Reduced Dynamical Models of Turbulent Flow

湍流简化动力学模型

• 批准号: RGPIN-2014-04035
• 负责人: Bowman, John
• 金额: $ 1.02万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=587566
• 关键词: Reduced; Dynamical; Models; Turbulent; Flow

Turbulence affects us on a daily basis: through weather patterns, on airplanes and ships, and in pipelines. However, the theoretical understanding of turbulence remains an elusive but important scientific challenge. While the Navier-Stokes equations provide an accurate description of ordinary fluids, our ability to solve these equations for fluids that behave chaotically is very limited. The problem of predicting energy, transport, and drag in highly turbulent flows defies even the incredible speed and huge memory of today's massively parallel computers. A recent advance, called implicit dealiasing, significantly reduces memory usage and computation time compared with conventional simulation techniques. We propose to implement implicit dealiasing on massively parallel computers so that computation can be performed simultaneously with communication. Our adaptive algorithm is optimized for distributed networks of multicore processors. To benchmark our algorithms, Professor Wendell Horton at The University of Texas has generously given our group access to the sixth fastest supercomputer in the world, the Dell Zeus C8220 cluster (Stampede) at the Texas Advanced Computer Center. This project will give Canadian students opportunities to work with state-of-the-art supercomputers that are far more powerful than anything currently available in our country. Even with implicit dealiasing, however, the numerical simulation of fully developed turbulence is still beyond reach, because of the huge range of space and time scales. For this reason, a subgrid model is often adopted to approximate the effects of unresolved small scales on the larger retained scales. A reliable method for determining the effective eddy viscosity due to deleted subgrid modes constitutes a major unsolved problem for numerical simulations of turbulence, where one only evolves large scale modes. Reduced models allow a simulation on today's computers to mimic computations that will likely not be directly possible even on the computers of the next century. The recent development of a method for predicting the statistical properties of two-dimensional homogeneous fluid turbulence, called pseudospectral reduction, provides us with a new tool for achieving this goal. The statistics predicted by this reduced model agree remarkably well with large-scale numerical simulation data, even in flows containing long-lived vortices. The Russian mathematician Kolmogorov conjectured that turbulent energy transfer is independent of scale, due to a presumed underlying self-similarity in the energy transfer. We propose to compute this flux directly, building on the recently discovered fast partial Fourier transform, to verify the degree to which this self-similarity actually holds. The ultimate goal is to use this information to join pseudospectral reduction with a large-scale simulation, yielding a dynamic subgrid model that removes exactly the right amount of energy from each of the scales near the subgrid scale cutoff. This would avoid the bottleneck and overdamping effects that commonly plague subgrid models used in modern large eddy simulations. By greatly increasing the efficiency of numerical simulations of turbulence, this research will lead to an improved ability to understand, predict, and possibly control, turbulence from a mathematical perspective. In addition, the computational tools developed in this work open up new interdisciplinary collaboration opportunities for Canadian researchers and industry. For example, implicit dealiasing would be beneficial to many disciplines where convolutions are used, including data mining, image processing, and signal processing.

湍流每天都在影响我们：通过天气模式，飞机和船舶以及管道。然而，对湍流的理论理解仍然是一个难以捉摸但重要的科学挑战。虽然Navier-Stokes方程提供了普通流体的精确描述，但我们解决这些方程的能力非常有限。 预测高度湍流中的能量、输运和阻力的问题，甚至挑战了当今大规模并行计算机令人难以置信的速度和巨大的内存。 最近的一个进步，称为隐式去混叠，显着减少内存使用和计算时间相比，传统的模拟技术。 我们建议在大规模并行计算机上实现隐式去混叠，以便计算可以与通信同时进行。我们的自适应算法是优化的分布式网络的多核处理器。为了对我们的算法进行基准测试，德克萨斯大学的温德尔霍顿教授慷慨地让我们小组使用了世界上第六快的超级计算机，德克萨斯高级计算机中心的戴尔宙斯C8220集群（Stampede）。该项目将为加拿大学生提供使用最先进的超级计算机的机会，这些计算机比我国目前可用的任何计算机都要强大得多。 然而，由于空间和时间尺度的巨大范围，即使使用隐式去混叠，充分发展的湍流的数值模拟仍然是遥不可及的。 由于这个原因，通常采用亚网格模式来近似未分辨的小尺度对较大保留尺度的影响。一个可靠的方法来确定有效的涡粘性由于删除的亚网格模式构成了一个主要的未解决的问题，湍流的数值模拟，其中一个只发展大尺度模式。简化模型允许在今天的计算机上进行模拟，以模仿即使在下一个世纪的计算机上也不可能直接实现的计算。 最近发展的一种用于预测二维均匀流体湍流的统计特性的方法，称为伪谱缩减，为我们提供了实现这一目标的新工具。 该简化模型预测的统计数据与大尺度数值模拟数据吻合得非常好，即使在包含长寿命涡的流动中也是如此。 俄罗斯数学家柯尔莫哥洛夫（Kolmogorov）指出，湍流能量传递与尺度无关，这是由于能量传递中假定的潜在自相似性。我们建议直接计算这个流量，建立在最近发现的快速部分傅立叶变换，以验证这种自相似性实际上持有的程度。最终目标是利用这些信息将伪谱缩减与大规模模拟结合起来，产生一个动态亚网格模型，该模型可以从亚网格尺度截止点附近的每个尺度中精确地去除适量的能量。这将避免瓶颈和过阻尼效应，通常困扰现代大涡模拟中使用的亚网格模型。 通过大大提高湍流数值模拟的效率，这项研究将提高从数学角度理解、预测和控制湍流的能力。 此外，这项工作中开发的计算工具为加拿大研究人员和工业界开辟了新的跨学科合作机会。例如，隐式去混叠将有利于使用卷积的许多学科，包括数据挖掘，图像处理和信号处理。