Adaptive, Non-stiff, and Stochastic Methods for Phase Field Fluid Models

相场流体模型的自适应、非刚性和随机方法

• 批准号: 0609996
• 负责人: Hector Ceniceros
• 金额: $ 22.54万
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2009-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0609996&HistoricalAwards=false
• 关键词: Adaptive; Non; stiff; Stochastic; Methods

The investigator proposes to develop innovative numerical methods for conservative phase field models of multi-phase and complex fluids. The new methods will becapable of resolving accurately and efficiently the disparate time and length scales involved in topological changes and complex interface morphologies, in the dynamics of the micro-scale structures, and in the effect of stochastic thermal fluctuations in phase transitions. Those capabilities will be obtained with novel space and time adaptive methods that take into account the mathematical structure and multi-scale nature of the models and their solutions. The methods will be designed to be free of high order stability constraints and will be of optimal computational cost. An effective, innovative coupling of stochastic and deterministic formulations is also proposed.Complex fluids found in a wide variety of industrial applications such as emulsions, foams, and polymeric solutions are characterized by multiple components, several coexisting phases, and structural heterogeneities spanning a broad range of length scales. The macroscopic behavior and properties of these fluid mixtures are a function of the intricate nonlinear coupling of the flow with micro- or nano- structures. The understanding of the dynamics of these systems is thus of significant scientific and technological interest. Computer simulation can play an instrumental role toward aiding in achieving this goal. The development of these numerical methods is the central objective of this proposal. The proposed research will be conducted in a multi-disciplinary environment and will also serve an important education goal: the interdisciplinary education and training of undergraduate and graduate students. An integral part of this project is also a sustained effort to promote and broaden the participation of underrepresented groups and the use of innovative pedagogic initiatives with ties with the industrial sector.

这位研究人员建议为多相和复杂流体的保守相场模型开发创新的数值方法。新方法将能够准确和有效地分辨不同的时间和长度尺度，包括拓扑变化和复杂的界面形态，微观尺度结构的动力学，以及相变中随机热涨落的影响。这些能力将通过考虑到模型及其解的数学结构和多尺度性质的新的空间和时间自适应方法来获得。该方法的设计将不受高阶稳定性的限制，并将具有最优的计算成本。在乳液、泡沫和聚合物溶液等广泛的工业应用中发现的复杂流体的特征是多组分、多个共存相以及跨越大范围长度尺度的结构不均一性。这些流体混合物的宏观行为和性质是流动与微米或纳米结构的复杂非线性耦合的函数。因此，了解这些系统的动力学具有重大的科学和技术意义。计算机模拟可以在帮助实现这一目标方面发挥重要作用。这些数值方法的发展是这项提议的中心目标。拟议的研究将在多学科环境中进行，并将服务于一个重要的教育目标：本科生和研究生的跨学科教育和培训。该项目的一个组成部分也是持续努力，以促进和扩大代表不足群体的参与，并利用与工业部门有联系的创新教学举措。