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    The Mass-Conservative Cell-Integrated Semi-Lagrangian Advection Scheme on the Sphere

    Source: Monthly Weather Review:;2002:;volume( 130 ):;issue: 003::page 649
    Author:
    Nair, Ramachandran D.
    ,
    Machenhauer, Bennert
    DOI: 10.1175/1520-0493(2002)130<0649:TMCCIS>2.0.CO;2
    Publisher: American Meteorological Society
    Abstract: A mass-conservative cell-integrated semi-Lagrangian (CISL) scheme is presented and tested for 2D transport on the sphere. The total mass is conserved exactly and the mass of each individual grid cell is conserved in general. The scheme is based on a general scheme developed by Machenhauer and Olk that has increased cost effectiveness without loss of accuracy, compared to the CISL scheme of Ran?i?. A regular latitude?longitude grid is used on the sphere and upstream trajectories from the corner points of the regular grid cells (the Eulerian cells) define the corner points of the departure cells. The sides in these so-called Lagrangian cells are generally defined as straight lines in a (?, ?) plane, where ? is the longitude and ? is the sine of the latitude. The mass distribution within each Eulerian grid cell is defined by quasi-biparabolic functions, which are used to integrate analytically the mass in each Lagrangian computational cell. The auxiliary computational cells are polygons with each side parallel to the coordinate axis. Also, the computational cells have the same area as the Lagrangian cells they approximate. They were introduced in order to simplify the analytical integrals of mass. Near the poles, the east and west sides of certain Lagrangian cells cannot be approximated by straight lines in the (?, ?) plane, and are instead represented by straight lines in polar tangent plane coordinates. Each of the latitudinal belts of Lagrangian cells in the polar caps are split up into several latitudinal belts of subcells, which can be approximated by computational cells as in the case of cells closer to the equator. One latitudinal belt in each hemisphere, which encloses the Eulerian pole (singular belt), is treated in a special way. First the total mass in the singular belt is determined and then it is redistributed among the cells in the belt using weights determined by a traditional SL scheme at the midpoints of the cells. By this procedure the total mass is still conserved while the conservation is only approximately maintained for the individual cells in the singular belt. These special treatments in the polar caps fit well into the general structure of the code and can be implemented with minor modifications in the code used for the rest of the sphere. Compared to two other conservative advection schemes implemented on the sphere the CISL scheme used here was found to be competitive in terms of accuracy for the same resolution. In addition the CISL scheme has the advantage over these schemes that it is applicable for Courant numbers larger than one. In plane geometry the scheme of Ran?i? had an overhead factor of 2.5 in CPU time compared to a traditional bicubic semi-Lagrangian scheme. This factor is reduced to 1.1 for the Machenhauer and Olk scheme on the plane while on the sphere the factor is found to be 1.28 for the present scheme. This overhead seems to be a reasonable price to pay for increased accuracy and exact mass conservation.
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      The Mass-Conservative Cell-Integrated Semi-Lagrangian Advection Scheme on the Sphere

    URI
    http://yetl.yabesh.ir/yetl1/handle/yetl/4204958
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    • Monthly Weather Review

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    contributor authorNair, Ramachandran D.
    contributor authorMachenhauer, Bennert
    date accessioned2017-06-09T16:14:14Z
    date available2017-06-09T16:14:14Z
    date copyright2002/03/01
    date issued2002
    identifier issn0027-0644
    identifier otherams-63903.pdf
    identifier urihttp://onlinelibrary.yabesh.ir/handle/yetl/4204958
    description abstractA mass-conservative cell-integrated semi-Lagrangian (CISL) scheme is presented and tested for 2D transport on the sphere. The total mass is conserved exactly and the mass of each individual grid cell is conserved in general. The scheme is based on a general scheme developed by Machenhauer and Olk that has increased cost effectiveness without loss of accuracy, compared to the CISL scheme of Ran?i?. A regular latitude?longitude grid is used on the sphere and upstream trajectories from the corner points of the regular grid cells (the Eulerian cells) define the corner points of the departure cells. The sides in these so-called Lagrangian cells are generally defined as straight lines in a (?, ?) plane, where ? is the longitude and ? is the sine of the latitude. The mass distribution within each Eulerian grid cell is defined by quasi-biparabolic functions, which are used to integrate analytically the mass in each Lagrangian computational cell. The auxiliary computational cells are polygons with each side parallel to the coordinate axis. Also, the computational cells have the same area as the Lagrangian cells they approximate. They were introduced in order to simplify the analytical integrals of mass. Near the poles, the east and west sides of certain Lagrangian cells cannot be approximated by straight lines in the (?, ?) plane, and are instead represented by straight lines in polar tangent plane coordinates. Each of the latitudinal belts of Lagrangian cells in the polar caps are split up into several latitudinal belts of subcells, which can be approximated by computational cells as in the case of cells closer to the equator. One latitudinal belt in each hemisphere, which encloses the Eulerian pole (singular belt), is treated in a special way. First the total mass in the singular belt is determined and then it is redistributed among the cells in the belt using weights determined by a traditional SL scheme at the midpoints of the cells. By this procedure the total mass is still conserved while the conservation is only approximately maintained for the individual cells in the singular belt. These special treatments in the polar caps fit well into the general structure of the code and can be implemented with minor modifications in the code used for the rest of the sphere. Compared to two other conservative advection schemes implemented on the sphere the CISL scheme used here was found to be competitive in terms of accuracy for the same resolution. In addition the CISL scheme has the advantage over these schemes that it is applicable for Courant numbers larger than one. In plane geometry the scheme of Ran?i? had an overhead factor of 2.5 in CPU time compared to a traditional bicubic semi-Lagrangian scheme. This factor is reduced to 1.1 for the Machenhauer and Olk scheme on the plane while on the sphere the factor is found to be 1.28 for the present scheme. This overhead seems to be a reasonable price to pay for increased accuracy and exact mass conservation.
    publisherAmerican Meteorological Society
    titleThe Mass-Conservative Cell-Integrated Semi-Lagrangian Advection Scheme on the Sphere
    typeJournal Paper
    journal volume130
    journal issue3
    journal titleMonthly Weather Review
    identifier doi10.1175/1520-0493(2002)130<0649:TMCCIS>2.0.CO;2
    journal fristpage649
    journal lastpage667
    treeMonthly Weather Review:;2002:;volume( 130 ):;issue: 003
    contenttypeFulltext
    DSpace software copyright © 2002-2015  DuraSpace
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    DSpace software copyright © 2002-2015  DuraSpace
    نرم افزار کتابخانه دیجیتال "دی اسپیس" فارسی شده توسط یابش برای کتابخانه های ایرانی | تماس با یابش
    yabeshDSpacePersian