张寅钲,陈春刚,沈学顺,肖锋,李兴良. 2023. 适用于非静力大气模式的完全平衡多矩约束有限体积方法. 气象学报,81(4):619-629. DOI: 10.11676/qxxb2023.20220182
引用本文: 张寅钲,陈春刚,沈学顺,肖锋,李兴良. 2023. 适用于非静力大气模式的完全平衡多矩约束有限体积方法. 气象学报,81(4):619-629. DOI: 10.11676/qxxb2023.20220182
Zhang Yinzheng, Chen Chungang, Shen Xueshun, Xiao Feng, Li Xingliang. 2023. A well-balanced multi-moment constrained finite volume method for nonhydrostatic atmospheric models. Acta Meteorologica Sinica, 81(4):619-629. DOI: 10.11676/qxxb2023.20220182
Citation: Zhang Yinzheng, Chen Chungang, Shen Xueshun, Xiao Feng, Li Xingliang. 2023. A well-balanced multi-moment constrained finite volume method for nonhydrostatic atmospheric models. Acta Meteorologica Sinica, 81(4):619-629. DOI: 10.11676/qxxb2023.20220182

适用于非静力大气模式的完全平衡多矩约束有限体积方法

A well-balanced multi-moment constrained finite volume method for nonhydrostatic atmospheric models

  • 摘要: 大气数值模式离散垂直动量方程时,一般而言气压梯度力和重力不易维持严格的静力平衡关系。为精确平衡数值离散的垂直气压梯度力和重力,基于高精度多矩约束有限体积方法引入完全平衡数值公式,即以满足静力平衡关系的热力学参考态对重力源项进行数值离散构造,发展了适用于非静力大气的完全平衡多矩约束有限体积方法。一维标准数值试验表明,完全平衡多矩约束有限体积方法能在较粗糙的计算网格点上保持静力平衡参考态的数值计算误差在计算机的单精度( 10^-6 )和双精度( 10^-14 )水平,在具有小量级扰动的初始条件下,完全平衡多矩约束有限体积方法能较好地模拟扰动的传播,二维非静力热泡试验进一步验证了完全平衡多矩约束有限体积方法对非静力大气运动的模拟能力。数值试验结果验证了所发展方法的完全平衡属性和适用性,这为非静力大气模式发展提供了良好参考价值。

     

    Abstract: The exact discrete hydrostatic balance cannot be kept in general when the vertical momentum equation is discretized in atmospheric numerical models. In order to exactly balance the discrete vertical pressure gradient force and gravity force, a well-balanced multi-moment constrained finite volume method for nonhydrostatic atmospheric flow is developed by introducing a well-balanced numerical formulation, in which a numerical reconstruction of the gravity source term is conducted in terms of a thermodynamic reference state that satisfies the hydrostatic balance. One-dimensional benchmarks show that the well-balanced multi-moment constrained finite volume method can maintain the numerical error of the hydrostatic reference state up to machine round off with a coarse grid spacing and can well simulate the propagation of small perturbations even in case of initial small perturbation. Two-dimensional nonhydrostatic thermal bubble test further confirms its ability of simulating nonhydrostatic atmospheric motion accurately. The above numerical experiments have verified the well-balanced property and applicability of the well-balanced multi-moment constrained finite volume method, which provides a good reference for the development of nonhydrostatic atmospheric models.

     

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