Advanced Search
Article Contents

Application of the Characteristic CIP Method to a Shallow Water Model on the Sphere


doi: 10.1007/s00376-009-9148-6

  • Semi-implicit algorithms are popularly used to deal with the gravitational term in numerical models. In this paper, we adopt the method of characteristics to compute the solutions for gravity waves on a sphere directly using a semi-Lagrangian advection scheme instead of the semi-implicit method in a shallow water model, to avoid expensive matrix inversions. Adoption of the semi-Lagrangian scheme renders the numerical model always stable for any Courant number, and which saves CPU time. To illustrate the efficiency of the characteristic constrained interpolation profile (CIP) method, some numerical results are shown for idealized test cases on a sphere in the Yin-Yang grid system.
  • [1] LI Xingliang, SHEN Xueshun, PENG Xindong, XIAO Feng, ZHUANG Zhaorong, CHEN Chungang, 2013: An Accurate Multimoment Constrained Finite Volume Transport Model on Yin-Yang Grids, ADVANCES IN ATMOSPHERIC SCIENCES, 30, 1320-1330.  doi: 10.1007/s00376-013-2217-x
    [2] LI Xingliang, CHEN Dehui, PENG Xindong, XIAO Feng, CHEN Xiongshan, 2006: Implementation of the Semi-Lagrangian Advection Scheme on a Quasi-Uniform Overset Grid on a Sphere, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 792-801.  doi: 10.1007/s00376-006-0792-9
    [3] LI Xiaohan, PENG Xindong, LI Xingliang, 2015: An Improved Dynamic Core for a Non-hydrostatic Model System on the Yin-Yang Grid, ADVANCES IN ATMOSPHERIC SCIENCES, 32, 648-658.  doi: 10.1007/s00376-014-4120-5
    [4] Chen Jiabin, Wang Jun, 1996: Studies on Non-interpolating Semi-Lagrangian Scheme and Numerical Solution to KdV Equation, ADVANCES IN ATMOSPHERIC SCIENCES, 13, 265-268.  doi: 10.1007/BF02656869
    [5] LIU Lu, RAN Lingkun, SUN Xiaogong, 2015: Analysis of the Structure and Propagation of a Simulated Squall Line on 14 June 2009, ADVANCES IN ATMOSPHERIC SCIENCES, 32, 1049-1062.  doi: 10.1007/s00376-014-4100-9
    [6] LU Daren, YI Fan, XU Jiyao, 2004: Advances in Studies of the Middle and Upper Atmosphere and Their Coupling with the Lower Atmosphere, ADVANCES IN ATMOSPHERIC SCIENCES, 21, 361-368.  doi: 10.1007/BF02915564
    [7] Yang HE, Xiaoqian ZHU, Zheng SHENG, Wei GE, Xiaoran ZHAO, Mingyuan HE, 2022: Atmospheric Disturbance Characteristics in the Lower-middle Stratosphere Inferred from Observations by the Round-Trip Intelligent Sounding System (RTISS) in China, ADVANCES IN ATMOSPHERIC SCIENCES, 39, 131-144.  doi: 10.1007/s00376-021-1110-2
    [8] HUANG Bo, CHEN Dehui, LI Xingliang, LI Chao, , 2014: Improvement of the Semi-Lagrangian Advection Scheme in the GRAPES Model: Theoretical Analysis and Idealized Tests, ADVANCES IN ATMOSPHERIC SCIENCES, 31, 693-704.  doi: 10.1007/s00376-013-3086-z
    [9] WANG Xiaocong, LIU Yimin, WU Guoxiong, Shian-Jiann LIN, BAO Qing, 2013: The Application of Flux-Form Semi-Lagrangian Transport Scheme in a Spectral Atmosphere Model, ADVANCES IN ATMOSPHERIC SCIENCES, 30, 89-100.  doi: 10.1007/s00376-012-2039-2
    [10] Jie TANG, Chungang CHEN, Xueshun SHEN, Feng XIAO, Xingliang LI, 2021: A Positivity-preserving Conservative Semi-Lagrangian Multi-moment Global Transport Model on the Cubed Sphere, ADVANCES IN ATMOSPHERIC SCIENCES, 38, 1460-1473.  doi: 10.1007/s00376-021-0393-7
