SHINE: Faster Boundary-Conforming Simulations of Solar Convection on Unstructured Grids

要想更快更准确地预测太空天气，就需要开发太阳条件的模型。本项目通过推进可压缩高阶非结构谱差（CHORUS）编码，建立了湍流太阳对流的计算模型。该跨学科项目将资助两名研究生（包括一名女博士生）和一名本科生研究助理。PI将与NOAA的空间天气预报中心以及NCAR的高空观测站合作，以开放源代码的形式更广泛地传播CHORUS++。该项目以前所未有的能力捕获太阳对流的分层和非均匀性，加快了CHORUS代码的计算效率，提高了其研究太阳对流的精度，并进一步利用CHORUS代码的能力揭示了多尺度太阳对流，进而扩展到密度分层和旋转影响下湍流热对流的基本物理。CHORUS出色的并行效率使其能够实现捕获太阳对流区（SCZ）强烈湍流性质所必需的高计算分辨率。本课题将从三个方面对CHORUS进行改进：1)设计符合边界的超限映射，彻底消除等参数映射带来的数值误差；2)空间精度从三阶（p2个元素）提升到六阶（p5个元素）；3) p-精细化和局部时间步进功能将配备更高的空间和时间分辨率。由此产生的CHORUS++代码将比CHORUS快100倍以上。太阳大气中的湍流是由热对流驱动的，热对流将热量从太阳内部深处输送到表层，并在表层辐射到太空。紊流对流反过来又建立了平均流量和调节太阳变率的流体动力发电机作用。形成非均匀性的一个重要因素是对流区气体密度的极端变化，这种变化在动力长度和时间尺度上产生了相应的差异。由上层边界层辐射冷却驱动的小热羽流在更深处合并成更大规模的相干结构。这种巨大的动态范围带来了巨大的建模挑战，推动了计算流体动力学的极限，需要局部网格细化和局部时间步进进行并行计算。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Faster and more accurate predictions of space weather require model development of solar conditions. This project develops a computational model for turbulent solar convection by advancing the Compressible High-Order Unstructured Spectral difference (CHORUS) code. This interdisciplinary project will support two graduate students including a female Ph.D. student as well as an undergraduate research assistant. The PI will collaborate with NOAA’s Space Weather Prediction Center as well as NCAR’s High Altitude Observatory for broader dissemination of CHORUS++ as open-source code. This project accelerates the computational efficiency of CHORUS code and improves its accuracy for studying solar convection with an unprecedented capability to capture its hierarchical and inhomogeneous nature, and further exploits the capabilities of CHORUS to shed new light on multi-scale solar convection, and by extension, the fundamental physics of turbulent thermal convection under the influence of density stratification and rotation. The excellent parallel efficiency of CHORUS allows it to achieve the high computational resolution necessary to capture the intensely turbulent nature of the Sun’s convection zone (SCZ). In this project, CHORUS will be improved in three aspects: 1) a boundary- conforming transfinite mapping will be designed to completely remove numerical errors induced by iso-parametric mapping; 2) the order of accuracy in space will be improved from third-order (p2 elements) to sixth-order (p5 elements); and 3) p-refinements and local time stepping capabilities will be equipped for higher resolution in both space and time. The resultant CHORUS++ code will be over 100 times faster than CHORUS. Turbulence in the solar atmosphere is driven by thermal convection which transports heat from the deep solar interior to the surface layers where it is radiated into space. Turbulent convection in turn establishes mean flows and hydrodynamic dynamo action that regulates solar variability. An essential factor in establishing inhomogeneity is the extreme variation in gas density of order 1 million across the convection zone, which produces a commensurate disparity in the dynamical length and time scales. Small thermal plumes driven by radiative cooling in the upper boundary layer merge into larger-scale coherent structures deeper down. This vast dynamical range poses formidable modeling challenges that push the limits of computational fluid dynamics that require local mesh refinements and local time stepping for parallel computations.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.