Krylov solvers in a vertical‐slice version of the semi‐implicit semi‐Lagrangian AROME model,Quarterly Journal of the Royal Meteorological Society

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Krylov solvers in a vertical‐slice version of the semi‐implicit semi‐Lagrangian AROME model
Quarterly Journal of the Royal Meteorological Society ( IF 3.0 ) Pub Date : 2021-01-15 , DOI: 10.1002/qj.3976
Th. Burgot ₁ , L. Auger ₁ , P. Bénard ₁

Affiliation

To circumvent the scalability problem due to global communication involved in spectral transforms, a vertical‐slice version of the dynamical core where all calculations are performed in grid‐point space has been built for AROME, Météo‐France's operational limited‐area model. It is shown in an idealized but nevertheless physically relevant framework that, despite this major change, it is possible to keep the other main characteristics of the model (constant‐coefficient semi‐implicit scheme, semi‐Lagrangian transport scheme, A‐grid, mass‐based coordinate, etc.). A Krylov solver is used to solve the implicit problem. Using the solution given by the spectral model as a reference in terms of quality and required accuracy in an operational context, the chosen parameters of the Krylov solver are carefully tuned to maximize its convergence speed. The Krylov solver consists of several applications of a sparse operator, whose stencil is similar to that of the operator applied during the small time step of split‐explicit schemes traditionally used in HEVI (Horizontally Explicit/Vertically Implicit) models. HEVI models are considered particularly scalable in the current parallelization paradigm and are used as a reference for scalability in this study. Results show that a fast convergence can be reached, such that only a few applications of the sparse operator are required. This suggests an improvement in scalability compared to the spectral version. Experiments have been formulated regardless of the future strategy considered for temporal and spatial resolutions, i.e., increasing spatial resolution while either maintaining a high Courant number or reducing it.

中文翻译：

半隐式半拉格朗日AROME模型的垂直切片版本中的Krylov求解器

为了避免由于频谱转换中涉及的全局通信而导致的可伸缩性问题，已为法国梅托-法国的运营有限区域模型AROME构建了动态核心的垂直切片版本，其中，所有计算均在网格点空间中执行。在理想化但在物理上相关的框架中显示，尽管进行了重大更改，但仍可以保留模型的其他主要特征（常数系数半隐式方案，半拉格朗日输运方案，A网格，质量-基于坐标等）。Krylov求解器用于解决隐式问题。使用频谱模型给出的解作为操作上下文中质量和所需精度的参考，精心调整了Krylov解算器的选定参数，以最大化其收敛速度。Krylov求解器由稀疏算子的多个应用程序组成，其模版类似于传统上在HEVI（水平显式/隐式隐式）模型中使用的分裂显式方案的小时间步所应用的算符。在当前的并行化范例中，HEVI模型被认为特别可伸缩，并且在本研究中被用作可伸缩性的参考。结果表明可以实现快速收敛，因此仅需要稀疏运算符的少数应用程序。与频谱版本相比，这表明可伸缩性得到了改善。无论考虑到时间和空间分辨率的未来策略如何，都已制定了实验，即在保持高Courant数或减少它的同时增加空间分辨率。

更新日期：2021-01-15

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