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，影响我们生活的决策每天都是基于湍流的预测而做出的，获得湍流的准确预测是全球变化估计、天气预报、淡水供应、提高发动机的能源效率等方面的一个核心挑战。控制污染物的扩散和设计生物医学设备湍流是一个高度不规则的系统，其特征是涉及各种尺度的非线性相互作用的混沌特性变化。这些特征会产生很高的计算复杂度，这使得即使使用现代超级计算机，也无法对湍流进行直接数值模拟，以将所有特征解析到最小尺度，而是使用湍流模型进行实际湍流模拟，以绕过混沌细节并减少复杂性。该项目旨在开发一系列新的系综平均湍流模型及其解决方案的新颖数值方法，扩展有效湍流模拟的当前适用性和计算限制，这可能具有考虑到湍流在几乎所有地球物理和工业流动中的显着影响，将开发一个全面的教育计划，为学生提供计算流体的系统培训。湍流建模仍然是最重要的科学挑战之一，其基本方法是寻求近似合适的（系综、时间、流体速度的平均（或空间）平均值而不是点速度本身是湍流统计理论中最直观的方法，但由于与相关的计算成本极高，目前尚未用于工业流的实际湍流模拟。最近，新开发的系综算法打破了这一僵局，该算法可以在每个时间步访问完整的系综，从而为开发系综平均纳维-斯托克斯方程的湍流模型提供了新的直接可能性。该项目的研究人员将在新的集合平均框架下开发一系列基于集合的变分多尺度方法（VMS）湍流模型和新颖的数值方法，用于实际的湍流模拟。将开发新的无条件稳定的集合算法来快速求解。该项目将为湍流建模和模拟提供新途径，并建立新的严格数值分析解决方案。如何在面对牛顿混沌时做出有效的近似。该奖项反映了 NSF 的法定使命，并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，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

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

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