Collaborative Research: Extreme-scale Ready High-order Methods for Astrophysical and Laboratory Turbulence

天体物理现象本质上涉及多物理和多尺度的非线性耦合。用来检验理论模型的计算工具的数学准确性和效率极大地影响了科学结果。因此，天体物理学界长期以来一直专注于开发计算准确的数值算法，以提高解的精度、稳定性和效率。这个项目解决了开发新的方法来解决这些问题的挑战，并将这些方法纳入Flash社区代码，以便接触到天体物理学社区的大量受众。这项工作存在于应用数学和计算数学、统计高斯过程(GP)数据预测和天体物理学的结合点。参与美国国家科学基金会资助的外展活动将有助于教育未被充分代表的社区学院的学生学习计算天体物理学。利用经过验证的模拟对年轻科学家进行天体物理和实验室湍流方面的培训也有助于满足国家的关键需求。本研究将利用新的高阶GP空间重建方法和新的单步高阶时间积分方法，开发高精度、新的算法，而只需适度的复杂性。这一强大的预测工具将在大规模并行的高性能架构上运行。首先，利用新的GP方法克服了大多数有限体积激波捕捉天体物理程序中的二阶瓶颈。GP算法提供了一个简单的数学框架，用于计算高精度的体积平均与逐点量，以及多维空间重建。第二个重要的发展是自适应网格加密网格结构中的一种高效的高阶时间积分方法。这需要在每个单元面的单个正交点进行单步时间更新，这将在极端规模的并行模拟中提供最有效的算法框架。最后，对包括天体物理和实验室湍流在内的关键天体物理流动问题基于解的准确性、误差和计算性能的模拟结果进行比较，将展示这些进步的影响和好处。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Astrophysical phenomena inherently involve multi-physics and multi-scales that are nonlinearly coupled. The mathematical accuracy and efficiency of the computational tools used to test theoretical models hugely impact the scientific outcomes. The astrophysics community has thus long focused on developing computationally accurate numerical algorithms that give improved solution accuracy, stability, and efficiency. This project tackles the challenge of developing new approaches to address these problems, and incorporating these methods in the FLASH community code in order to reach a large audience in the astrophysics community. The work lies at the nexus of applied and computational mathematics, statistical Gaussian Process (GP) data predictions, and astrophysics. Involvement in NSF-supported outreach will help to educate under-represented community college students in computational astrophysics. Training young scientists in astrophysical and laboratory turbulence using validated simulations also helps to meet a critical national need.This study will develop high-order accurate, novel algorithms with only modest complexity, using a new high-order GP spatial reconstruction approach and a novel single-step high-order temporal integration method. This powerful predictive tool will run on massively parallel high-performance architectures. The study involves, firstly, using the novel GP approach to overcome the second-order bottleneck in most finite-volume shock-capturing astrophysics codes. The GP algorithms provide a simple mathematical framework for computing highly accurate volume-averaged versus pointwise quantities, and multidimensional spatial reconstructions. The second important development is an efficient high-order temporal integration method in adaptive mesh refinement grid configurations. This requires a single-step time update at a single quadrature point per cell face, which will provide the most efficient algorithmic framework in extreme-scale parallel simulations. Finally, comparing simulation results based on solution accuracy, errors, and computational performance for key astrophysical flow problems, including astrophysical and laboratory turbulence, will demonstrate the impact and benefit of these advances.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.