IMA PIP Workshop on Numerical Modeling of Complex Fluids and MHD

IMA PIP 复杂流体数值模拟和 MHD 研讨会

• 批准号: 0964344
• 负责人: James Brannick
• 金额: $ 1.12万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-06-01 至 2011-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0964344&HistoricalAwards=false
• 关键词: IMA; PIP; Workshop; Numerical; Modeling

The most common origin and manifestation of anomalous phenomena in complex fluids are different ``elastic'' effects. These can be ascribed to the elasticity of deformable particles, elastic repulsion between charged liquid crystals, polarization of colloids or multi-component phases, elastic effects due to microstructures formation, or bulk elastic effects due to the presence of polymer molecules in viscoelastic complex fluids. Mathematically, such elastic effects can be represented in terms of internal variables. Examples of such internal variables are: the orientational order parameter in liquid crystals, the distribution density function in the dumb-bell model for polymeric materials, the magnetic field in magnetohydrodynamic fluids, and the volume fraction in mixtures of different materials. The different rheological and hydrodynamic properties of these materials can in turn be attributed to the special coupling between the transport of these internal variables and the induced elastic stresses which typically manifest on all scales, and to a large extent determine the specific properties of the system, such as the stability and regularity of particle configurations and the likelihood of specific pattern formations in the system. The understanding of such complex mechanisms which couple different physical scales is crucial in designing accurate mathematical and numerical models and algorithms in order to simulate such systems. This workshop is based on the premise that gaining significant new results and thereby obtaining deeper insight and understanding of materials described by complex fluids (e.g., polymers, emulsions, liquid crystals, magnetorheological fluids, blood suspensions) requires a combined approach consisting of experiment, modeling, analysis, and simulation. The primary objective of the workshop is thus to gather students, junior faculty, and experts to discuss new integrated modeling techniques that properly address the fundamental unresolved issues common to studies of complex fluids: consistency of models with physics, rigorous analysis of the models, numerical and scientific computing issues, and the experimental verification and validation of the predictive capabilities of the mathematical and numerical models. Modeling and simulating the rich pool of designer and smart materials described by complex fluids requires marshaling interdisciplinary research forces to develop and analyze mathematical models and computational tools for such problems. Recently, numerous methodologies and frameworks have been developed in an aim to capture the various time and length scales involved in studies of such complex materials. This workshop will gather key contributors to the development of these new multiscale modeling and simulations techniques, with the aim of introducing these ideas to students and young researchers and also promoting interdisciplinary research on complex fluids applications amongst participants in the future. The workshop will highlight topics from interrelated research areas for both deterministic and stochastic computational approaches, concentrating on: an Energetic Variational approach for multiscale modeling and simulation; computationally and experimentally guided model validation and further development of robust adaptive numerical models and solution methods.

复杂流体中异常现象最常见的来源和表现形式是不同的“弹性”效应。这可以归因于可变形颗粒的弹性、带电液晶之间的弹性排斥、胶体或多组分相的极化、微观结构形成的弹性效应或粘弹性复杂流体中聚合物分子的存在导致的整体弹性效应。从数学上讲，这种弹性效应可以用内部变量来表示。这些内部变量的例子有：液晶中的取向有序参数、聚合物材料哑铃模型中的分布密度函数、磁流体中的磁场以及不同材料混合物中的体积分数。这些材料不同的流变性和流体力学性质可以归因于这些内部变量的传输和诱导的弹性应力之间的特殊耦合，这些应力通常表现在所有尺度上，并且在很大程度上决定了系统的特定属性，例如粒子构型的稳定性和规律性以及在系统中形成特定图案的可能性。对这种复杂的机制的理解对于设计精确的数学和数值模型和算法以模拟这种系统是至关重要的。本研讨会的前提是，要获得重要的新成果，从而对复杂流体(如聚合物、乳液、液晶、磁流变液、血液悬浮液)所描述的材料有更深的了解，需要一种由实验、建模、分析和模拟组成的综合方法。因此，研讨会的主要目标是聚集学生、初级教师和专家讨论新的集成建模技术，以恰当地解决复杂流体研究中常见的基本未解决问题：模型与物理的一致性、模型的严格分析、数值和科学计算问题，以及数学和数值模型预测能力的实验验证和确认。对由复杂流体描述的丰富的设计者和智能材料进行建模和模拟，需要组织跨学科的研究力量来开发和分析此类问题的数学模型和计算工具。最近，已经开发了许多方法和框架，目的是捕捉研究这种复杂材料所涉及的各种时间和长度尺度。本次研讨会将聚集开发这些新的多尺度建模和模拟技术的主要贡献者，目的是向学生和年轻研究人员介绍这些想法，并在未来的参与者中促进对复杂流体应用的跨学科研究。讲习班将重点介绍确定性和随机计算方法相关研究领域的主题，重点是：用于多尺度建模和模拟的充满活力的变分方法；通过计算和实验指导的模型验证以及进一步发展稳健的自适应数值模型和求解方法。