Adaptive high-fidelity computational fluid dynamics

随着计算硬件和算法的快速和持续发展，基于模拟的分析已经成为工程实践中不可或缺的工具。在航天工程中，设计和分析复杂的航天系统的需要导致了偏微分方程组(PDE)的新的数值方法的发展，其应用包括空气动力学。模拟能力的持续进步对于设计更高效、更安全、更可持续和更经济的下一代工程系统至关重要。 我的研究计划专注于开发PDE的自动化解决方案技术；我的愿景是将用户从处理数值问题的任务中解放出来，并使行业、政府和学术界更广泛的研究人员和工程师群体能够访问基于模拟的分析的巨大潜力。实现自动化仿真的关键是自适应数值计算，它可以优化分配可用的计算资源，以可靠和高效的方式为工程师的问题提供准确的答案。尽管现有的自适应有限元和模型降阶方法在学术应用上显示出巨大的潜力，但它们缺乏以全自动方式解决复杂工业问题的稳健性。在三个紧密耦合的项目中，该计划将开发更健壮的流动解算器、误差估计、适应机制和模型缩减策略。该计划寻求在基础数学分析方面的进步，以及现实世界问题的算法演示。一方面，需要仔细的数学分析，并有可证明的结果，以正式地表征方法的性能。另一方面，大规模的数值演示对于评估用于实际工业应用的方法的实际性能和促进技术转让是必不可少的。 该计划的目标应用是复杂三维几何结构上的湍流空气动力流动，这是一类在航空航天工业中有直接影响的问题。此外，开发的自适应技术将应用于空气动力学以外的广泛工程问题，包括反应流、固体力学、声学、电磁学以及多物理问题。该计划还将培训学生在计算科学和工程领域，这是一个快速增长的领域，结合科学，工程，数学和计算机科学，以应对21世纪的工程挑战。

With rapid and sustained advances in computing hardware and algorithms, simulation-based analysis has become an indispensable tool in engineering practice. In aerospace engineering, the need to design and analyze complex aerospace systems has resulted in the development of novel numerical methods for partial differential equations (PDEs) with applications including aerodynamics. Continued advances in simulation capabilities are crucial to design next-generation engineering systems that are more efficient, safer, more sustainable, and more economical. My research program focuses on the development of automated solution technologies for PDEs; my vision is to free users from the task of handling numerical issues and to make the vast potential of simulation-based analysis accessible to broader groups of researchers and engineers in industry, government, and academia. The key to realize automated simulations is adaptive numerical computing, which optimally allocates available computing resources to provide an accurate answer to engineers' questions in a reliable and efficient manner. While demonstrating significant potential in academic applications, the existing adaptive finite element and model reduction methods lack robustness to solve complex industrial problems in a fully automatic manner. In three tightly coupled projects, the program will develop more robust flow solvers, error estimates, adaptation mechanics, and model reduction strategies. The program seeks advances in fundamental mathematical analysis as well as demonstration of algorithms for real-world problems. On one hand, careful mathematical analysis, with provable results, is needed to formally characterize the performance of methods. On the other hand, large-scale numerical demonstrations are essential to assess the practical performance of methods for real-world industrial applications and to facilitate technology transfer. The target application of the proposed program is turbulent aerodynamic flows over complex three-dimensional geometries, a class of problems with a direct impact in aerospace industries. In addition, the adaptive techniques developed will apply to a wide range of engineering problems outside of aerodynamics, including reacting flows, solid mechanics, acoustics, electromagnetics, as well as multiphysics problems. The program will also train students in the field of computational science and engineering, a rapidly growing field that combines sciences, engineering, mathematics, and computer science to address engineering challenges in the 21st century.