Computational Problems in Multicomponent Materials and Multiphase Fluids

这个提议的主要目的是研究多组分流体和多相材料行为的基本过程。我们将通过（1）开发和应用最先进的数值方法进行大规模计算和（2）重要组成过程的分析，数值和建模研究。更具体地说，我们的重点将是开发，实施和分析连续更现实的模型，在固/固相变的微观结构的扩散演化。我们对多相流体的研究包括三元流体流动的研究，其中只有两种组分是不混溶的。这些项目涉及基本的物理过程，其现象学是理解真实的流体行为和固体材料性质的基础。两者的特点是存在多个组成部分，复杂的模式形成和/或奇点（即空间复杂性）。虽然这些过程出现在非常不同的物理现象（流体与固体），都涉及自由边界问题，其中边界界面的运动，分离不同的组件，是由表面能和不稳定性或多体相互作用之间的竞争驱动的。因此，它们可以使用一套通用的分析和计算工具来处理。这些问题的高度非线性性质使得快速，准确和强大的数值方法对他们的研究至关重要。在这个提议中，我们将数学和数值分析，建模和大规模科学计算结合起来，以研究流体力学和材料科学中的某些基本问题。 我们的重点将是发展，实施和分析连续更现实的模型的扩散演变的微观结构在固/固相变。 这些转变是处理多组分金属合金如钢的一种重要方法.该过程的结果是形成多相微观结构，这是设定合金的宏观机械性能（即刚度、强度和韧性）的关键变量。微观结构的特征在于通过界面彼此分离的不同金属组分的区域。我们研究的目标是准确地建模和模拟合金中微观结构的形成，以便为冶金学家提供生成具有理想材料性能的新合金的配方。我们对多相流体的研究涉及对广泛用于化学生产和废物处理的液/液萃取过程进行建模。在这些过程中，两种（或多种）流体接触，其中一种流体中的污染物优先扩散到另一种流体中。因此，第一流体被清洁，然后被提取。在这些过程中，两种（或多种）流体相互接触，其中一种流体中的污染物优先扩散到另一种流体中，第一种流体因此被净化，然后被提取。如果被污染的流体破碎成小液滴，则界面面积和因此的传质增加。我们将使用分析，建模和大规模的科学计算来研究这些系统中的反应和混合速率。本工作的最终目的是为提高液/液萃取器的性能提供理论基础。虽然上述两个问题产生于非常不同的物理过程（流体与固体），但它们在相关现象受到各自界面处的表面张力的强烈影响的意义上是相似的。因此，它们可以使用常见的分析和计算工具进行研究。这些问题的高度复杂性使得快速，准确和强大的数值方法对他们的研究至关重要。

The main objective of this proposal is to investigate processes fundamental to the behavior of multicomponent fluids andmultiphase materials. We will do this by (1) developing and applying state-of-the-art numerical methods to large scale computation and (2)analytical, numerical and modelling studies of important constituent processes. More specifically, our focus will be on developing, implementing and analyzing successively more realistic models of the diffusional evolution of microstructure in solid/solid phase transitions. Our investigation of multiphase fluids includes a study of ternary fluid flow where only two of the components are immiscible. These projects 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 problemswhere 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 numericalanalysis, modelling, and large-scale scientific computation to studycertain fundamental problems in fluid dynamics and materialsscience. Our focus will be on developing, implementing and analyzingsuccessively more realistic models of the diffusional evolution of microstructure in solid/solid phase transitions. These transformationsare an important method of processing multicomponent metallic alloys suchsuch as steels. The result of this process is the formation of a multiphasemicrostructure, which is a key variable in setting the macroscopicmechanical properties (i.e. stiffness, strength and toughness) of thealloy. 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. Our investigation of multiphase fluids involves modelling liquid/liquid extraction processes that are widely used in chemical production and waste processing. In these processes, two (or more) fluids are placed in contact and a contaminant in one of the fluids diffuses preferentially into another. The first fluid thus is cleaned and is then extracted. In these processes, two (or more) fluids are placed in contactand a contaminant in one of the fluids diffuses preferentially into another.The first fluid thus is cleaned and is then extracted. If the contaminated fluid is broken up into small droplets, the interfacial area and hence mass transfer is increased. We will use analysis, modeling and large scale scientific computation to study reaction and mixing rates within these systems. The ultimate goal of this work is to provide a theoretical foundation for improving the performance of liquid/liquid extractors.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.