Fluid-structure interaction with multi-layered structures: a new class of partitioned schemes

流固耦合(FSI)问题在许多应用中都会出现。它们包括工程中的多物理问题，如气动弹性和螺旋桨涡轮机，以及生物流体应用，如自我推进生物体，流体-细胞相互作用，以及血流和心血管组织之间的相互作用。由于这些问题的强非线性和多物理性质，对它们的全面研究仍然是一个挑战。更糟糕的是，在许多生物应用中，这种结构由几层组成，每一层都有不同的机械特性。例如，动脉壁就是这种情况。模拟不可压缩粘性流体与多层结构之间相互作用的FSI求解器将是这类问题计算研究中不可缺少的工具。到目前为止，还没有这样的血流动力学FSI解算器，这里提出的工作是朝着这个方向迈出的第一步。研究人员正在开发一套稳定的松散耦合分区格式，用于求解一类非线性移动边界、流-多结构相互作用问题。所提出的方案是基于一种新的Lie算子分裂的实现，其设计方式是使离散化问题的能量模仿连续问题的能量。该程序在FSI问题领域开辟了一个新的领域，揭示了一些以前没有研究过的新特征，例如研究了具有质量的流体-结构界面的正则化效应。建议的方案类将使用名为LifeV的开源解算器库来实施和优化以实现高性能计算。这将使这项研究的产品可供涉及广泛应用的大量用户使用。这是一项令人兴奋的、新颖的研究，需要开发原创的数学和计算技术，以推动心血管血流的重要应用。研究人员正在开发一种计算软件，该软件将首次捕捉到人类动脉壁不同层之间的相互作用，因为它们与脉动的血流相互作用。这项研究是由超声斑点跟踪方法的最新进展所推动的，这些方法揭示了在高肾上腺素的情况下，动脉壁内不同层之间存在显著的应变。人们注意到，这一现象在心血管疾病发展中的作用尚未被探索。本研究开发的计算模型将为研究这一现象对人体心血管系统的生理学和病理生理学的影响提供不可或缺的工具。这项研究的结果将通过开放源码对不同的科学学科产生影响，用户可以免费获得。这里提出的工作承诺在休斯顿大学、匹兹堡大学、埃默里大学和休斯顿的德克萨斯医学中心之间建立强有力的合作伙伴关系。将通过学生教育、对学生和初级教师的指导以及组织跨学科会议/讲习班进一步实现更广泛的影响。这两名调查人员都是在教育和指导妇女和少数群体方面有过往记录的女性，这一做法将在整个项目中继续下去。

Fluid-structure interaction (FSI) problems arise in many applications. They include multi-physics problems in engineering such as aeroelasticity and propeller turbines, as well as biofluidic application such as self-propulsion organisms, fluid-cell interactions, and the interaction between blood flow and cardiovascular tissue. A comprehensive study of these problems remains to be a challenge due to their strong nonlinearity and multi-physics nature. To make things worse, in many biological applications the structure is composed of several layers, each with different mechanical characteristics. This is, for example, the case with arterial walls. A FSI solver that simulates the interaction between an incompressible, viscous fluid and a multi-layered structure would be an indispensable tool for the computational studies of this class of problems. To date, there are no such FSI solvers for hemodynamics, and the work proposed here makes a first step in this direction. The investigators are developing a set of stable loosely-coupled partitioned schemes for solving a class of nonlinear moving boundary, fluid-multi-structure interaction problems. The proposed schemes are based on a novel implementation of the Lie operator splitting, which is designed in such a way that the energy of the discretized problem mimics the energy of the continuous problem. The proposed program opens up a new field within the area of FSI problems, bringing to light several new features that have not been studied before, such as the study of the regularizing effects of fluid-structure interfaces with mass. The proposed class of schemes will be implemented and optimized for high performance computing using an open source library of solvers called LifeV. This will make the products of this research accessible to a large set of users involving a broad range of applications.This is an exciting, novel study requiring the development of original mathematical and computational techniques motivated by important applications in cardiovascular flow. The investigators are developing a computational software that will, for the first time, capture the interaction between different layers of the human arterial walls as they interact with pulsating blood flow. This study is motivated by the most recent advances in ultrasound speckle tracking methods, which reveal that in high adrenaline situations, there is significant strain between different layers within arterial walls. It has been noted that the role of this phenomenon in the development of cardiovascular disease has not been explored yet. The computational models developed in this study will provide an indispensable tool for the study of the influence of this phenomenon on the physiology and pathophysiology of the human cardiovascular system. The results from this research will have impact across different scientific disciplines through an open source code, which will be freely available to users. The work proposed here promises to develop a strong partnership between the University of Houston, the University of Pittsburgh, Emory University, and the Texas Medical Center in Houston. The broader impacts will be further achieved through student education, mentoring of students and junior faculty, and organization of interdisciplinary conferences/workshops. Both investigators are women with a track record in education and mentoring women and minorities, and this practice will continue throughout this project.