FRG: Collaborative Research: Computational Methods for Complex Fluids: Adaptivity, Fluid-Structure Interaction, and Applications in Biology

许多生物系统涉及浸没在粘弹性流体中的柔性结构（例如，生殖道中的精子，肠道和肺部的细菌，肺部粘液的纤毛运输）。在某些情况下，如肺部纤毛驱动的运输，这些结构在多流体环境中运作。尽管几十年的工作，明确的挑战仍然是开发合适的计算工具来模拟复杂的流固相互作用。该项目的目标是为这些模拟开发和分析准确的计算方法，并建立这些工具的高性能开源实现，以供其他研究人员使用。新的计算工具和实验测量将用于对黏液的力学行为产生新的见解。粘液为每个人体器官提供了保护屏障，许多疾病和失调都与粘液病理有关（例如，肺（慢性阻塞性肺病、囊性纤维化、哮喘）、胃（溃疡）、生殖道（不育症））。此外，作为这些项目的一部分开发的工具不仅适用于黏液，还适用于食品工业、个人护理产品以及制药应用，包括药物和药物输送系统。该项目还将为数学科学领域的研究生和博士后研究人员提供广泛的跨学科培训。本项目的具体研究目标是：1)开发和分析流固耦合和复杂流体流固耦合问题的高效高阶精确数值方法；2)通过与项目合作者的实验数据对比验证这些方法；3)建立工业和生物系统的数学模型，包括微珠流变学、纤体同步和输送、悬浮液的相分离。以往粘弹性流体数值方法的研究主要是由工程应用驱动的，而生物应用则提出了新的挑战：活动软结构的大变形和复杂的流变学。尽管过去已经努力了解复杂流体中活动结构的动力学，但仍然存在一个重大的瓶颈：缺乏准确，高效，自适应的粘弹性流体-结构相互作用和流体-流体界面的数值方法和软件。研究小组的目标是在生物学和工程学的应用和实验数据的指导下，建立、验证和应用这项技术。

Many biological systems involve flexible structures immersed in viscoelastic fluids (e.g., sperm in the reproductive tract, bacteria in the gut and lung,ciliary transport of mucus in the lung). In some cases, such as cilia-driven transport in the lung, these structures operate in a multi-fluid environment. Despite decades of work explicit challenges remain with developing suitable computational tools for the modeling of the complex fluid-structure interactions. The goal of this project is to develop and analyze accurate computational methods for these simulations, and to establish high-performance open-source implementations of these tools to be used by other researchers. The new computational tools together with experimental measurements will be used to generate new insight into the mechanical behavior of mucus. Mucus provides a protective barrier for every human organ, and many diseases and disorders are associated with mucus pathology (e.g., in the lung (COPD, cystic fibrosis, asthma), stomach (ulcers),reproductive tract (infertility)). Moreover, tools developed as part of these projects have applications beyond mucus: to the food industry, for personal care products, as well as pharmaceutical applications, including drugs and drug delivery systems. The project will also provide broad interdisciplinary training for graduate students and postdoctoral researchers in the mathematical sciences.The specific research objectives of this project are 1) to develop and analyze efficient higher-order accurate numerical methods for fluid-structure interaction and fluid-fluid interaction problems involving complex fluids, 2) to validate these methods by comparison to experimental data of project collaborators, and 3) to develop mathematical models of industrial and biological systems, including microbead rheology, ciliar synchronization and transport, and phase separation of suspensions. Previous research on numerical methods for viscoelastic fluids has been driven by engineering applications, while biological applications pose new challenges: large deformations of active soft structures and complex rheology. Despite past efforts to understand the dynamics of active structures in complex fluids, a significant bottleneck persists: the lack of accurate, efficient, adaptive numerical methods and software for viscoelasstic fluid-structure interaction and fluid-fluid interfaces. The research team aims to build, validate, and apply this technology, guided by applications and experimental data from biology and engineering.