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，重点研究如何更好地利用风能、优化飞机飞行以及预测天气和气候的研究就是这种情况。基本上，所有具有实际意义的流动都是动荡的。尽管有超过50年的深入研究，准确和计算上可行的湍流预测仍然是我们最大的挑战之一。在过去几十年中，显然需要在两个方面取得重大进展。首先，对于中等湍流，需要开发能够准确预测流动的模拟方法。第二，对于高度湍流，需要开发混合模拟方法（将联合收割机不同的模拟工具结合起来），以实现最佳的流动预测。不幸的是，这两种类型的目前现有的模拟方法遭受严重的数学问题（计算不稳定性，缺乏控制）。一个详细的研究计划来解决这些问题，结合精心组织的计划，以证明新的模拟方法的好处。在这一努力下开发的新的计算模拟方法将使，例如，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：开发准确且计算可行的湍流模拟方法，这与各种技术问题高度相关。研究将在两个主要方向进行。轨道1的方向是动态大涡模拟（LES）的方法，使正确的预测低和中等雷诺数流动的发展。轨道2方向是发展包括LES和雷诺平均Navier-Stokes（RANS）方程的混合方法。使用这种混合RANS LES方法是最有前途的方式来最佳地预测在高雷诺数的流动。轨道1和轨道2方法的当前发展遭受严重的数学问题（动态LES的不稳定性，在混合RANS-LES中RANS和LES模式的控制的缺乏，这些方法的流动分辨率的程度的确定）。一个详细的研究计划，以解决这些问题，并证明新的模拟方法的优点将被追求。该项目将产生广泛的影响。传播计划具体规定向社区广泛有效地传播项目成果和代码。除了演讲和期刊论文的介绍外，基本的项目结果将张贴在湍流研究社区的主网页上。该教育计划具体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在流体动力学中使用随机方法的暑期学校。将通过将项目结果引起NSF、NASA和DOE以及其他研究人员对该领域问题的关注来为社会提供服务，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.