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Geometrically optimized projection bases for parametric model reduction for large-scale fluid dynamics systems

用于大型流体动力学系统参数模型简化的几何优化投影基础

基本信息

批准号：
259082702
负责人：
Dr. Ralf Zimmermann
金额：
--
依托单位：
Oden Institute for Computational Engineering and Sciences
依托单位国家：
德国
项目类别：
Research Fellowships
财政年份：
2014
资助国家：
德国
起止时间：
2013-12-31 至 2014-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/259082702?language=en
关键词：
Geometrically optimized projection bases parametric

项目摘要

Fluid dynamics play a fundamental role in modeling a large variety of physical systems. Examples of practical interest include automotive and aeronautical aerodynamics, hydrodynamics and weather and climate modeling. The enormous costs associated with wind tunnel test campaigns using scaled models or real-scale prototypes render the deployment of Computational Fluid Dynamics an indispensable tool for treating industrial fluid flow problems. However, computing flow solutions over a continuous parameter range, say from start to landing of an aircraft or repeatedly within a design optimization loop, leads to numerical problems reaching easily computation times of several weeks. Hence, parametric reduced order modeling of high-dimensional systems becomes essential. Here, the term parametric means that the reduced order model can be adapted efficiently to parameter changes. The most prominent approaches to model order reduction all have in common that the original large-scale model is projected onto suitable subspaces spanned by low-dimensional bases. The projection bases essentially determine the approximation quality of the resulting reduced order models. In order to account for the underlying parametric dependency, it is suggested in the current literature to apply interpolation techniques on matrix manifolds for computing projection bases at arbitrary parameter conditions. The main objective of the proposed research project is to enhance the prediction capabilities of the projection bases by optimizing a suitable goal function on the matrix manifold in question, which actually measures the approximation quality. This multidisciplinary problem can be tackled only by combining tools from numerics and differential geometry, while additionally taking the engineering aspects of the problem into account. It is planned to demonstrate the applicability and benefit of the proposed method for real-life test cases.

流体动力学在模拟各种物理系统中起着基础性的作用。实际感兴趣的例子包括汽车和航空空气动力学，流体动力学和天气和气候建模。与使用比例模型或真实比例原型的风洞测试活动相关的巨大成本使得计算流体动力学的部署成为处理工业流体流动问题的不可或缺的工具。然而，在连续的参数范围内计算流动解决方案，比如从飞机开始到着陆或在设计优化循环内重复计算，导致数值问题很容易达到几周的计算时间。因此，高维系统的参数化降阶建模变得至关重要。这里，术语参数意味着降阶模型可以有效地适应参数变化。最突出的方法，以模型降阶都有一个共同点，即原来的大规模模型投影到合适的子空间由低维基地。投影基基本上决定了所得到的降阶模型的近似质量。为了说明潜在的参数依赖性，在当前的文献中，建议在矩阵流形上应用插值技术来计算任意参数条件下的投影基。拟议的研究项目的主要目标是通过优化一个合适的目标函数的矩阵流形上的问题，这实际上措施的近似质量，以提高预测能力的投影基地。这个多学科的问题只能通过结合数值和微分几何的工具来解决，同时还考虑到问题的工程方面。计划证明所提出的方法在实际测试用例中的适用性和益处。