Numerical Analysis, Analysis and Modeling of Fluid Motion

准确，有效和可靠的预测量在湍流（重点拟议的研究）迫使系统和综合对抗的基本问题，在建模，分析，数值分析和计算的湍流，其中许多是联系在一起的基本问题，在其他流动问题和其他领域的数学。相互关联的研究子项目包括：（i）大的相干涡流的教育和由模型或数值产生的假涡流的检测，（ii）流体流动方程的高精度和有效可解的正则化的开发和数值分析，（iii）不适定问题的新算法和应用，（iv）可压缩湍流的LES模型的开发和其声学噪声预测的分析，㈤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转换; ㈥流体-结构相互作用中的非耦合多物理场流体流动问题、地下水-地表水模型和大气-海洋耦合引起的流体-流体问题; ㈤时间松弛正则化的精确数值分析。 准确、有效和可靠地预测湍流中的量在许多应用中是一个至关重要的问题，这些应用包括全球气候变化、国土安全（生物或化学制剂的扩散）、污染扩散、能源效率和生物医学设备设计。大涡模拟是一种湍流模拟方法，其中大的特征从流动的精细细节中分离出来进行数值模拟。在大涡模拟方面，来之不易的经验和理解已经增长，因此该方法现在可以成功地模拟基准湍流，效率和可靠性。科学和工业应用是与其他物理效应耦合的流体流动方程系统。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灵敏度和不确定性，以及在具有更大内存的更快计算机上查询来自更细网格的大量数据的方法。这些问题是拟议研究的重点。培养博士生为这个重要，困难，跨学科，迷人和美丽的领域做出贡献是拟议努力的很大一部分。

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.