Adaptive high-fidelity computational fluid dynamics

点击翻译按钮获取中文摘要

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.