Modelling and simulation of complex fluid flows with interfaces, multi-physics and multiple scales

该建议涉及流体动力学中的问题，其中底层流体流动与一些其他物理、生物或化学过程相互作用。 感兴趣的流程来自各种工业、工程和生物医学应用，可以根据两个主题进行组织： 主题一：流体-结构相互作用，包括可变形的，弹性结构浸入不可压缩流体。应用包括木浆纤维悬浮液的流动;心脏或耳蜗（或内耳）等充满流体的器官的生物力学;以及水母，鱿鱼或海洋蠕虫等生物体的游泳行为。 主题二：多孔介质中的多相流动，其中流动与热传输，相变或反应化学耦合。其应用包括树木的液流;土壤或混凝土中的水分吸收;以及氢燃料电池中冷凝气体的流动。 我解决所有这些问题的方法都遵循一个共同的策略：（1）建立一个基于仔细的物理推理的详细的数学模型;（2）使用数学技术，如渐近性，线性稳定性分析或周期均匀化，以简化控制方程，并获得洞察解决方案的行为;以及（3）开发一种精确和有效的数值算法，该算法可以用于执行广泛的模拟，并根据解析解和实验数据来验证模型。 主题一和主题二下列出的问题包括各种各样的物理现象和数值求解技术。然而，有几个共同的方面，统一了建模和计算问题，在这项工作中出现： * 解分量之间强耦合的非线性偏微分方程组; * 内部或边界层的存在以及可以从多尺度分析和/或自适应数值方法的使用中受益的广泛的空间尺度;以及 * 由于时间尺度变化很大，需要使用隐式时间步进算法，从而导致数值刚性。 该提案的一个定义特征是数学分析和算法开发之间的紧密相互作用，其中利用有关分析解决方案的知识，对数值方法的选择和具体的算法改进做出明智的决定。这项工作应该有显着的影响，在开发新的解决方案的算法，以及先进的知识复杂的多物理流现象。 例如，心脏血流不稳定性的详细知识可能会导致对心律失常的更好理解，而对枫树树液流动的新见解可能会用于优化树液收获实践。 许多子项目涉及与公司或其他非学术合作伙伴的合作，这将有助于确保成果在工业中实际投入使用。

This proposal is concerned with problems in fluid dynamics where an underlying fluid flow interacts with some other physical, biological or chemical process. The flows of interest originate from a variety of industrial, engineering and biomedical applications that can be organized under two themes: Theme I: Fluid-structure interaction involving deformable, elastic structures immersed in an incompressible fluid. Applications include flow of wood pulp fiber suspensions; biomechanics of fluid-filled organs such as the heart or cochlea (or inner ear); and swimming behavior of organisms such as jellyfish, squid or marine worms. Theme II: Multiphase flow in a porous medium, where the flow is coupled with heat transport, phase change, or reaction chemistry. Applications include sap flow in trees; water uptake in soil or concrete; and flow of condensing gases in hydrogen fuel cells. My approach to solving all of these problems follows a common strategy: (1) develop a detailed mathematical model based on careful physical reasoning; (2) employ mathematical techniques such as asymptotics, linear stability analysis or periodic homogenization to simplify the governing equations and to obtain insight into solution behavior; and (3) develop an accurate and efficient numerical algorithm, which can be used to perform extensive simulations and validate the model against both analytical solutions and experimental data. The problems listed under Themes I and II encompass a diverse range of physical phenomena and numerical solution techniques. Nevertheless, there are several common aspects that unify the modelling and computational issues arising in this work: * systems of nonlinear partial differential equations with strong coupling between solution components; * presence of interior or boundary layers and a wide range of spatial scales that can benefit from the use of multiscale analysis and/or adaptive numerical methods; and * numerical stiffness arising from widely varying time scales that necessitates use of implicit time-stepping algorithms. A defining characteristic of this proposal is the tight interplay between mathematical analysis and algorithm development, wherein knowledge about the analytical solution is exploited to make informed decisions about the choice of numerical method and specific algorithmic improvements. This work should have significant impact in terms of developing novel solution algorithms as well as advancing knowledge of complex multi-physics flow phenomena. For example, detailed knowledge of cardiac flow instabilities could lead to improved understanding of heart arrhythmias, and new insights into sap flow in maple trees may be used to optimize sap harvesting practices. Many sub-projects involve collaborations with companies or other non-academic partners, which will help to ensure that results are actually put into practical use in industry.