    [11] Lucas HARRIS, 2021: A New Semi-Lagrangian Finite Volume Advection Scheme Combines the Best of Both Worlds, ADVANCES IN ATMOSPHERIC SCIENCES, 38, 1608-1609.  doi: 10.1007/s00376-021-1181-0
    [12] Wang Yunfeng, Wu Rongsheng, Wang Yuan, Pan Yinong, 1999: Application of Variational Algorithms in Semi-Lagrangian Framework, ADVANCES IN ATMOSPHERIC SCIENCES, 16, 419-430.  doi: 10.1007/s00376-999-0020-5
    [13] Liao Dongxian, 1989: A Regional Spectral Nested Shallow Water Equation Model, ADVANCES IN ATMOSPHERIC SCIENCES, 6, 393-402.  doi: 10.1007/BF02659074
    [14] ZHANG Lifeng, WANG Xingbao, ZHANG Ming, 2003: Spatial and Time Structure of a Gravity Wave in Horizontal Atmosphere of Heterogeneous Stratification, ADVANCES IN ATMOSPHERIC SCIENCES, 20, 29-36.  doi: 10.1007/BF03342047
    [15] Li Guoping, Lu Jinghua, 1996: Some Possible Solutions of Nonlinear Internal Inertial Gravity Wave Equations in the Atmosphere, ADVANCES IN ATMOSPHERIC SCIENCES, 13, 244-252.  doi: 10.1007/BF02656866
    [16] Zhu Xun, 1987: ON GRAVITY WAVE-MEAN FLOW INTERACTIONS IN A THREE DIMENSIONAL STRATIFIED ATMOSPHERE, ADVANCES IN ATMOSPHERIC SCIENCES, 4, 287-299.  doi: 10.1007/BF02663599
    [17] Zhang Zhenyue, 1988: TROPICAL GRAVITY-ATMOSPHERIC LONG WAVE AND THE WALKER CIRCULATION, ADVANCES IN ATMOSPHERIC SCIENCES, 5, 265-276.  doi: 10.1007/BF02656751
    [18] ZHONG Linhao, FENG Shide, GAO Shouting, 2005: Wind-Driven Ocean Circulation in Shallow Water Lattice Boltzmann Model, ADVANCES IN ATMOSPHERIC SCIENCES, 22, 349-358.  doi: 10.1007/BF02918749
    [19] Haochen LI, Chen YU, Jiangjiang XIA, Yingchun WANG, Jiang ZHU, Pingwen ZHANG, 2019: A Model Output Machine Learning Method for Grid Temperature Forecasts in the Beijing Area, ADVANCES IN ATMOSPHERIC SCIENCES, 36, 1156-1170.  doi: 10.1007/s00376-019-9023-z
    [20] Tracy MOFFAT-GRIFFIN, Mike J. TAYLOR, Takuji NAKAMURA, Andrew J. KAVANAGH, J. Scott HOSKING, Andrew ORR, 2017: 3rd ANtarctic Gravity Wave Instrument Network (ANGWIN) Science Workshop, ADVANCES IN ATMOSPHERIC SCIENCES, 34, 1-3.  doi: 10.1007/s00376-016-6197-5

Get Citation+

Export:  

Share Article

Manuscript History

Manuscript received: 10 July 2010
Manuscript revised: 10 July 2010
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Application of the Characteristic CIP Method to a Shallow Water Model on the Sphere

  • 1. State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing 100081,College of Atmospheric Sciences, Lanzhou University, Lanzhou 730000,State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing 100081,Institute of Mechanics, Chinese Academy of Sciences, Beijing 100081, Tokyo Institute of Technology, Tokyo, Japan

Abstract: Semi-implicit algorithms are popularly used to deal with the gravitational term in numerical models. In this paper, we adopt the method of characteristics to compute the solutions for gravity waves on a sphere directly using a semi-Lagrangian advection scheme instead of the semi-implicit method in a shallow water model, to avoid expensive matrix inversions. Adoption of the semi-Lagrangian scheme renders the numerical model always stable for any Courant number, and which saves CPU time. To illustrate the efficiency of the characteristic constrained interpolation profile (CIP) method, some numerical results are shown for idealized test cases on a sphere in the Yin-Yang grid system.

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return