Collaborative Research: Phase-field models, algorithms and simulations for multiphase complex fluids

合作研究：多相复杂流体的相场模型、算法和模拟

• 批准号: 1419053
• 负责人: Jie Shen
• 金额: $ 15万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-09-01 至 2017-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1419053&HistoricalAwards=false
• 关键词: Collaborative; Research; Phase; field; models

Mixtures of two or more immiscible viscous and/or complex fluid components are widely used in many science and engineering applications, in particular, in designing advanced materials involving polymers, composites, gels, liquid crystals, etc. It is expected that the proposed models and numerical methods/simulations will contribute to a better understanding of the complex physical and mathematical issues related to multiphase complex fluids, and provide valuable information for the design of advanced materials and on the rheological and hydrodynamic properties of complex fluids. The proposed research will also provide valuable opportunities for undergraduate and graduate students to engage in interdisciplinary research with strong ties to biological and engineering material systems, to learn critical skills of computational and applied mathematics, and to develop state-of-the-art numerical tools for science and engineering applications.Flows of multiphase complex fluid mixtures usually involve the coupling of microstructures, interfacial morphology and macroscopic hydrodynamics. The complexity of these nonlinear couplings presents many mathematical challenges for modeling and algorithm development, numerical analysis and implementation. The proposed research aims at overcoming these challenges to design efficient and accurate numerical algorithms for nonlinear multiphase complex fluid systems that couple the microstructure, moving material interfaces and hydrodynamics. Very few efforts have been made to address these numerical challenges. This project will result in numerical schemes which satisfy discrete energy dissipation laws, and which allow large time steps and controllable error and capture the interfacial dynamics accurately. In addition, the developed predictive tools and numerical simulations will extend the applicability of mathematical analysis and numerical codes to physical problems of current interest, and contribute to a better understanding of pressing science and engineering applications.

两种或多种不混溶的粘性和/或复杂的液体成分的混合物广泛用于许多科学和工程应用中，特别是在设计涉及聚合物，复合材料，凝胶，液晶等的先进材料时。数值方法/仿真将有助于更好地理解与多相复杂流体相关的复杂物理和数学问题，并为高级材料的设计以及复杂流体的流变和流体动力特性提供有价值的信息。拟议的研究还将为本科和研究生提供宝贵的机会，以与生物学和工程材料系统有着密切的联系，学习计算和应用数学的关键技能并开发最先进的数值工具，从事跨学科研究。对于科学和工程应用，多相复杂流体混合物的流通常涉及微结构，界面形态和宏观流体动力学的耦合。这些非线性耦合的复杂性为建模和算法开发，数值分析和实现带来了许多数学挑战。拟议的研究旨在克服这些挑战，以设计有效，准确的数值算法，用于将微观结构，移动材料界面和流体动力学的非线性多相复杂流体系统设计。很少有努力解决这些数字挑战。该项目将导致数值方案满足离散的能量耗散定律，并允许大量时间步骤和可控误差并准确捕获界面动力学。此外，开发的预测工具和数值模拟将将数学分析和数值代码的适用性扩展到当前兴趣的物理问题，并有助于更好地理解紧迫的科学和工程应用程序。