Computations and Analysis of Fluids and Materials

流体和材料的计算和分析

• 批准号: 9706931
• 负责人: John Lowengrub
• 金额: $ 13.8万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-08-15 至 2001-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9706931&HistoricalAwards=false
• 关键词: Computations; Analysis; Fluids; Materials

9706931 Lowengrub The main objective of this proposal is to investigate the dynamics of fluid-fluid and solid-solid interfaces by (1) developing and applying state-of-the-art numerical methods to large scale computation and (2) performing analytical, numerical and modelling studies of important constituent processes. Specifically, the focus will be on studying topological transitions in fluids and the diffusional evolution of microstructure in solids. These areas involve fundamental physical processes whose phenomenology is basic to understanding the behavior of real fluids and the material properties of solids. Both are characterized by the presence of multiple constitutive components, complex pattern formation and/or singularities (i.e. spatial complexity). Although these processes arise in very different physical phenomena (fluids versus solids), both involve free boundary problems where the motion of a bounding interface, separating the different components, is driven by a competition between surface energy and either an instability or multi-body interactions. As such, they can be treated using a common set of analytical and computational tools. The highly nonlinear nature of these problems makes fast, accurate and robust numerical methods essential to their study. In this proposal, we bring together mathematical and numerical analysis, modelling, and large-scale scientific computation to study certain fundamental problems in fluid dynamics and materials science. For instance, one problem we will consider concerns changes in the topology of interfaces between different fluids. Such changes occur, for example, when liquid jets pinch off into droplets and when droplets of one fluid reconnect with another. These topological transitions occur in many practical applications involving transport, mixing, and separation of petroleum, chemical, and food products as well as in environmental applications such as oil spills. Often, reaction and mixing rates within these systems are controlled directly by the detailed dynamics of the transition processes. Thus, there is a need to understand these dynamics in order to develop accurate engineering models for mixing and reaction rate prediction. We will use analysis, modelling and large scale scientific computation to investigate the detailed dynamics of break-up and reconnection of fluid interfaces. Another problem we will consider involves solid-state diffusional phase transformations. These transformations are an important method of processing multicomponent metallic alloys such such as steels. The result of this process is the formation of a multiphase microstructure, which is a key variable in setting the macroscopic mechanical properties (i.e. stiffness, strength and toughness) of the alloy. The microstructure is characterized by regions of different metallic components separated from one another by interfaces. The goal of our research is to accurately model and simulate the formation of microstructure in alloys in order to provide metallurgists with a recipe for generating new alloys with desirable material properties. Although the two problems described above arise from very different physical processes (fluids versus solids), they are similar in the sense that the relevant phenomena is strongly influenced by surface tension at the respective interfaces. Consequently, they can be studied using common analytical and computational tools. The highly complex nature of these problems makes fast, accurate and robust numerical methods essential to their study.

9706931 LowenGrub该提案的主要目的是通过（1）开发和应用最先进的数值方法来研究流体流体和固体接口的动力学，并将最先进的数值方法应用于大规模计算，以及（2）对重要组成过程的分析，数值和建模研究进行分析，数值和建模研究。具体而言，重点将放在研究流体中的拓扑转变以及固体中微观结构的扩散演化。这些领域涉及基本的物理过程，其现象学是理解实际流体行为和固体材料特性的基础。两者的特征是存在多个本构成分，复杂的模式形成和/或奇异性（即空间复杂性）。 尽管这些过程以非常不同的物理现象（流体与固体）的形式出现，但两者都涉及自由边界问题，在这些问题中，边界界面的运动（分隔不同的组件）是由表面能量与不稳定性或多体相互作用之间的竞争驱动的。 因此，可以使用一组共同的分析和计算工具对其进行处理。这些问题的高度非线性性质使他们的研究必不可少的快速，准确和鲁棒的数值方法。 在此提案中，我们将数学和数值分析，建模和大规模科学计算汇总在一起，以研究流体动力学和材料科学中的某些基本问题。 例如，我们将考虑一个问题是涉及不同流体之间界面拓扑的变化。例如，当液体喷头捏入液滴时，而一种流体的液滴与另一种液体重新连接时，会发生这种变化。这些拓扑转换发生在许多实际应用中，包括石油，化学和食品的运输，混合和分离以及诸如溢油等环境应用。通常，这些系统内的反应和混合速率直接由过渡过程的详细动力学控制。 因此，有必要了解这些动力学，以开发用于混合和反应速率预测的准确工程模型。我们将使用分析，建模和大规模科学计算来研究流体界面的分解和重新连接的详细动力学。 我们将考虑的另一个问题涉及固态扩散相变。这些转换是处理多组分金属合金（例如钢）的重要方法。该过程的结果是形成了多相微观结构，这是设置合金的宏观机械性能（即刚度，强度和韧性）的关键变量。微观结构的特征是不同金属组件的区域通过接口相互分离。我们研究的目的是准确模拟和模拟合金中微结构的形成，以便为冶金学家提供具有理想材料特性的新合金的配方。 尽管上面描述的两个问题是由非常不同的物理过程（流体与固体）产生的，但它们是相似的，因为相关现象受到相应接口处的表面张力的强烈影响。 因此，可以使用常见的分析和计算工具对其进行研究。 这些问题的高度复杂性质使他们的研究必不可少，快速，准确，鲁棒。