Fluid-multi-layered-structure interaction problems

流体-多层结构相互作用问题

• 批准号: 1311709
• 负责人: Suncica Canic
• 金额: $ 20.46万
• 依托单位: University of Houston
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-06-15 至 2019-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1311709&HistoricalAwards=false
• 关键词: Fluid; multi; layered; structure; interaction

Fluid-structure interaction (FSI) problems arise in many applications. The widely known examples are aeroelasticity and biofluids. In biofluidic applications, such as, e.g., the study of interaction between blood flow and cardiovascular tissue, the coupling between the fluid and the relatively light structure is highly nonlinear, requiring sophisticated ideas for the study of their solutions. In the blood flow application, the problems are further exacerbated by the fact that the walls of major arteries are composed of several layers, each with different mechanical characteristics. No results exist so far that analyze solutions to fluid-structure interaction problems in which the structure is composed of several different layers. The proposed research takes a first step in this direction by proposing a program to study the existence of solutions to a class of FSI problems describing the interaction between a multi-layered structure and the flow of an incompressible, viscous fluid, giving rise to a fully coupled, nonlinear moving boundary, fluid-multi-structure interaction problem. The analysis relies on a novel, loosely coupled, partitioned, time-marching numerical scheme, and on novel compactness arguments providing convergence of the numerical scheme to a weak solution of the nonlinear fluid-multi-layered structure interaction problem. The proposed program opens up a new field within the area of FSI problems. This work brings to light several features that have not been studied before. In particular, this work reveals a new regularizing mechanism in FSI problems that is due to the presence of a fluid-structure interface with mass. The inertia of the fluid-structure interface regularizes the evolution of the entire FSI solution.This is an exciting, novel study requiring the development of original mathematical techniques motivated by an important biological application: the interaction between blood flow and human arterial walls. It is well-known that arterial walls are composed of several layers, each with different mechanical characteristics and thickness. The healthy physiology and the pathophysiology of the human cardiovascular system are significantly affected by the pulsation of arterial walls during each cardiac cycle. However, the interaction between the different arterial wall layers and their interaction with blood flow is still not completely understood. For example, recent developments in ultrasound speckle tracking methods revealed significant shear strain between the different layers of arterial walls in high adrenaline situations. The consequences of this phenomenon on the initiation of cardiovascular disease are yet to be understood. The proposed research makes a step in this direction by designing mathematical models, and by analyzing solutions of the mathematical models that capture fluid-structure interaction between blood flow and arterial walls in the case when arterial walls are modeled as multi-layered structures. No mathematical results exist so far in this area, and the proposed research opens up a new area in the field of fluid-structure interaction problems. The work proposed here promises to develop a strong partnership between the University of Houston, the University of Pittsburgh, the University of Zagreb, and the Texas Medical Center in Houston. The PI is a woman, and active recruitment of minorities and women to participate in this research is proposed.

许多应用中都会出现流固耦合 (FSI) 问题。众所周知的例子是气动弹性和生物流体。在生物流体应用中，例如研究血流和心血管组织之间的相互作用，流体和相对较轻的结构之间的耦合是高度非线性的，需要复杂的想法来研究其解决方案。在血流应用中，由于主动脉壁由多层组成，每层具有不同的机械特性，这一事实进一步加剧了问题。迄今为止，还没有分析结构由多个不同层组成的流固耦合问题的解决方案的结果。这项研究在这个方向上迈出了第一步，提出了一个程序来研究一类 FSI 问题的解的存在性，这些问题描述了多层结构与不可压缩粘性流体流动之间的相互作用，从而产生了完全耦合的非线性移动边界流体-多结构相互作用问题。该分析依赖于一种新颖的、松耦合的、分区的、时间推进的数值方案，以及新颖的紧致性论证，该论证提供了数值方案对非线性流体-多层结构相互作用问题的弱解的收敛性。拟议的计划在 FSI 问题领域开辟了一个新领域。这项工作揭示了一些以前没有研究过的特征。特别是，这项工作揭示了 FSI 问题中的一种新的正则化机制，这是由于存在质量的流固界面。流体-结构界面的惯性使整个 FSI 解决方案的演化规律化。这是一项令人兴奋的新颖研究，需要开发由重要的生物应用（血流与人体动脉壁之间的相互作用）推动的原始数学技术。众所周知，动脉壁由多层组成，每层具有不同的机械特性和厚度。每个心动周期期间动脉壁的搏动对人类心血管系统的健康生理和病理生理有显着影响。然而，不同动脉壁层之间的相互作用以及它们与血流的相互作用仍不完全清楚。例如，超声波散斑跟踪方法的最新发展揭示了在高肾上腺素情况下动脉壁不同层之间存在显着的剪切应变。这种现象对心血管疾病发生的影响尚不清楚。本研究通过设计数学模型，并分析数学模型的解，在动脉壁建模为多层结构的情况下，捕获血流与动脉壁之间的流固相互作用，从而朝这个方向迈出了一步。迄今为止，该领域还没有任何数学成果，而这项研究开辟了流固耦合问题领域的新领域。这里提出的工作有望在休斯顿大学、匹兹堡大学、萨格勒布大学和休斯顿德克萨斯医学中心之间建立强有力的合作伙伴关系。 PI 为女性，建议积极招募少数族裔和女性参与本研究。