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    A Time-Splitting Scheme for the Elastic Equations Incorporating Second-Order Runge–Kutta Time Differencing

    Source: Monthly Weather Review:;1998:;volume( 126 ):;issue: 007::page 1992
    Author:
    Wicker, Louis J.
    ,
    Skamarock, William C.
    DOI: 10.1175/1520-0493(1998)126<1992:ATSSFT>2.0.CO;2
    Publisher: American Meteorological Society
    Abstract: A forward-in-time splitting method for integrating the elastic equations is presented. A second-order Runge?Kutta time integrator (RK2) for the large-time-step integration is combined with the forward?backward scheme in a manner similar to the Klemp and Wilhelmson method. The new scheme produces fully second-order-accurate integrations for advection and gravity wave propagation. The RK2 scheme uses upwind discretizations for the advection terms and is easily combined with standard vertically semi-implicit techniques so as to improve computational efficiency when the grid aspect ratio becomes large. A stability analysis of the RK2 split-explicit scheme shows that it is stable for a wide range of advective and acoustic wave Courant numbers. The RK2 time-split scheme is used in a full-physics nonhydrostatic compressible cloud model. The implicit damping properties associated with the RK2?s third-order horizontal differencing allows for a significant reduction in the value of horizontal filtering applied to the momentum and pressure fields, while qualitatively the solutions appear to be better resolved than solutions from a leapfrog model.
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      A Time-Splitting Scheme for the Elastic Equations Incorporating Second-Order Runge–Kutta Time Differencing

    URI
    http://yetl.yabesh.ir/yetl1/handle/yetl/4204125
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    • Monthly Weather Review

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    contributor authorWicker, Louis J.
    contributor authorSkamarock, William C.
    date accessioned2017-06-09T16:12:02Z
    date available2017-06-09T16:12:02Z
    date copyright1998/07/01
    date issued1998
    identifier issn0027-0644
    identifier otherams-63153.pdf
    identifier urihttp://onlinelibrary.yabesh.ir/handle/yetl/4204125
    description abstractA forward-in-time splitting method for integrating the elastic equations is presented. A second-order Runge?Kutta time integrator (RK2) for the large-time-step integration is combined with the forward?backward scheme in a manner similar to the Klemp and Wilhelmson method. The new scheme produces fully second-order-accurate integrations for advection and gravity wave propagation. The RK2 scheme uses upwind discretizations for the advection terms and is easily combined with standard vertically semi-implicit techniques so as to improve computational efficiency when the grid aspect ratio becomes large. A stability analysis of the RK2 split-explicit scheme shows that it is stable for a wide range of advective and acoustic wave Courant numbers. The RK2 time-split scheme is used in a full-physics nonhydrostatic compressible cloud model. The implicit damping properties associated with the RK2?s third-order horizontal differencing allows for a significant reduction in the value of horizontal filtering applied to the momentum and pressure fields, while qualitatively the solutions appear to be better resolved than solutions from a leapfrog model.
    publisherAmerican Meteorological Society
    titleA Time-Splitting Scheme for the Elastic Equations Incorporating Second-Order Runge–Kutta Time Differencing
    typeJournal Paper
    journal volume126
    journal issue7
    journal titleMonthly Weather Review
    identifier doi10.1175/1520-0493(1998)126<1992:ATSSFT>2.0.CO;2
    journal fristpage1992
    journal lastpage1999
    treeMonthly Weather Review:;1998:;volume( 126 ):;issue: 007
    contenttypeFulltext
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