魏杰姝,陈春刚,张寅钲,唐杰,沈学顺,肖锋,李兴良. 2024. 适用于非静力大气模式的近似黎曼求解器应用研究. 气象学报,82(3):371-384. DOI: 10.11676/qxxb2024.20230130
引用本文: 魏杰姝,陈春刚,张寅钲,唐杰,沈学顺,肖锋,李兴良. 2024. 适用于非静力大气模式的近似黎曼求解器应用研究. 气象学报,82(3):371-384. DOI: 10.11676/qxxb2024.20230130
Wei Jieshu, Chen Chungang, Zhang Yinzheng, Tang Jie, Shen Xueshun, Xiao Feng, Li Xingliang. 2024. The application of approximate Riemann solver for nonhydrostatic atmospheric models. Acta Meteorologica Sinica, 82(3):371-384. DOI: 10.11676/qxxb2024.20230130
Citation: Wei Jieshu, Chen Chungang, Zhang Yinzheng, Tang Jie, Shen Xueshun, Xiao Feng, Li Xingliang. 2024. The application of approximate Riemann solver for nonhydrostatic atmospheric models. Acta Meteorologica Sinica, 82(3):371-384. DOI: 10.11676/qxxb2024.20230130

适用于非静力大气模式的近似黎曼求解器应用研究

The application of approximate Riemann solver for nonhydrostatic atmospheric models

  • 摘要: 基于多矩非静力大气模式,开展了3类垂向近似黎曼求解器应用研究。多矩非静力大气模式具有高精度与数值守恒特性,其垂向采用守恒的有限差分格式进行数值离散,而网格单元边界通量计算是通过求解黎曼问题来实现的,因此采用合适的近似黎曼求解器对准确模拟非静力大气垂直运动显得十分关键。LLF(Local Lax-Friedrich)、LMARS(Low Mach Approximate Riemann Solver)和HLLC(Harten-Lax-van Leer Contact)为计算流体力学(CFD)中常用的3种近似黎曼求解器,它们的计算代价和复杂程度逐渐增加。一维标准数值试验表明:LLF计算最为经济,但具有较强的耗散;LMARS具有适用于大气流动的假设,对于数值粘性的控制较好且计算量不大;HLLC建立的三波模型可以避免对中间特征场的过度数值耗散。基于LLF近似黎曼求解器计算经济的特点,通过优化LLF近似黎曼求解器各特征波动的粘性系数,能够实现与LMARS、HLLC近似黎曼求解器相同的性能,且计算代价最小。二维非静力数值试验表明,优化的LLF近似黎曼求解器能够规避常规LLF近似黎曼求解器的数值耗散过大问题,正确模拟小尺度非静力垂直运动,达到更复杂的LMARS、HLLC近似黎曼求解器模拟效果且并未增加计算量,这为非静力大气数值模式提供了良好的参考价值。

     

    Abstract: An application study of three kinds of vertical approximate Riemann solvers have been carried out based on a multi-moment nonhydrostatic atmospheric model, which has the characteristics of high accuracy and numerical conservation. The conservative finite difference scheme is used in the vertical direction and the numerical flux in the cell boundary is realized by solving the Riemann problem, which plays a key role in accurately simulating vertical motion in the nonhydrostatic atmosphere. LLF (Local Lax-Friderich), LMARS (Low Mach Approximate Riemann Solver) and HLLC (Harten-Lax-van Leer Contact) are three kinds of approximate Riemann solvers commonly used in the computational fluid dynamics (CFD), and their computational cost and complexity are gradually increasing. One-dimensional standard numerical test show that the cost of LLF solver is the lowest, yet it has strong dissipation. LMARS is assumed to be suitable for atmospheric flow, and its numerical viscosity is not so large and the cost of computation is modest. The inclusion of the third wave in HLLC can avoid excessive numerical dissipation of the intermediate characteristic field. By adjusting the coefficient of the largest eigenvalue of different eigenwaves in LLF solver, the optimized LLF solver can achieve the same performance as that by the relatively complex LMARS and HLLC approximate Riemann solvers, and remain the lowest computational cost. Two-dimensional nonhydrostatic numerical test indicate that the optimized LLF approximate Riemann solver correctly simulates small-scale nonhydrostatic vertical motion and is competitive with the more complex LMARS and HLLC approximate Riemann solvers without increasing the amount of computation. This result provides a good reference for the study of nonhydrostatic atmospheric numerical models.

     

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