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

具有界面、多物理场和多尺度的复杂流体流动的建模和仿真

• 批准号: RGPIN-2016-04088
• 负责人: Stockie, John
• 金额: $ 2.11万
• 依托单位: Simon Fraser University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=666006
• 关键词: Modelling; simulation; complex; fluid; flows

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.**

该提案涉及流体动力学问题，其中潜在的流体流动与其他一些物理、生物或化学过程相互作用。 感兴趣的流动源自各种工业、工程和生物医学应用，可以根据两个主题进行组织： ******主题 I：涉及浸入不可压缩流体中的可变形弹性结构的流固相互作用。应用包括木浆纤维悬浮液的流动；心脏或耳蜗（或内耳）等充满液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 II：多孔介质中的多相流，其中流动与热传递、相变或反应化学耦合。应用包括树木中的液流；土壤或混凝土中的吸水量； *****我解决所有这些问题的方法遵循一个共同的策略：（1）基于仔细的物理推理开发详细的数学模型； (2) 采用渐进、线性稳定性分析或周期均质化等数学技术来简化控制方程并深入了解解的行为； (3) 开发准确高效的数值算法，可用于执行广泛的模拟并根据解析解和实验数据验证模型。***主题 I 和 II 下列出的问题涵盖各种物理现象和数值求解技术。尽管如此，有几个共同的方面统一了这项工作中出现的建模和计算问题：***** 解分量之间具有强耦合的非线性偏微分方程系统； **** 存在内部或边界层以及广泛的空间尺度，可以受益于多尺度分析和/或自适应数值方法的使用； **** 由于时间尺度变化很大而产生的数值刚度，需要使用隐式时间步进算法。 ***该提案的一个决定性特征是数学分析和算法开发之间的紧密相互作用，其中利用有关解析解的知识来就数值方法的选择和特定算法改进做出明智的决策。这项工作应该在开发新颖的解决算法以及增进复杂多物理流现象的知识方面产生重大影响。 例如，对心脏血流不稳定性的详细了解可以提高对心律失常的理解，并且对枫树汁液流动的新见解可以用于优化汁液采集实践。 许多子项目涉及与公司或其他非学术合作伙伴的合作，这将有助于确保结果真正投入到工业中的实际应用。 **