IMA PIP Workshop on Numerical Modeling of Complex Fluids and MHD

复杂流体中异常现象最常见的来源和表现是不同的“弹性”效应。这些可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，由于微观结构形成而产生的弹性效应，或由于粘弹性复杂流体中聚合物分子的存在而产生的体弹性效应。数学上，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：液晶中的定向有序参数，高分子材料哑铃模型中的分布密度函数，磁流体动力学流体中的磁场，以及不同材料混合物中的体积分数。这些材料的不同流变学和流体动力学性质可以反过来归因于这些内部变量的输运和通常在所有尺度上表现出来的诱导弹性应力之间的特殊耦合，并且在很大程度上决定了系统的特定性质，例如颗粒构型的稳定性和规律性以及系统中特定图案形成的可能性。了解这种耦合不同物理尺度的复杂机制对于设计精确的数学和数值模型和算法以模拟此类系统至关重要。本次研讨会的前提是，获得重要的新结果，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入的了解和理解，需要一个由实验、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，以适当地解决复杂流体研究中常见的基本未解决的问题：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的预测能力的实验验证和验证。建模和模拟由复杂流体描述的设计师和智能材料的丰富池需要组织跨学科研究力量来开发和分析这些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，目的是捕捉这些复杂材料研究中涉及的各种时间和长度尺度。本次研讨会将聚集这些新的多尺度建模和模拟技术发展的关键贡献者，目的是向学生和年轻研究人员介绍这些想法，并促进未来参与者之间复杂流体应用的跨学科研究。研讨会将重点介绍确定性和随机计算方法的相关研究领域的主题，重点是：多尺度建模和模拟的能量变分方法；计算和实验指导模型验证和鲁棒自适应数值模型和求解方法的进一步发展。

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.