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.

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、特征对齐的网格来获得准确的预测;这些网格很难构建，而且需要大量用户。该项目的主要目的是开发新的模拟技术，以消除现代CFD方法对激波主导湍流的底层网格的极端敏感性。该方法将在许多科学学科，包括航空航天，天体物理，生物和环境流量有用。这项研究工作将与一项教育计划相补充，该计划包括印第安纳州五年级学生的动手流体动力学模块，本科生的夏季研究计划，以及非线性流形近似的教育活动，该活动将以在线内容，会议短期课程，和开源软件。这个项目将开发的理论和算法基础，使用非线性流形的基础，保真度CFD模拟，一个未开发的研究前沿，以规避现有方法的局限性，关于复杂的流动现象。将构建特定的非线性流形，以使基本近似空间适应通用网格上的复杂流动特征：（1）三角流形表示边界层，（2）成分映射表示粘性激波，（3）自动编码器表示更一般的特征，包括湍流涡流和流动不稳定性。通过根据流动特征而不是网格来定制底层近似空间，非线性近似可以显著提高每个自由度的精度，并降低计算流体动力学预测相对于基于线性近似空间的传统方法对计算网格的敏感性。因此，该项目具有很大的潜力，可以提供一种新型的和变革性的CFD技术，提高精度，可靠性和冲击主导湍流高保真模拟的自动化。新方法的可扩展实施将在一个开源的Julia求解器中传播，以促进该项目的发展向研究界的过渡。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。