best balance between efficiency and accuracy.
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      The Forward–in-Time Upstream Advection Scheme: Extension to Higher Orders

    URI
    http://yetl.yabesh.ir/yetl1/handle/yetl/4201712
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    contributor authorTremback, Craig J.
    contributor authorPowell, James
    contributor authorCotton, William R.
    contributor authorPielke, Roger A.
    date accessioned2017-06-09T16:06:12Z
    date available2017-06-09T16:06:12Z
    date copyright1987/02/01
    date issued1987
    identifier issn0027-0644
    identifier otherams-60982.pdf
    identifier urihttp://onlinelibrary.yabesh.ir/handle/yetl/4201712
    description abstractA generalized forward-in-time upstream advective operator following the methodology of Crowley is developed and advective schemes of orders 1 through 10 are tested analytically and numerically. Flux forms of these schemes are also derived with Crowley?s methodology. It is shown that thew flux forms do not reduce to the advective form with constant velocity and grid spacing for schemes of order 3 and higher and they are not as accurate as the advective form. A new flux form is derived which does reduce to the advective form under the conditions of constant velocity and grid spacing. The schemes were tested in two dimensions using time splitting. In the rotating cone test, the advective and new flux forms performed identically, while the other flux form had larger dissipation and dispersion errors. In the deformational flow field test, the advective forms were unstable for both time steps tested. Use flux forms were less unstable for the higher Courant number and the domain as a whole was stable for the lower Courant number. With respect to order of the various forms, the schemes performed consistent with the linear stability analysis; errors decrease as the order of the scheme becomes greater. The sixth-order schemes appear to be the best balance between efficiency and accuracy.
    publisherAmerican Meteorological Society
    titleThe Forward–in-Time Upstream Advection Scheme: Extension to Higher Orders
    typeJournal Paper
    journal volume115
    journal issue2
    journal titleMonthly Weather Review
    identifier doi10.1175/1520-0493(1987)115<0540:TFTUAS>2.0.CO;2
    journal fristpage540
    journal lastpage555
    treeMonthly Weather Review:;1987:;volume( 115 ):;issue: 002
    contenttypeFulltext
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