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

作　　者：张寅钲 陈春刚[3] 沈学顺[2,4] 肖锋 李兴良[2,4] ZHANG Yinzheng;CHEN Chungang;SHEN Xueshun;XIAO Feng;LI Xingliang(Chinese Academy of Meteorological Sciences,Beijing 100081,China;CMA Earth System Modeling and Prediction Centre,Beijing 100081,China;Xi'an Jiaotong University,Xi'an 710049,China;National Meteorological Centre,Beijing 100081,China;Department of Mechanical Engineering,Tokyo Institute of Technology,Tokyo 152-8850,Japan)

机构地区：[1]中国气象科学研究院,北京100081 [2]中国气象局地球系统数值预报中心,北京100081 [3]西安交通大学,西安710049 [4]国家气象中心,北京100081 [5]东京工业大学机械工程系,东京152-8850

出　　处：《气象学报》2023年第4期619-629,共11页Acta Meteorologica Sinica

基　　金：国家自然科学基金项目(42275168);国家重点研发计划项目(2017YFC1501901)。

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。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.

关 键 词：完全平衡 多矩约束有限体积方法 非静力大气 气压梯度力 重力源项 

分 类 号：P435[天文地球—大气科学及气象学]