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

1236505 Vasilyev基于小波的偏微分方程数值求解方法的最新进展，结合小波分析的独特性质，明确识别和隔离局部动态主导的流动结构，使其成为可行的建议开发智能方法湍流模拟，紧密结合数值和物理建模。该研究的总体目标是开发一种强大的和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进行可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。空间可变小波阈值策略将用于模型形式自适应。小波阈值将使用反馈控制在空间和时间上演变，以保证仅解析湍流动能或湍流耗散率的先验指定分数。采用这种策略，自适应基于小波的直接数值模拟（WDNS）、相干涡模拟（CVS）、随机相干自适应大涡模拟（SCALES）和自适应基于小波的非定常雷诺平均纳维尔-斯托克斯（WURANS）模拟之间的转换是自然的：WURANS模式转换为亚网格尺度模式，用于SCALES，用于CVS和WDNS方法，作为分辨湍流动能或分辨湍流的百分比耗散率从0%增加到100%。这将为提议的WDNS、CVS、SCALES和WURANS方法学的新的基于物理的集成奠定基础。所提出的方法的优点是，所有的模型（WDNS，CVS，SCALES，WURANS）使用相同的基于小波的自适应策略来解决和跟踪的自适应计算网格上的含能量的漩涡。通过将其与Brinkman惩罚相结合，以强制执行任意复杂性的坚实边界，将进一步增强该方法。将所提出的方法与Brinkman惩罚相结合的一个独特优势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精度。所提出的分层可变保真度方法将被广泛验证的一些基准问题，如湍流通道流，湍流后向台阶，湍流在平面非对称扩散器，和湍流过去的圆形和方形的圆柱体。本文中开发的算法专门解决了湍流的高效和负担得起的数值模拟的问题，当经典方法未能在可靠的预测建模方面取得进展时。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，这是目前很难或不可能使用传统的数值算法来解决。预计这项研究将深入了解湍流的复杂多尺度物理学，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，并分发作为项目一部分开发的软件工具，供包括政府实验室在内的科学界广泛使用。新的集成涡流捕获方法对湍流起重要作用的所有技术努力都具有潜在的革命性影响。航空、推进、运输和能源只是其中几个潜在的领域。在自由表面流动、磁流体动力学和非线性偏微分方程中的其他应用范围是巨大的。作为该项目一部分产生的高分辨率结果预计将被科学界广泛使用。

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.