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三维变量配置对惯性重力波频散性模拟的影响
IMPACT OF THREE DIMENSIONAL VARIABLE CONFIGURATION SCHEME ON SIMULATION OF INERTIA GRAVITATIONAL WAVE WITH DISPERSION PROPERTIES
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摘要: 在线性斜压原始方程组的基础上，从频率和群速方面讨论了由水平网格 (C、Z网格) 和垂直网格 (L、CP、LZ、LY网格) 组合而成的几种三维网格 (C/L、C/CP、Z/LZ、Z/LY) 的计算频散性并分析了各种网格出现偏差的原因，结果表明三维网格C/CP (水平网格为C网格垂直网格为Charney-Phillips网格) 与Z/LZ（水平网格为Z网格垂直网格为LZ网格）计算频散性能较好。从而为原始方程大气模式选取三维网格提供指导。Abstract: In the framework of linear baroclinic primitive equations, calculation is undertaken for dispersion of inertia gravitational waves in different kinds of 3D (three-dimensional) grids from the perspective of frequency and group velocity, and the reason of the deviation in various grids is analyzed. The results indicate that such 3D structures as C/CP (horizontal grids with Arakawa C grids, and vertical with Charney-Phillips) and Z/LZ (horizontal grids with Z grids, and vertical with LZ) are superior to others in the computational dispersion properties, thereby providing a guidance to the selection of 3D grids applicable to atmospheric primitive equation models.
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Key words:
- 3D grid;
- Inertial gravitational wave;
- Dispersion property;
- Simulation
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[1] Winninghoff F J. On the adjustment toward a geostrophic balance in a simple primitive equation model with application to the problems of initialization and objective analysis: [Ph D. thesis]. Los Angeles: University of California, 1968. [2] 刘宇迪, 祁桂军, 李昕东, 等.水平网格计算频散性的研究.应用气象学报, 2001, 12(2): 140-149. http://qikan.camscma.cn/jams/ch/reader/view_abstract.aspx?file_no=20010220&flag=1 [3] 刘宇迪, 朱红伟.垂直网格计算频散性的研究.应用气象学报, 2001, 12(3): 348-357. http://qikan.camscma.cn/jams/ch/reader/view_abstract.aspx?file_no=20010346&flag=1 [4] 刘宇迪, 季仲贞, 祁桂军, 等.几种垂直跳点网格计算频散性的对比研究.大气科学, 2001, 25(4): 523-535. http://www.cnki.com.cn/Article/CJFDTOTAL-DQXK200104008.htm [5] Liu Yudi, Ji Zhongzhen, Wang Bin. Computational dispersion properties of vertical staggered grids in nonhydrostatical models. Adv. Atmos. Sci, 2002, 19(3): 528-543. doi: 10.1007/s00376-002-0084-y [6] 刘宇迪.垂直变量配置与惯性重力波的模拟.解放军理工大学学报 (自然科学版), 2001, 2(6): 86-89. http://www.cnki.com.cn/Article/CJFDTOTAL-JFJL200106021.htm [7] 刘宇迪, 季仲贞, 朱红伟, 等.水平网格对Rossby的影响.气象学报, 2002, 60(1): 76-84. http://www.cnki.com.cn/Article/CJFDTOTAL-QXXB200201008.htm [8] Arakawa A, Lamb V R. Computational dynamical processes of the UTLA general circulation model. In: Chang J. Ed. Methods in Computational Physics. Academic Press, 1977. 173-265. [9] Rondall D A. Geostrophic adjustment and the finite difference shallow water equations. Monthly Weather Review, 1994, 122: 1371-1377. doi: 10.1175/1520-0493(1994)122<1371:GAATFD>2.0.CO;2 [10] Collatz L. The numerical treatment of differential equations. New York: Springer-Verlag, 1966. [11] Fox-Rabinovitz M. Computational dispersion of horizontal staggered grids for atmospheric and ocean models. Mon.Wea. Rev, 1991, 119: 1624-1639. doi: 10.1175/1520-0493(1991)119<1624:CDPOHS>2.0.CO;2 [12] Song Y, Tang T. Dispersion and group velocity in numerical schemes for three-dimensional hydrodynamic equation. J. Comput. Phys., 1993, 105: 72-82. doi: 10.1006/jcph.1993.1054 [13] Wajsowicz R C. Free planetary waves in finite-difference numerical models. J. Phys. Oceanogr. 1986, 16:773-789. doi: 10.1175/1520-0485(1986)016<0773:FPWIFD>2.0.CO;2 -
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