Fluid-multi-layered-structure interaction problems

流固耦合（FSI）问题出现在许多应用中。广为人知的例子是空气弹性和生物流体。在生物流体应用中，例如研究血流与心血管组织之间的相互作用，流体与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，由于大动脉壁由几层组成，每层具有不同的机械特性，因此问题进一步加剧。对于由多层结构组成的流固相互作用问题，目前还没有分析解决方案的结果。本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描述多层结构与不可压缩粘性流体流动之间相互作用的FSI问题的解的存在性，从而产生一个完全耦合的非线性运动边界，流体-多结构相互作用问题。该分析依赖于一种新颖的、松散耦合的、分区的、时间推进的数值格式，以及一种新颖的紧性参数，为非线性流体-多层结构相互作用问题的弱解提供了数值格式的收敛性。该计划在FSI问题领域开辟了一个新的领域。这项工作揭示了以前没有研究过的几个特征。特别是，这项工作揭示了一种新的规则机制，在FSI问题中，这是由于流体结构界面与质量的存在。流固界面的惯性使整个FSI解决方案的演变规律化。这是一项令人兴奋的、新颖的研究，需要开发原始的数学技术，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，动脉壁是由几层组成的，每一层都有不同的力学特性和厚度。在每个心脏周期中，动脉壁的脉动对人体心血管系统的健康生理和病理生理都有显著影响。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未完全了解。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不同动脉壁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。本研究通过设计数学模型，并分析了当动脉壁被建模为多层结构时，血流与动脉壁之间流体结构相互作用的数学模型的解，朝着这个方向迈出了一步。这一领域目前尚无数学结果，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伙伴关系。PI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.