Abstract
A 3D compressible nonhydrostatic dynamic core based on a three-point multi-moment constrained finite-volume (MCV) method is developed by extending the previous 2D nonhydrostatic atmospheric dynamics to 3D on a terrain-following grid. The MCV algorithm defines two types of moments: the point-wise value (PV) and the volume-integrated average (VIA). The unknowns (PV values) are defined at the solution points within each cell and are updated through the time evolution formulations derived from the governing equations. Rigorous numerical conservation is ensured by a constraint on the VIA moment through the flux form formulation. The 3D atmospheric dynamic core reported in this paper is based on a three-point MCV method and has some advantages in comparison with other existing methods, such as uniform third-order accuracy, a compact stencil, and algorithmic simplicity. To check the performance of the 3D nonhydrostatic dynamic core, various benchmark test cases are performed. All the numerical results show that the present dynamic core is very competitive when compared to other existing advanced models, and thus lays the foundation for further developing global atmospheric models in the near future.
摘要
在原来二维非静力大气模式框架基础上, 本文采用3点多矩约束有限体积格式发展了一个含地形的三维完全可压缩非静力有限体积大气模式动力框架. 多矩约束有限体积方法定义了两类矩: (1)点值(PV矩), (2)体积积分平均值(VIA矩). 通过大气控制方程, 单元网格内未知变量(即PV矩)的时间演变得以更新; 而积分平均值(VIA矩)通过有限体积通量形式方法更新其时间演变, 进而保证了数值的严格守恒. 与现有的其他方法相比, 本文发展的三维大气模式框架所采用的3点多矩约束有限体积算法, 具有一致的3阶精度, 模板紧致和算法简洁等优势. 为了检验发展的三维大气模式框架性能, 本文进行了各种标准数值测试包括陡峭地形数值测试, 数值模拟结果表明新发展的三维大气模式框架可与现有的先进大气模式相媲美. 本研究为进一步发展全球多矩约束有限体积模式奠定基础.
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Acknowledgments
This work was supported by the National Key Research and Development Program of China (Grant Nos. 2017YFC1501901 and 2017YFA0603901) and the Beijing Natural Science Foundation (Grant No. JQ18001).
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Article Highlights
• A 3D nonhydrostatic atmospheric dynamic core is built by using a three-point MCV method.
• The MCV scheme used in the present model ensures rigorous numerical conservation, and has a compact stencil and algorithmic simplicity.
• The widely-used standard benchmark tests indicate that the MCV atmospheric model is very competitive when compared to other existing advanced models.
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Qin, Q., Shen, X., Chen, C. et al. A 3D Nonhydrostatic Compressible Atmospheric Dynamic Core by Multi-moment Constrained Finite Volume Method. Adv. Atmos. Sci. 36, 1129–1142 (2019). https://doi.org/10.1007/s00376-019-9002-4
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DOI: https://doi.org/10.1007/s00376-019-9002-4
Key words
- multi-moment constrained finite-volume method
- nonhydrostatic
- dynamic core
- topography
- height-based terrain-following coordinate