Reduced Order Models of the Navier-Stokes Equations of Fluid Flows

流体流动纳维-斯托克斯方程的降阶模型

• 批准号: 1435474
• 负责人: Earl Dowell
• 金额: $ 47.95万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-01 至 2018-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1435474&HistoricalAwards=false
• 关键词: Reduced; Order; Models; Navier; Stokes

Turbulence is the apparently random motion that occurs commonly in almost all fluid flows. It has been called one of the most challenging unsolved problems in Newtonian physics. The aggregate cost to our society resulting from our incomplete understanding of turbulence is significant. Consider, for example, the environmental and economic costs associated with sub-optimal performance of virtually every fluid-thermal system such as internal combustion engines and air-conditioners. It is usually not possible to directly and routinely simulate turbulent flow because its multi-scale characteristics require prohibitively high computational resources. Even when adequate computational resources are available, simulations often provide too little understanding of the solutions they produce. There are significant scientific and engineering benefits in developing and studying (reduced-order) models of turbulence that retain the needed physical fidelity while substantially reducing the size and cost of the computational model. The ultimate goal of reduced-order modeling of turbulence is to provide efficient and accurate solutions with minimal reliance on auxiliary empirical models. Empirical models are inherently undesirable because they degrade simulation accuracy and reliability.The research objective of this project is to develop a reduced-order modeling approach to turbulent fluid flows that is free of empirical closure models. Unlike traditional approaches, the new methodology does not rely on empirical turbulence modeling or ad hoc modification of the Navier-Stokes equations. It provides spatial basis functions different from the usual proper orthogonal decomposition basis function in that, in addition to optimally representing the solution, the new basis functions also provide stable reduced-order models. The approach is illustrated with three test cases: two-dimensional flow inside a square lid-driven cavity, two-dimensional mixing layer, and three-dimensional turbulent flow around the Ahmed body. Future work will extend this method to more complex flows including the effects of higher spatial dimensions and higher flow velocities (Reynolds numbers).

湍流是一种明显的随机运动，几乎在所有的流体流动中都普遍存在。它被称为牛顿物理学中最具挑战性的未解决问题之一。我们对动荡的不完全理解给我们的社会造成的总成本是巨大的。例如，考虑与几乎每个流体热系统（如内燃机和空调）的次优性能相关的环境和经济成本。 由于湍流的多尺度特性需要非常高的计算资源，因此通常不可能直接和常规地模拟湍流。即使有足够的计算资源，模拟往往提供太少的了解他们产生的解决方案。在开发和研究湍流的（降阶）模型中有显着的科学和工程效益，这些模型保留了所需的物理保真度，同时大大降低了计算模型的尺寸和成本。湍流降阶模型的最终目标是在最小程度上依赖于辅助经验模型的情况下提供有效和准确的解。经验模型由于降低了模拟的精度和可靠性而不受欢迎，本课题的研究目标是开发一种不依赖经验封闭模型的湍流降阶模拟方法。与传统的方法不同，新的方法不依赖于经验湍流模型或专门修改的Navier-Stokes方程。它提供了不同于通常的正交分解基函数的空间基函数，除了最佳地表示解之外，新的基函数还提供稳定的降阶模型。该方法示出了三个测试用例：二维流动内的一个正方形的盖子驱动的空腔，二维混合层，三维湍流周围的艾哈迈德机构。未来的工作将扩展这种方法更复杂的流动，包括更高的空间尺寸和更高的流速（雷诺数）的影响。