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场和多尺度非线性耦合。用于测试理论模型的计算工具的数学准确性和效率极大地影响着科学成果。因此，天体物理学界长期以来一直致力于开发计算精确的数值算法，以提高求解的准确性、稳定性和效率。该项目解决了开发解决这些问题的新方法的挑战，并将这些方法合并到FLASH社区代码中，以便在天体物理学社区中获得大量受众。这项工作是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。参与nsf支持的外展活动将有助于教育代表性不足的社区大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学和实验室湍流方面的培训也有助于满足国家的关键需求。本研究将使用一种新的高阶GP空间重建方法和一种新的单步高阶时间积分方法，开发出高阶精确、复杂度适中的新算法。这个强大的预测工具将运行在大规模并行的高性能架构上。首先，利用新的GP方法克服了大多数有限体积激波捕获天体物理代码中的二阶瓶颈。GP算法提供了一个简单的数学框架，用于计算高度精确的体积平均量和点方向量，以及多维空间重建。第二个重要的发展是一种高效的高阶时间积分方法在自适应网格细化网格配置。这需要在每个单元面上的单个正交点进行单步时间更新，这将为极端尺度并行模拟提供最有效的算法框架。最后，比较关键天体物理流动问题（包括天体物理和实验室湍流）的求解精度、误差和计算性能的模拟结果，将展示这些进展的影响和好处。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。

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.