Numerical Analysis, Analysis and Modeling of Fluid Motion

流体运动的数值分析、分析和建模

• 批准号: 0810385
• 负责人: William Layton
• 金额: $ 27.85万
• 依托单位: University of Pittsburgh
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-07-01 至 2012-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0810385&HistoricalAwards=false
• 关键词: Numerical; Analysis; Modeling; Fluid; Motion

The accurate, efficient and reliable prediction of quantities in turbulent flows (the focus of the proposed research) forces systematic and integrated confrontation of basic issues in the modeling, analysis, numerical analysis and computation of turbulent flows, many of which are linked to basic issues in other flow problems and other areas of mathematics. Interconnected research sub-projects include: (i) Eduction of large coherent vortices and detection of false vortices created by models or numerics, (ii) Development and numerical analysis of high accuracy and efficiently solvable regularizations of fluid flow equations, (iii) New algorithms for ill-posed problems and applications, (iv) Development of LES models for compressible turbulence and analysis of their acoustic noise predictions, (v) Mathematical foundation for time-averaged large eddy simulation: continuous transitioning between direct numerical simulation, large eddy simulation and Reynolds averaged turbulence models, (vi) Uncoupling multi-physics fluid flow problems in fluid-structure interaction, groundwater-surface water models and fluid-fluid problems motivated by atmosphere-ocean coupling, and (v) Precise numerical analysis of time relaxation regularizations. The accurate, efficient and reliable prediction of quantities in turbulent flows is a problem of fundamental importance in many applications ranging from global climate change, homeland security (dispersion of biological or chemical agents), pollution dispersal, energy efficiency and biomedical device design. Large eddy simulation is an approach to turbulent flows in which the large features are separated from the fine details of a flow for a numerical simulation. Hard-won experience and understanding has grown in large eddy simulation so that the methods can now successfully simulate benchmark turbulent flows efficiency and reliably. Scientific and industrial applications are systems of fluid flow equations coupled to other physical effects. These require even greater efficiency and accuracy than benchmark turbulent flow problems. To make progress into these industrial and scientific applications, large eddy simulation now requires systematic methods for assessing sensitivity and uncertainty as well as methods for interrogating the large amounts of data coming out of the finer meshes on faster computers with larger memories. These issues are the focus of the proposed research. Training PhD students to contribute to this important, difficult, interdisciplinary, fascinating and beautiful area is a large part of the proposed effort.

对湍流量的准确、高效和可靠的预测(拟议的研究重点)迫使人们系统地、综合地面对湍流的建模、分析、数值分析和计算中的基本问题，其中许多问题与其他流动问题和其他数学领域的基本问题有关。相互关联的研究子项目包括：(I)由模型或数值产生的大相干涡的教育和伪涡的检测，(Ii)流体流动方程的高精度和有效可解的正则化的发展和数值分析，(Iii)不适定问题和应用的新算法，(Iv)可压缩湍流的大涡模型的发展和声学预测的分析，(V)时间平均大涡模拟的数学基础：直接数值模拟、大涡模拟和雷诺平均湍流模型之间的连续过渡，(Vi)流固耦合中的多物理流体流动问题，地下水-地表水模型和大气-海洋耦合引起的流体-流体问题，以及(V)时间松弛规律的精确数值分析。在全球气候变化、国土安全(生物或化学制剂的扩散)、污染扩散、能源效率和生物医疗设备设计等许多应用中，准确、高效和可靠的湍流量预测是一个重要的问题。大涡模拟是一种将流动的大特征与细微细节分离出来进行数值模拟的湍流模拟方法。在大涡模拟中积累了来之不易的经验和认识，从而使这些方法现在可以成功地高效可靠地模拟基准湍流。科学和工业应用是流体流动方程与其他物理效应相耦合的系统。这些问题需要比基准湍流问题更高的效率和精度。为了在这些工业和科学应用中取得进展，大涡模拟现在需要系统的方法来评估敏感性和不确定性，以及在速度更快、内存更大的计算机上查询来自更精细网格的大量数据的方法。这些问题是拟研究的重点。培训博士生为这个重要的、困难的、跨学科的、引人入胜的和美丽的领域做出贡献是拟议中的努力的一大部分。