CAREER: New Algorithms and Models for Turbulence in Incompressible Fluids

职业：不可压缩流体湍流的新算法和模型

• 批准号: 2143331
• 负责人: Nan Jiang
• 金额: $ 46.28万
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-08-01 至 2027-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2143331&HistoricalAwards=false
• 关键词: CAREER; New; Algorithms; Models; Turbulence

Turbulence is ubiquitous in nature, and decisions that affect our life are made daily based on predictions of turbulent flows. Obtaining accurate predictions of turbulent flows is a central challenge in global change estimation, weather forecasting, freshwater supply, improving the energy efficiency of engines, controlling dispersal of contaminants, and designing biomedical devices. A turbulent flow is a highly irregular system, characterized by chaotic property changes involving a wide range of scales in nonlinear interaction with each other. These features yield a high computational complexity, which makes direct numerical simulations of turbulent flows that aim at resolving all features down to the smallest scales infeasible even with modern supercomputers. Instead, turbulence models are used for practical turbulence simulations to bypass the chaotic details and reduce the computational complexity. This project aims to develop a new family of ensemble averaged turbulence models and novel numerical methods for their solution, extending current applicability and computational limitations of effective turbulence simulations, which may have a great impact on numerous applications in aeronautics, hydraulics, chemical engineering, oceanography, meteorology, astrophysics, and geophysics, considering turbulence’s prominent influence in almost all geophysical and industrial flows. A comprehensive educational program will be developed to provide students with systematic training in computational fluid dynamics and bring them up to date on current research topics in this field. Turbulence modeling remains one of the most important scientific challenges. The fundamental approach for turbulence modeling is to seek to approximate suitable (ensemble, time, or spatial) averages of fluid velocity instead of pointwise velocity itself. Ensemble averaging is the most intuitive approach from the statistical theory for turbulence, but it is currently not in use for practical turbulence simulations of industrial flows due to the extremely high computational cost associated with ensemble simulations. This deadlock is recently broken with newly developed ensemble algorithms that give access to the full ensemble at every time step and thus open new and direct possibilities for developing turbulence models for the ensemble averaged Navier-Stokes equations. In this project the investigator will develop a new family of ensemble-based variational multiscale method (VMS) turbulence models and novel numerical methods under the new framework of ensemble averaging for practical turbulent flow simulations. New unconditionally stable ensemble algorithms will be developed for fast solution of the new ensemble-based VMS turbulence models and to effectively overcome the backflow instability for turbulent flows with open boundary conditions. This project will provide new avenues to turbulence modeling and simulations and build a new rigorous numerical analysis addressing how to make effective approximations in the face of Newtonian chaos.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.

湍流在自然界中无处不在，影响我们生活的决定每天都是基于对湍流的预测做出的。获得湍流的准确预测是全球变化估计、天气预报、淡水供应、提高发动机能源效率、控制污染物扩散和设计生物医学设备的核心挑战。紊流是一种高度不规则的系统，其特点是在相互非线性相互作用中发生大范围的混沌性质变化。这些特征产生了很高的计算复杂性，这使得旨在解决所有特征到最小尺度的湍流的直接数值模拟即使使用现代超级计算机也是不可行的。湍流模型用于实际的湍流模拟，以绕过混沌细节，降低计算复杂度。考虑到湍流在几乎所有的地球物理和工业流动中都有突出的影响，本项目旨在开发一种新的集合平均湍流模型和新的数值方法来解决它们，扩展当前有效湍流模拟的适用性和计算局限性，这可能对航空、水力学、化学工程、海洋学、气象学、天体物理学和地球物理学的许多应用产生重大影响。一个全面的教育计划将为学生提供系统的训练，在计算流体动力学，并使他们在该领域的最新研究课题。湍流建模仍然是最重要的科学挑战之一。湍流建模的基本方法是寻求近似流体速度的合适（集合、时间或空间）平均值，而不是逐点速度本身。集合平均是湍流统计理论中最直观的方法，但由于与集合模拟相关的极高计算成本，目前尚未用于工业流动的实际湍流模拟。最近，新开发的集成算法打破了这一僵局，该算法可以访问每个时间步的完整集成，从而为开发集成平均Navier-Stokes方程的湍流模型开辟了新的和直接的可能性。在这个项目中，研究者将在新的集合平均框架下开发一系列新的基于集合的变分多尺度方法（VMS）湍流模型和新的数值方法，用于实际的湍流模拟。新的无条件稳定集成算法将用于快速求解新的基于集成的VMS湍流模型，并有效克服开放边界条件下湍流的回流不稳定性。该项目将为湍流建模和模拟提供新的途径，并建立一个新的严格的数值分析，解决如何在面对牛顿混沌时做出有效的近似。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。

项目成果

Artificial compressibility SAV ensemble algorithms for the incompressible Navier-Stokes equations

• DOI: 10.1007/s11075-022-01382-z
• 发表时间: 2022-08
• 期刊: Numerical Algorithms
• 影响因子: 2.1
• 作者: N. Jiang;Huanhuan Yang

Numerical investigation of two second-order, stabilized SAV ensemble methods for the Navier–Stokes equations

• DOI: 10.1007/s10444-022-09977-9
• 发表时间: 2022-10
• 期刊: Advances in Computational Mathematics
• 影响因子: 1.7
• 作者: N. Jiang;Huanhuan Yang

Unconditionally stable, second order, decoupled ensemble schemes for computing evolutionary Boussinesq equations

• DOI: 10.1016/j.apnum.2023.06.011
• 发表时间: 2023-10
• 期刊: Applied Numerical Mathematics
• 影响因子: 2.8
• 作者: N. Jiang;Huanhuan Yang