Hierarchical Adaptive Variable Fidelity Approach for Incompressible Wall-Bounded Turbulent Flow Simulations

不可压缩壁界湍流模拟的分层自适应可变保真度方法

• 批准号: 1236505
• 负责人: Oleg Vasilyev
• 金额: $ 30万
• 依托单位: University of Colorado at Boulder
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-08-01 至 2015-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1236505&HistoricalAwards=false
• 关键词: Hierarchical; Adaptive; Variable; Fidelity; Approach

1236505VasilyevLatest advancements in wavelet-based numerical methodologies for the solution of partial differential equations, combined with the unique properties of wavelet analysis to unambiguously identify and isolate localized dynamically dominant flow structures, make it feasible to propose development of intelligent methods for turbulent flow simulation that tightly integrate numerics and physicsbased modeling. The overall goal of the research is to develop a robust and computationally efficient predictive computational approach, capable of performing variable fidelity numerical simulation of transitional and turbulent incompressible flows for different flow conditions including turbulent flow separation, turbulent boundary layers, shear layers, and jets. Spatially variable wavelet thresholding strategy will be used for model form adaptation. The wavelet threshold will evolve in space and time using feedback control to guarantee that only a priori specified fraction of turbulent kinetic energy or turbulence dissipation rate is resolved. With such a strategy the transition between adaptive Wavelet-based Direct Numerical Simulation (WDNS), the Coherent Vortex Simulation (CVS), the Stochastic Coherent Adaptive Large Eddy Simulation (SCALES), and adaptive Wavelet-based Unsteady Reynolds Averaged Navier-Stokes (WURANS) simulations regimes is natural: the WURANS models switch to subgrid scale model for SCALES to no model for CVS and WDNS approaches as the percentage of the resolved turbulent kinetic energy or resolved turbulence dissipation rate increases from 0% to 100%. This will form a basis for the proposed new physics-based integration of WDNS, CVS, SCALES, and WURANS methodologies. The strength of the proposed methodology is that all models (WDNS, CVS, SCALES, WURANS) use the same wavelet based adaptation strategy to resolve and tracks the energy-containing eddies on the adaptive computational mesh. The approach will be further enhanced by integrating it with Brinkman penalization to enforce solid boundaries of arbitrary complexity. A unique advantage of combining the proposed approach with Brinkman penalization is the ability to enforce boundary conditions to a specified precision without a significant computational overhead. The proposed hierarchical variable fidelity approach will be extensively validated for a number of benchmark problems such as turbulent channel flow, turbulent flow over backward facing step, turbulent flow in a planar asymmetric diffuser, and turbulent flow past circular and square cylinders. The algorithms developed herein specifically address problems of efficient and affordable numerical simulations of turbulent flows, when classical methods have failed to yield progress in reliable predictive modeling. The research will push the envelope of computational capabilities of modeling multi-scale physics of high Reynolds number turbulent flows and will make possible the simulations of high Reynolds number turbulent flows, which currently are difficult or impossible to solve using conventional numerical algorithms. It is expected that the research will provide insight into the complex multi-scale physics of turbulent flows, improve our understanding of fluid turbulence, and even provide engineers with a vital design tool that completely eliminates the onerous overhead of current grid generation methods. An additional aim of this project is in education and dissemination of the newly developed approach and in distribution of the software tools to be developed as a part of the project for the wide use by the scientific community including government laboratories. The new integrated eddy capturing approach has potentially revolutionary impact on all technological endeavors in which turbulent flow plays an important role. Aeronautics, propulsion, transportation and energy are just a few potential areas for this. The range of other applications in free-surface flows, MHD, and nonlinear PDEs in general is tremendous. High resolution results generated as a part of this project are expected to be broadly used by the scientific community.

1236505 vasilyev基于小波的偏微分方程数值解法的最新进展，结合小波分析明确识别和分离局部动态优势流结构的独特特性，使得提出将数值和基于物理的建模紧密结合的湍流模拟智能方法成为可能。该研究的总体目标是开发一种鲁棒且计算效率高的预测计算方法，能够对不同流动条件下的过渡和湍流不可压缩流动进行变保真度的数值模拟，包括湍流分离、湍流边界层、剪切层和射流。采用空间可变小波阈值策略进行模型形态自适应。小波阈值利用反馈控制在空间和时间上演化，以保证只有先验指定的湍流动能或湍流耗散率被分解。有了这样的策略，基于小波的自适应直接数值模拟（WDNS）、相干涡模拟（CVS）、随机相干自适应大涡模拟（SCALES）和基于小波的自适应非定常雷诺平均纳维-斯托克斯（WURANS）模拟机制之间的过渡是自然的：当解决的湍流动能百分比或解决的湍流耗散率从0%增加到100%时，对于scale方法，WURANS模型从亚网格尺度模型切换到CVS和WDNS方法的无模型。这将为提出的新的基于物理的WDNS、CVS、SCALES和WURANS方法集成奠定基础。该方法的优点在于，所有模型（WDNS、CVS、SCALES、WURANS）都使用相同的基于小波的自适应策略来解析和跟踪自适应计算网格上的含能量涡流。该方法将通过与Brinkman惩罚相结合来进一步增强，以强制执行任意复杂性的固体边界。将所提出的方法与Brinkman惩罚相结合的一个独特优点是能够在没有显著计算开销的情况下将边界条件强制执行到指定的精度。所提出的分层可变保真度方法将在许多基准问题中得到广泛验证，例如湍流通道流动，后面向台阶的湍流，平面非对称扩散器中的湍流以及经过圆形和方形圆柱体的湍流。本文开发的算法专门解决了当经典方法未能在可靠的预测建模方面取得进展时，高效和负担得起的湍流数值模拟问题。该研究将推动高雷诺数湍流多尺度物理建模的计算能力，并将使高雷诺数湍流的模拟成为可能，目前使用传统的数值算法很难或不可能解决。预计该研究将为湍流的复杂多尺度物理提供见解，提高我们对流体湍流的理解，甚至为工程师提供一个重要的设计工具，完全消除当前网格生成方法的繁重开销。该项目的另一个目的是教育和传播新开发的方法，并分发作为该项目的一部分将开发的软件工具，供科学界包括政府实验室广泛使用。新的综合涡流捕获方法对湍流扮演重要角色的所有技术努力具有潜在的革命性影响。航空、推进、运输和能源只是几个潜在的领域。在自由表面流动、MHD和非线性偏微分方程中的其他应用范围是巨大的。作为该项目的一部分产生的高分辨率结果有望被科学界广泛使用。