Numerical analyses of Runge-Kutta implicit-explicit schemes for horizontally explicit, vertically implicit solutions of atmospheric models
Numerical analyses of Runge-Kutta implicit-explicit schemes for horizontally explicit, vertically implicit solutions of atmospheric models
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大气模型水平显式、垂直隐式解的龙格-库塔隐式-显式方案的数值分析
DOI：
10.1002/qj.2246
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发表时间：
2014
影响因子：
8.9
通讯作者：
Lock S
中科院分区：
文献类型：
--
作者：
Lock S
随着兆级计算的前景，只需要局部数据的计算方法变得特别有吸引力。因此，大气模式的典型区域分解意味着水平显式，垂直隐式（HEVI）时间推进方案值得进一步关注。在这一分析中，龙格库塔隐式显式计划从文献中分析其稳定性和准确性，使用冯诺依曼稳定性分析的两个线性系统。注意支付的数值相，以表明相速度和群速度的行为。在分析是易处理的，分析导出的表达式被认为是。对于更复杂的情况下，放大因子已被数值生成和相关的振幅和相位诊断。对描述声波的系统的分析必须将三个合成本征值归因于系统的三个物理模式。为此，设计了一系列算法来跟踪频率空间上的特征值。该结果使得能够分析该方案是否精确地保持非发散模式;以及是否存在群速度方向上的伪反转或声学模式对的阻尼不对称的证据。频率范围涵盖下一代高分辨率天气模型到粗分辨率气候模型;比较了在同一时间间隔内，HEVI格式的多个稳定性约束的较短时间步与全隐式格式的单次积分所累积的误差。两个已在大气模式中使用的格式“Trap 2（2，3，2）”和“UJ 3（1，3，2）”，被确定为在所有分析中提供一致的良好稳定性和相位代表性。此外，根据计算成本的简单测量，'Trap 2（2，3，2）'是最便宜的。
With the prospect of exascale computing, computational methods requiring only local data become especially attractive. Consequently, the typical domain decomposition of atmospheric models means horizontally explicit, vertically implicit (HEVI) time‐stepping schemes warrant further attention. In this analysis, Runge–Kutta implicit–explicit schemes from the literature are analysed for their stability and accuracy using a von Neumann stability analysis of two linear systems. Attention is paid to the numerical phase to indicate the behaviour of phase and group velocities. Where the analysis is tractable, analytically derived expressions are considered. For more complicated cases, amplification factors have been numerically generated and the associated amplitudes and phase diagnosed. Analysis of a system describing acoustic waves has necessitated attributing the three resultant eigenvalues to the three physical modes of the system. To do so, a series of algorithms has been devised to track the eigenvalues across the frequency space. The result enables analysis of whether the schemes exactly preserve the non‐divergent mode; and whether there is evidence of spurious reversal in the direction of group velocities or asymmetry in the damping for the pair of acoustic modes. Frequency ranges that span next‐generation high‐resolution weather models to coarse‐resolution climate models are considered; and a comparison is made of errors accumulated from multiple stability‐constrained shorter time‐steps from the HEVI scheme with a single integration from a fully implicit scheme over the same time interval.Two schemes, ‘Trap2(2,3,2)’ and ‘UJ3(1,3,2)’, both already used in atmospheric models, are identified as offering consistently good stability and representation of phase across all the analyses. Furthermore, according to a simple measure of computational cost, ‘Trap2(2,3,2)’ is the least expensive.