Mathematical Foundations of Future Turbulent Flow Simulations

使用计算模拟方法是解决涉及流体流动的许多具有挑战性的问题的要求。例如，在侧重于改进风能利用、优化飞机飞行以及天气和气候预测的研究方面，情况就是如此。基本上，所有与实际相关的流动都是动荡的。尽管进行了50多年的密集研究，但对湍流的准确和计算可行的预测仍然是我们面临的最大挑战之一。过去几十年来，显然需要取得重大进展，特别是在两个方向上。首先，对于中等湍流度的流动，需要开发能够进行准确流动预测的模拟方法。其次，对于高度湍动的流动，需要开发混合模拟方法(结合不同的模拟工具)，以实现最佳流动预测。遗憾的是，目前这两种类型的模拟方法都存在严重的数学问题(计算不稳定、缺乏控制)。提出了一个解决这些问题的详细研究计划，以及一个精心组织的计划，以展示新模拟方法的好处。在这一努力下将开发的新的计算模拟方法将使例如能够更有效地利用风能和优化飞机飞行。该项目解决了最紧迫的数学问题之一：开发准确且在计算上可行的湍流模拟方法，这与各种技术问题高度相关。研究将从两个主要方向进行。轨道1的方向是动态大涡模拟(LES)方法的发展，这些方法能够正确预测低和中等雷诺数的流动。轨道2的方向是发展包含大涡模拟和雷诺平均的N-S方程的混合方法。使用这种混合RANS-LES方法是在高雷诺数下最有希望预测流动的方法。目前轨道1和轨道2方法的发展面临着严重的数学问题(动态LES的不稳定性，混合RAN中RAN和LES模式的缺乏控制，以及这些方法的流动分辨率的确定)。将制定详细的研究计划，以解决这些问题，并展示新的模拟方法的优势。该项目将产生重大的更广泛的影响。传播计划规定了向社区广泛和有效地分发项目成果和代码。除了演讲和期刊论文的介绍外，基本的项目结果将发布在湍流研究社区的主页上。教育计划规定了几个教育影响，包括为研究生和教职员工组织一个关于使用流体动力学中的随机方法的暑期班。将通过将项目结果提请NSF、NASA和美国能源部以及其他在该领域寻求问题的研究人员的注意来向社会提供服务，以说明处理相关湍流预测的新机会。

The use of computational simulation methods is a requirement to address many challenging problems involving fluid flow. This is the case, for example, with regard to research focused on the improved use of wind energy, the optimization of aircraft flight, and the prediction of weather and climate. Basically all flows of practical relevance are turbulent. Despite intense research of more than fifty years, accurate and computationally feasible predictions of turbulent flows are still one of our biggest challenges. Over the last decades it became clear that significant progress is needed in particular in two directions. First, with respect to moderately turbulent flows, the development of simulation methods is needed that enable exact flow predictions. Second, with respect to highly turbulent flows, the development of hybrid simulation methods (which combine different simulation tools) is needed that enable optimal flow predictions. Unfortunately, currently existing simulation methods of these two types suffer from serious mathematical problems (computational instabilities, the lack of control). A detailed research plan for solving these problems combined with a carefully organized plan for demonstrating the benefits of new simulation methods are presented. The new computational simulation methods to be developed under this effort will enable, e.g., a much more efficient use of wind energy and optimization of aircraft flight. The project addresses one of the most pressing mathematical problems: the development of accurate and computationally feasible simulation methods for turbulent flows, which is highly relevant to a variety of technical problems. Research will be performed in two main directions. The track 1 direction is the development of dynamic Large Eddy Simulation (LES) methods that enable correct predictions of low and moderate Reynolds number flows. The track 2 direction is the development of hybrid methods involving LES and Reynolds-Averaged Navier-Stokes (RANS) equations. The use of such hybrid RANS-LES methods is the most promising way to optimally predict flows at high Reynolds numbers. The current development of track 1 and track 2 methods suffers from serious mathematical problems (the instability of dynamic LES, the lack of control of RANS and LES modes in hybrid RANS-LES, the determination of the degree of flow resolution of these methods). A detailed research plan for solving these problems and demonstrating the advantages of novel simulation methods will be pursued. The project will have significant broader impacts. The dissemination plan specifies the broad and efficient distribution of project results and codes to the community. In addition to the presentation of talks and journal papers, the basic project results will be posted on the main web page of the turbulence research community. The education plan specifies several educational impacts including the organization of a summer school on the use of stochastic methods in fluid dynamics for graduate students and faculty. Service to the society will be provided by bringing project results to the attention of NSF, NASA, and DOE, as well as other researchers pursuing questions in this field, to illustrate new opportunities to deal with relevant turbulent flow predictions.