Integrated Variable Fidelity Eddy Capturing Approach for Turbulent Flow Simulations

本研究解决了长期以来对集成自适应涡流捕获方法的需求，该方法能够对复杂几何形状的非定常湍流进行可变保真度的数值模拟。最近数值模拟与实验的详细比较清楚地显示了捕捉主要的三维湍流特征的重要性。由于直接数值模拟（DNS）对高湍流的计算成本过高，解决主导流动物理的所有涡流的唯一计算可行的替代方案是大涡流模拟（LES）。然而，目前的LES方法最多依赖于一个区域网格适应策略，以尽量减少解决大涡流的计算成本。虽然这些方法是对规则网格的改进，但它们无法解决空间间歇相干涡流的高波数分量，而这些涡流是湍流的典型特征。同时，在断断续续的相干涡流之间的区域，流动被过度分解。PI最近开发的随机相干自适应大涡模拟（SCALES）方法是LES方法的最新改进，该方法通过使用动态网格自适应策略来解决最具能量的相干结构，从而解决了传统LES方法的缺点。这种新颖的方法现在已经证明了动态解析和跟踪的能力。相干涡流中能量最高的部分，同时使用场压缩，导致类似LES的自由度数量减少。这个想法将更进一步，应用空间可变的小波阈值策略，以确保只有先验指定的湍流动能、亚网格尺度耗散或其他统计量被解决。有了这样的策略，基于自适应小波的DNS （WDNS）、相干涡模拟（CVS）和SCALES模式之间的转换是自然的：随着分解的湍流动能或亚网格尺度耗散的百分比的增加，SCALES模型从用于CVS的亚网格尺度模型切换到没有用于WDNS方法的模型。这将为集成自适应变保真度（WDNS/CVS/SCALES）涡流捕获方法的新策略奠定基础。最后，为了使计划方法成为实用的工程工具，它将与布林克曼惩罚相结合，以强制执行任意复杂性的固体边界。将这种基于动态小波的网格自适应策略与Brinkman惩罚相结合的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的精度。这种结合的方法将大大减少工时（与繁琐的网格生成相关）和计算成本。该项目的最终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。

CBET-0756046VasilyevThis study addresses the longstanding need for an integrated adaptive eddy capturing approach capable of performing variable fidelity numerical simulations of unsteady turbulent flows in complex geometries. Recent detailed comparison of numerical simulations with experiments has clearly shown the importance of capturing the dominant three-dimensional turbulent flow features. Due to prohibitive computational cost of the Direct Numerical Simulations (DNS) for highly turbulent flows, the only computationally feasible alternative to resolve all eddies that dominate flow physics is Large Eddy Simulation (LES). However, current LES methodologies rely on, at best, a zonal grid adaptation strategy to attempt to minimize computational cost in resolving large eddies. While an improvement over regular grids, these methodologies fail to resolve the high wave-number components of the spatially intermittent coherent eddies that typify turbulent flows. At the same time, the flow is over-resolved in regions between the intermittent coherent eddies. Recent improvement of the LES methodology, namely the Stochastic Coherent Adaptive Large Eddy Simulation (SCALES) approach, recently developed by PI, addresses shortcomings of traditional LES approaches by using a dynamic grid adaptation strategy that resolves the most energetic coherent structures. This novel methodology has now demonstrated the ability to dynamically resolve and ?track? the most energetic part of the coherent eddies, while using a field compression that results in a reduction in the number of degrees of freedom similar to LES. This idea is to be taken one step further by applying spatially variable wavelet thresholding strategy to ensure that only a priori specified fraction of turbulent kinetic energy, subgrid scale dissipation or other statistical quantities are resolved. With such a strategy the transition between adaptive wavelet based DNS (WDNS), Coherent Vortex Simulation (CVS), and SCALES regimes is natural: the SCALES models switch to subgrid scale model for CVS to no model for WDNS approach as the percentage of the resolved turbulent kinetic energy or subgrid scale dissipation increases. This will form a basis for the new strategy of the integrated adaptive variable fidelity (WDNS/CVS/SCALES) eddy capturing approach. Finally, to make a planned methodology a practical engineering tool, it will be combined with Brinkman penalization to enforce solid boundaries of arbitrary complexity. A unique advantage of combining this dynamic wavelet-based grid adaptation strategy with Brinkman penalization is the ability to enforce boundary conditions to a specified precision without a significant computational overhead. The combined approach will allow for a significant cost reduction in man hours (associated with tedious grid generation) and computational costs. The final 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.