Adaptive high-fidelity computational fluid dynamics

随着计算硬件和算法的快速和持续发展，基于仿真的分析已经成为工程实践中不可或缺的工具。在航空航天工程中，设计和分析复杂航空航天系统的需要导致了偏微分方程（PDEs）的新型数值方法的发展，其应用包括空气动力学。仿真能力的持续进步对于设计更高效、更安全、更可持续、更经济的下一代工程系统至关重要。******我的研究项目侧重于pde自动化解决方案技术的开发；我的愿景是将用户从处理数值问题的任务中解放出来，并将基于模拟的分析的巨大潜力提供给工业、政府和学术界的更广泛的研究人员和工程师群体。实现自动化仿真的关键是自适应数值计算，优化分配可用的计算资源，以可靠、高效的方式为工程师的问题提供准确的答案。现有的自适应有限元和模型简化方法虽然在学术应用中显示出巨大的潜力，但在全自动解决复杂工业问题方面缺乏鲁棒性。在三个紧密耦合的项目中，该计划将开发更强大的流求解器、误差估计、适应机制和模型缩减策略。该计划寻求基础数学分析的进步，以及对现实世界问题的算法演示。一方面，需要仔细的数学分析和可证明的结果来正式描述方法的性能。另一方面，大规模的数值演示对于评估实际工业应用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形状上的湍流气动流动，这是一类对航空航天工业有直接影响的问题。此外，所开发的自适应技术将广泛应用于空气动力学以外的工程问题，包括反应流动、固体力学、声学、电磁学以及多物理场问题。该项目还将培养计算科学与工程领域的学生，这是一个结合了科学、工程、数学和计算机科学的快速发展领域，旨在应对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.