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

一种高效、实用、准确的湍流数值模拟方法在计算流体力学中对龙卷风、飓风、飞机设计和其他与湍流相关的领域的研究具有重要意义。由于计算资源的限制，很难对全尺寸涡旋进行数值求解。科学家们发现，小尺度涡旋有相似之处，但大尺度涡旋却截然不同。大涡模拟只解决了大尺度的旋涡，并留下了次网格尺度用于建模。因此，大涡模拟的精度由网格模型决定。在大多数实际湍流模拟中，仍然采用涡粘性的概念。然而，现有的大多数亚格子模式仍然使用分辨率切变来计算涡动粘性，这与物理不一致，特别是在切变为主的区域，如湍流边界层中的层流亚层，涡度/切变较大，而涡度/切变较大，而涡动粘性为零。这种不一致是由于误解了涡旋强度是用涡度来衡量的。采用壁面函数或在壁面附近人为调整的补救方法不能解决一致性问题。Liutex是一个新的物理量，它准确地表示了涡旋或涡旋的方向和强度。以往的直接数值模拟表明，Liutex在湍流边界层耗散区域具有相似性，这为利用Liutex构建新的亚网格模式奠定了基础。本项目旨在为大型涡流模拟社区开发一个可靠、高效的Liutex亚网格模式。Liutex是对涡旋的严格数学定义，可正确区分流体旋转和剪切。Liutex用于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旋是非常合理的，因为涡旋是涡旋，涡旋是Liutex。本项目计划(1)开发一个新的基于Liutex的子网格模型，(2)开发一个新的基于Liutex的动态子网格模型，(3)在各种计算流体力学的情况下测试新的模型，如后台阶流、S管流和翼型绕流，(4)评估新的基于Liutex的子网格模型的效果，并将其与其他现有的子网格模型进行比较。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，子网格模型的发展将使几乎所有与流体相关的研究领域和工程应用受益，包括空气动力学、流体动力学、气象学(例如飓风和龙卷风)、生物流动(例如血液流动和呼吸流动)、天文学(例如太阳风暴)等。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.