Mesh-free resolvent analysis for operator-based discovery of large-scale coherent structures: implementation and the example of the stratified wake behind a sphere

流动不稳定和大规模的相干结构（如漩涡）通常会导致航空航天飞行器更快的加热和不必要的阻力，并且可能是热带气旋等天气事件形成的固有因素。在计算航空科学、自然科学和环境工程中，需要基于预测物理的大规模湍流相干结构建模工具。新的数值方法将被开发，以更好地模拟技术和自然湍流在三维复杂几何。传播策略的目标是使本项目开发的数值工具免费提供给来自不同背景和学科领域的研究人员。此外，新工具将用于研究生水平的课程。这项研究为自然界和工程中复杂流动的高阶精确解析分析提供了机会。该方法的一个关键推动因素是在无网格径向基函数离散化计算方面的最新突破。与从残差估计近似离散雅可比矩阵的方法相比，所提出的方法允许将离散化的精度调整到任意高阶，使用无网格方法显着简化了复杂域的离散化和局部网格细化，并且可以作为一个独立的工具应用于来自不同数值或实验来源的流动数据。为了证明所开发的技术的能力，该项目研究了密度分层流中钝体后面的尾流。基于算子解析模式与利用谱固有正交分解计算的经验模式之间的理论对应关系，本研究对两种方法的分层尾流物理进行了比较研究。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Flow instabilities and large-scale coherent structures (e.g. vortices) often lead to faster heating and unwanted drag on aerospace vehicles and can be inherent in the formation of weather events such as tropical cyclones. Predictive physics-based modeling tools for large-scale coherent structures in turbulent flows are needed in computational aeroscience, natural science, and environmental engineering. Novel numerical approaches will be developed to better simulate technical and natural turbulent flows in three-dimensional complex geometries. The goal of the dissemination strategy is to make the numerical tools developed in this project freely accessible to researchers from diverse backgrounds and disciplinary areas. In addition, the new tool will be used in graduate level courses.This research identifies an opportunity to facilitate high-order accurate resolvent analyses of complex flows as they occur in nature and in engineering. A key-enabler for the proposed methodology is a recent break-through in the computation of mesh-free radial basis function discretization. In contrast to methods that approximate the discrete Jacobian from residual evaluations, the proposed method permits the adjustment of the accuracy of the discretization to arbitrarily high order, uses a mesh-free approach that significantly simplifies the discretization of complex domains and local grid refinement, and works as a stand-alone tool that can be applied to flow data from different numerical or experimental sources. To demonstrate the capabilities of the developed technology, the project investigates the wake flow behind bluff bodies in density-stratified flows. Motivated by the theoretical correspondence between operator-based resolvent modes and empirical modes computed using spectral proper orthogonal decomposition, the research conducts a comparative study of stratified wake physics using both methods.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.