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入粘弹性流体中的柔性结构（例如，生殖道中的精子、肠道和肺中的细菌、肺中粘液的纤毛运输）。在某些情况下，例如肺中纤毛驱动的运输，这些结构在多流体环境中运行。尽管几十年的工作明确的挑战仍然与开发合适的计算工具的复杂的流体-结构相互作用的建模。该项目的目标是开发和分析这些模拟的精确计算方法，并建立这些工具的高性能开源实现，供其他研究人员使用。 新的计算工具与实验测量一起将用于对粘液的机械行为产生新的见解。粘液为每个人体器官提供保护屏障，并且许多疾病和病症与粘液病理学相关（例如，肺（COPD、囊性纤维化、哮喘）、胃（溃疡）、生殖道（不育））。此外，作为这些项目的一部分开发的工具具有超出粘液的应用：食品工业，个人护理产品以及药物应用，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。该项目的具体研究目标是：1）开发和分析涉及复杂流体的流体-结构相互作用和流体-流体相互作用问题的高效高阶精度数值方法，2）通过与项目合作者的实验数据进行比较来验证这些方法，以及3）开发工业和生物系统的数学模型，包括微珠流变学、纤毛同步和运输以及悬浮液的相分离。以往的粘弹性流体数值方法的研究一直是由工程应用驱动的，而生物应用提出了新的挑战：大变形的活动软结构和复杂的流变学。尽管过去的努力，以了解复杂流体中的主动结构的动力学，一个显着的瓶颈仍然存在：缺乏准确的，有效的，自适应的数值方法和软件的粘弹性流体-结构相互作用和流体-流体界面。该研究团队的目标是建立，验证和应用这项技术，由生物学和工程学的应用和实验数据指导。

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.