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

更快和更准确地预测空间天气需要开发太阳条件模型。本计画借由可压缩高阶非结构光谱差分（CHORUS）程式，发展一个湍流太阳对流的计算模式。这个跨学科项目将支持两名研究生，包括一名女博士。学生以及本科生研究助理。PI将与NOAA的空间天气预报中心以及NCAR的高海拔天文台合作，以更广泛地传播CHORUS++作为开源代码。该项目加速了CHORUS代码的计算效率，提高了其研究太阳对流的准确性，具有前所未有的能力来捕捉其分层和不均匀的性质，并进一步利用CHORUS的能力来揭示多尺度太阳对流，并通过扩展，在密度分层和旋转的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）的强烈湍流性质所需的高计算分辨率。本项目将从三个方面对CHORUS进行改进：1）设计一个边界协调的超限映射，完全消除等参映射带来的数值误差; 2）空间精度从三阶提高到四阶（p2元素）到六阶（P5元件）;以及3）将配备P-改进和本地时间步进能力，以在空间和时间上获得更高的分辨率。由此产生的CHORUS++代码将比CHORUS快100倍以上。太阳大气层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面层，并在那里辐射到太空中。湍流对流反过来又建立了平均流和调节太阳变化的流体动力发电机作用。在建立不均匀性的一个重要因素是极端的变化，在气体密度的顺序100万整个对流区，这产生了一个相称的差异的动力学长度和时间尺度。由上边界层辐射冷却驱动的小热羽流在更深处合并成更大尺度的相干结构。这一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NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

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.