Fluid-multi-layered-structure interaction problems

流固耦合问题在很多应用中都会出现。广为人知的例子是气动弹性和生物流体。在生物流体应用中，例如，在研究血流和心血管组织之间的相互作用时，流体和相对较轻的结构之间的耦合是高度非线性的，需要复杂的思想来研究它们的解决方案。在血流应用中，由于主动脉的壁由几层组成，每层具有不同的机械特性，这一事实进一步加剧了问题。到目前为止，还没有结果存在，分析解决方案的流固耦合问题，其中的结构是由几个不同的层。建议的研究采取了第一步，在这个方向上提出了一个程序来研究一类FSI问题的解决方案的存在性描述的多层结构和不可压缩的粘性流体的流动之间的相互作用，从而产生一个完全耦合的，非线性的移动边界，流体多结构相互作用问题。分析依赖于一种新的，松散耦合，分区，时间推进的数值方案，和新的紧凑性参数提供收敛的数值方案的非线性流体多层结构相互作用问题的弱解。该方案开辟了一个新的领域内的FSI问题。这项工作揭示了一些以前没有研究过的特征。特别是，这项工作揭示了一个新的正规化机制，在流固耦合问题，这是由于存在一个流体结构界面与质量。流体-结构界面的惯性使整个FSI解的演化规律化，这是一个令人兴奋的新研究，需要发展原始的数学技术，其动机是一个重要的生物学应用：血液流动和人体动脉壁之间的相互作用。众所周知，动脉壁由若干层组成，每层具有不同的机械特性和厚度。人体心血管系统的健康生理学和病理生理学受到每个心动周期期间动脉壁的脉动的显著影响。然而，不同动脉壁层之间的相互作用及其与血流的相互作用仍然没有完全理解。例如，超声斑点跟踪方法的最新发展揭示了高肾上腺素情况下动脉壁不同层之间的显著剪切应变。这一现象对心血管疾病发生的影响尚不清楚。所提出的研究通过设计数学模型，并通过分析数学模型的解决方案，在动脉壁被建模为多层结构的情况下，捕获血流和动脉壁之间的流体-结构相互作用，在这个方向上迈出了一步。目前在这方面还没有数学结果，本文的研究为流固耦合问题的研究开辟了一个新的领域。这里提出的工作承诺在休斯顿大学，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伙伴关系。主要研究者是一名妇女，建议积极招募少数民族和妇女参与这项研究。

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.