Collaborative Research: Reduced Order Modeling of Realistic Noisy Flows

协作研究：现实噪声流的降阶建模

• 批准号: 1522656
• 负责人: Traian Iliescu
• 金额: $ 14.32万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-08-01 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1522656&HistoricalAwards=false
• 关键词: Collaborative; Research; Reduced; Order; Modeling

Many flows in engineering, geophysics, and medicine pose two significant challenges for computations. First, the computational resources that are available for the numerical simulations can accommodate only low spatial and temporal resolutions. Therefore, standard numerical methods usually yield extremely inaccurate results. To alleviate this, state-of-the-art numerical methods generally use spatial filtering to eliminate the noise (i.e., numerical artifacts). The second challenge posed by these realistic flows is that they require numerous repeated runs (e.g., to determine optimal parameters in automobile design or cardiovascular flow simulation, or to find appropriate initial conditions in weather forecasting and climate modeling). These repeated runs can tremendously increase the computational cost of the numerical simulations. Thus, low cost surrogate models (called reduced-order models) that target only the dominant flow structures are generally used. Combining state-of-the-art data generation methods and reduced-order modeling is required for an accurate and efficient numerical simulation of realistic flows. A simplistic attempt to combine these two approaches is, however, doomed to fail due to numerical instability, noisy data, and modeling inconsistency. This project aims to develop a framework that will transform reduced-order modeling into a robust tool that can tackle the challenges raised by realistic noisy flows in engineering, geophysics, and medicine. The numerical simulation of many realistic flows is fraught with difficulties (insufficient numerical resolution; numerical instability; need for repeated runs). To address these challenges, state-of-the-art numerical approaches are needed: large eddy simulation (LES) and regularized models tackle the lack of numerical resolution and the instability, whereas reduced-order models (ROMs) based on proper orthogonal decomposition (POD) balance the computational cost and accuracy when repeated runs are needed. A simplistic attempt to combine LES and regularized models with standard ROMs is, however, doomed to fail due to the following reasons: (i) standard ROMs are plagued by numerical instability; (ii) although LES and regularized models stabilize the numerical simulations, the data that they generate for ROMs is inherently noisy; and (iii) the modeling inconsistency between data generation (i.e., regularized and LES models) and ROMs can yield inaccurate results. This project will develop a modeling, theoretical, and computational framework that will transform reduced-order modeling into a robust tool that can tackle the challenges raised by realistic noisy flows. The main innovation is the explicit POD spatial filter, which bridges the inconsistency gap between the data generation (i.e., regularized and LES models) and ROMs. This breakthrough paves the way for the development of novel regularized ROMs and the introduction in a ROM setting of genuine LES models that use approximate deconvolution to recover subfilter-scale information. Over the last decades, a wealth of regularized and LES models have been highly developed in the engineering and geophysics communities. The explicit POD spatial filter represents the missing link that finally allows the leverage of these successful approaches in reduced-order modeling.

工程，地球物理学和药品的许多流动对计算构成了两个重大挑战。 首先，用于数值模拟的计算资源只能适应低空间和时间分辨率。 因此，标准数值方法通常产生极度不准确的结果。 为了减轻这种情况，最新的数值方法通常使用空间滤波来消除噪声（即数值伪像）。 这些现实流动提出的第二个挑战是它们需要大量重复运行（例如，确定汽车设计或心血管流动模拟中的最佳参数，或在天气预测和气候建模中找到适当的初始条件）。 这些重复运行可以大大增加数值模拟的计算成本。 因此，通常使用仅针对主要流量结构的低成本替代模型（称为还原阶模型）。 需要将最新的数据生成方法和减少订单建模组合起来，以便对现实流进行准确有效的数值模拟。 但是，将这两种方法结合起来的一种简单的尝试是，由于数值不稳定，嘈杂的数据和建模不一致而注定要失败。 该项目旨在开发一个框架，该框架将减少订购的建模变成一个可靠的工具，该工具可以应对工程，地球物理学和医学中现实的嘈杂流动所带来的挑战。 对许多现实流的数值模拟都充满了困难（数值分辨率不足；数值不稳定；需要重复运行）。 为了应对这些挑战，需要采用最新的数值方法：大型涡流模拟（LES）和正则化模型可以解决缺乏数值分辨率和不稳定性的问题，而基于适当的正交分解（POD）的降低订单模型（ROM）在需要重复运行时平衡计算成本和准确性。 然而，将LES和正则模型与标准ROM相结合的简单尝试是注定要失败，原因是：（i）标准ROM因数值不稳定而困扰； （ii）尽管LE和正规化模型稳定了数值模拟，但它们为ROM生成的数据本质上是嘈杂的； （iii）数据生成（即正则化和LES模型）和ROM之间的建模不一致可能产生不准确的结果。 该项目将开发一个建模，理论和计算框架，该框架将减小订单建模变成一个可靠的工具，该工具可以应对现实的嘈杂流动所带来的挑战。 主要的创新是显式的POD空间滤波器，它弥合了数据生成（即正规化和LES模型）和ROM之间的不一致差距。 这一突破为开发新颖的正则化ROM的发展铺平了道路，以及在真正的LES模型的ROM环境中介绍，这些模型使用近似反卷积来恢复子滤光器尺度信息。 在过去的几十年中，在工程和地球物理社区中，大量的正规化和LES模型得到了高度发展。 显式POD空间滤波器表示缺失的链接，该链接最终允许这些成功的方法在降低订购建模中的杠杆作用。