CAREER: Nonlinear Finite Element Manifolds for Improved Simulation of Shock-Dominated Turbulent Flows

职业：用于改进冲击主导的湍流模拟的非线性有限元流形

• 批准号: 2338843
• 负责人: Matthew Zahr
• 金额: $ 52.4万
• 依托单位: University of Notre Dame
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-12-01 至 2028-11-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2338843&HistoricalAwards=false
• 关键词: CAREER; Nonlinear; Finite; Element; Manifolds

Computational Fluid Dynamics (CFD) simulations are notoriously sensitive to the underlying grid for complex flows with boundary layers, shock waves, and turbulence. High-quality, highly refined, feature-aligned grids are usually required to obtain accurate predictions; these are difficult and user-intensive to construct. The principal aim of this project is to develop new simulation technology that eliminates the extreme sensitivity of modern CFD methods to the underlying grid for shock-dominated turbulent flows. The method will be useful across many scientific disciplines, including aerospace, astrophysical, biological, and environmental flows. This research effort will be complemented with an education plan that includes a hands-on fluid dynamics module for Indiana fifth graders, a summer research program for undergraduates, and an education campaign on nonlinear manifold approximations that will feature online content, conference short courses, and open-source software.This project will develop the theoretical and algorithmic foundations for using nonlinear manifolds as the basis for high-fidelity CFD simulations, an unexplored research frontier, to circumvent the limitations of existing methods with regard to complex flow phenomena. Specific nonlinear manifolds will be constructed to tailor the underlying approximation space to complex flow features on generic grids: (1) trigonometric manifolds to represent boundary layers, (2) compositional mappings to represent viscous shocks, and (3) autoencoders to represent more general features, including turbulent eddies and flow instabilities. By tailoring the underlying approximation space to the flow features instead of the grid, nonlinear approximations can dramatically improve the accuracy per degree of freedom and reduce the sensitivity of CFD predictions to the computational grid relative to conventional methods based on linear approximation spaces. As such, this project has great potential to deliver a novel and transformational CFD technology with enhanced accuracy, reliability, and automation of high-fidelity simulations of shock-dominated turbulent flows. A scalable implementation of the new approach will be disseminated in an open-source Julia solver to facilitate transition of the developments in this project to the research community.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.

众所周知，计算流体动力学 (CFD) 模拟对具有边界层、冲击波和湍流的复杂流动的底层网格非常敏感。通常需要高质量、高度精细、特征对齐的网格才能获得准确的预测；这些构建起来很困难并且需要大量用户。该项目的主要目标是开发新的模拟技术，消除现代 CFD 方法对冲击主导的湍流底层网格的极端敏感性。该方法将适用于许多科学学科，包括航空航天、天体物理学、生物和环境流。这项研究工作将得到一项教育计划的补充，其中包括印第安纳州五年级学生的流体动力学实践模块、本科生暑期研究计划以及非线性流形逼近教育活动，其中包括在线内容、会议短期课程和该项目将开发使用非线性流形作为高保真 CFD 模拟基础的理论和算法基础，这是一个尚未探索的研究前沿，以规避现有方法在复杂流动现象方面的局限性。将构建特定的非线性流形，以根据通用网格上的复杂流动特征定制底层近似空间：（1）三角流形来表示边界层，（2）组合映射来表示粘性冲击，以及（3）自动编码器来表示更一般的特征，包括湍流涡流和流动不稳定性。相对于基于线性近似空间的传统方法，通过根据流动特征而不是网格定制基础近似空间，非线性近似可以显着提高每个自由度的精度，并降低 CFD 预测对计算网格的敏感性。因此，该项目具有巨大的潜力，可以提供一种新颖的、变革性的 CFD 技术，提高冲击主导的湍流高保真模拟的准确性、可靠性和自动化程度。新方法的可扩展实施将在开源 Julia 求解器中传播，以促进该项目的开发成果向研究界的过渡。该奖项反映了 NSF 的法定使命，并通过使用基金会的知识进行评估，被认为值得支持。优点和更广泛的影响审查标准。