EAGER: Liutex-based Sub-Grid Model for Large Eddy Simulation of Turbulent Flow

一个有效的，实用的，准确的湍流数值模拟方法是重要的计算流体动力学的研究龙卷风，飓风，飞机设计，和其他相关领域的湍流。由于计算资源的限制，很难对所有尺寸的涡进行数值求解。科学家们发现，小尺度的漩涡有相似之处，而大尺度的漩涡则截然不同。大涡模拟只解决大尺度的旋涡，并留下亚网格尺度的建模。因此，亚网格模型的选择决定了大涡模拟的精度。在实际的湍流模拟中，涡粘性的概念仍然被采用。然而，现有的亚网格模型大多仍采用解析剪切来计算涡动粘性，这与实际情况不符，特别是在剪切占主导地位的区域，如湍流边界层中的层流亚层，涡量/剪切很大，但涡动粘性为零。这种不一致是由于误解了涡强度是用涡量来衡量的。使用壁函数或在壁区域附近人工调整的补救措施不能解决一致性问题。留特克斯是一个新的物理量，它精确地表示了涡旋或漩涡的方向和强度。以往的直接数值模拟结果表明，Liutex在湍流边界层耗散区具有相似性，这为利用Liutex构建新的亚网格模式奠定了基础。本项目旨在为大涡模拟界开发一个可靠、高效的基于Liutex的亚网格模式。Liutex是涡旋的严格数学定义，它正确区分了流体的旋转和剪切。引入Liutex从流体速度梯度中提取刚性旋转是湍流研究中的开创性工作。因此，用Liutex代替切变来模拟小尺度涡是非常合理的，因为涡就是涡，涡就是Liutex。本研究计划（1）开发新的基于Liutex的亚网格模型;（2）开发新的基于Liutex的动态亚网格模型;（3）在各种计算流体动力学情况下测试新模型，如后向台阶流、S形管道流和翼型绕流;（4）评估新的基于Liutex的亚网格模型的效果，并将其与其他现有的亚网格模型进行比较。新模型的代码将通过GitHub提供给社区。随着大涡模拟成为计算流体力学的主要工具之一，亚网格模型的发展取得突破性进展，将使包括空气动力学、流体力学、气象学等多学科研究领域中几乎所有与流体相关的研究领域和工程应用受益（例如飓风和龙卷风），生物流（例如血液流动和呼吸流动），天文学（例如太阳风暴），该奖项反映了NSF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进行评估，被认为值得支持审查标准。

An efficient, practical, and accurate numerical simulation method for turbulent flow is important in computational fluid dynamics for the study of tornadoes, hurricanes, aircraft design, and other turbulence-related areas. Due to the limitation of computation resources, it is hard to numerically resolve all-size vortices. Scientists have found that small-scale vortices have similarities although large-scale vortices are quite different. Large eddy simulation only resolves large-scale vortices and leaves sub-grid scales for modeling. Therefore, the accuracy of large eddy simulations is determined by the sub-grid models. The concept of eddy viscosity is still adopted in most practical turbulent flow simulations. However, most of the existing sub-grid models still use the resolved shear to calculate the eddy viscosity, which is inconsistent with the physics, especially in the shear-dominated regions like the laminar sublayer in turbulent boundary layers, where vorticity/shear is large, but eddy viscosity is zero. The inconsistency is caused by the misunderstanding that vortex strength is measured by vorticity. The remedy of using a wall function or artificial adjustment near the wall region cannot solve the consistency problem. Liutex is a new physical quantity exactly representing the direction and strength of a vortex or eddy. Previous direct numerical simulation has shown that Liutex has similarity in the dissipation subregion of the turbulent boundary layer, which paves the foundation for constructing a new sub-grid model by using Liutex.This project aims to develop a reliable and efficient Liutex-based sub-grid model for the large eddy simulation community. Liutex is a rigorous mathematical definition of vortex that correctly distinguishes fluid rotation and shear. The introduction of Liutex to extract the rigid rotation from the fluid velocity gradient is groundbreaking work in turbulence research. So, modeling small-scale vortices using Liutex instead of shear is very reasonable as eddy is vortex and vortex is Liutex. This project plans to (1) develop a new Liutex-based sub-grid model, (2) develop a new dynamic Liutex-based sub-grid model, (3) test new models in a variety of computational fluid dynamics cases such as backward step flow, S-duct flow, and flow around an airfoil, (4) evaluate the effect of new Liutex-based sub-grid model and compare it with other existing sub-grid models. The code of the new model will be provided to the community through GitHub. As large eddy simulation becomes one of the major tools of computational fluid dynamics, a breakthrough in the development of the sub-grid models will benefit almost all fluid-related research areas and engineering applications in multi-disciplinary research areas including aerodynamics, hydrodynamics, meteorology (hurricanes and tornadoes for example), bio-flow (blood flow and respiratory flow for example), astronomy (sun storm for example), etc.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.