Collaborative Research: Hybrid Fluid-Structure Interaction Material Point Method with applications to Large Deformation Problems in Hemodynamics

合作研究：混合流固耦合质点法及其在血流动力学大变形问题中的应用

• 批准号: 1912705
• 负责人: Max Gunzburger
• 金额: $ 10.04万
• 依托单位: Florida State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-08-01 至 2022-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1912705&HistoricalAwards=false
• 关键词: Collaborative; Research; Hybrid; Fluid; Structure

Heart valve associated issues in the human organism are the cause of cardiac arrest and heart failure, which may have devastating consequences on a person's health and even lead to death. While not necessarily fatal, pathologies associated with leg vein valves can nevertheless cause severe distress to the people affected and have a negative impact on their life with possibly major complications. For the treatment of valve associated diseases, the most common practice nowadays is the replacement of the malfunctioning valve with a prosthetic device. Unfortunately, prosthetic valves have issues with long term durability and post-implantation complications. Given the necessity of improving the design and selection of existing prosthetic valves, computational methodologies are becoming a valuable tool. The nature of blood flow inside a human valve renders the modeling problem considerably challenging from the mathematical and computational standpoints, as multiple physical phenomena mutually interact. Specifically, the major challenges are the large structural displacements experienced by the valve leaflets, while preserving accurate description of the hydrodynamic force at the fluid-solid interface. The focus of this project is on developing new fluid-structure interaction methodologies with specific interest in the case of large deformations. The important insight provided in this project will enable future valve design optimization while avoiding costly empirical design iterations. In addition to the obvious potential impact on society, the proposed project will be useful to many other applications in science and engineering, and also have beneficial impact on the training, education, and careers of junior researchers in an important, exciting, and mathematically, computationally, and societally impactful area of research. This project will support 2 graduate students per year for each year of the three year project.This project is about the development, analysis, and implementation of novel computational techniques for the coupling of finite element methods (FEMs) to material point methods (MPMs) in fluid-structure interaction (FSI) problems. The use of different discretization techniques for the study of multiscale and multiphysics problems is a powerful tool for computational simulations. For instance, one-dimensional models are coupled with multi-dimensional models for computational cost reduction, or FEMs are coupled with finite volume methods to exploit the advantages of the algorithmic and mathematical features of these two methods. With the same idea, the coupling of FEM with MPM represents a promising combination, if different deformation regimes occur within the dynamical regime of a physical model. As a matter of fact, the FEM reaches its best accuracy for small deformations whereas the MPM mixed Eulerian-Lagrangian formulation becomes beneficial when large deformations occur. FEM-MPM coupling has, in fact, been studied only by very few authors, including the PIs, and the coupling of an FSI framework with an MPM approach is yet to be explored. The use of the material point methodology would avoid the mesh entanglement issues that plague many existing FSI methods. To design the desired coupling approach, preliminary work is needed. First, the coupling between an MPM solid body immersed in an FEM fluid will be addressed, using benchmark problems from the FSI literature. At the same time, the mechanical properties of a solid body discretized with the mixed FSI-MPM approach will be studied and the accuracy of the method will be investigated using the Taylor bar test in which a cylinder impacts a rigid wall. Then, the knowledge gained from the preparatory work will be used to realize an FSI-MPM coupling methodology for biological valves, with the valve leaflets modeled with the MPM and the blood vessel and blood flow described in an FEM-FSI framework. Appropriate solvers and preconditioners will also be selected and studied because the discretized nonlinear and linear systems will likely be large and highly coupled. Lastly, the FSI-MPM coupling approach will also be applied for the simulations of stented arteries, with the stent described using the MPM. In this way, complex meshing procedure for the stent can be avoided, while capturing its dynamical behavior. The computational techniques developed within the proposed research will be applicable and prove to be invaluable tools for a broad spectrum of applications such as human valve fluid and structural dynamics, aerospace and civil engineering problems, dam breaking, and airfoil design, to name a few. All our findings will be implemented in FEMuS, an open source library written in C++ language, freely downloadable online. Our effort will hopefully contribute to the standardization of novel computational techniques that are currently available only in research software. Nevertheless, researchers from all over the world can potentially access our findings and join us in this effort, with a substantial speed up in the standardization procedure.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

人体有机体中与心脏瓣膜相关的问题是心脏骤停和心力衰竭的原因，这可能对人的健康造成毁灭性后果，甚至导致死亡。虽然不一定致命，但与腿部静脉瓣膜相关的病变可能会给受影响的人带来严重的痛苦，并对他们的生活产生负面影响，并可能出现严重的并发症。对于瓣膜相关疾病的治疗，当今最常见的做法是用假体装置更换故障瓣膜。不幸的是，人工瓣膜存在长期耐用性和植入后并发症的问题。鉴于改进现有人工瓣膜的设计和选择的必要性，计算方法正在成为一种有价值的工具。从数学和计算的角度来看，人体瓣膜内血流的性质使建模问题变得相当具有挑战性，因为多种物理现象相互作用。具体来说，主要的挑战是瓣膜小叶经历的大的结构位移，同时保持对流体-固体界面处的流体动力的准确描述。该项目的重点是开发新的流体-结构相互作用方法，特别关注大变形的情况。该项目提供的重要见解将使未来的阀门设计优化成为可能，同时避免昂贵的经验设计迭代。除了对社会具有明显的潜在影响外，拟议的项目还将对科学和工程领域的许多其他应用有用，并且还会对初级研究人员在重要的、令人兴奋的数学领域的培训、教育和职业产生有益的影响。具有计算和社会影响力的研究领域。该项目将在三年项目中每年支持 2 名研究生。该项目是关于将有限元方法 (FEM) 与质点方法 (MPM) 耦合的新型计算技术的开发、分析和实施流固耦合 (FSI) 问题。使用不同的离散化技术来研究多尺度和多物理问题是计算模拟的强大工具。例如，将一维模型与多维模型结合以降低计算成本，或者将有限元法与有限体积方法结合以利用这两种方法的算法和数学特征的优势。出于同样的想法，如果物理模型的动态范围内出现不同的变形范围，那么 FEM 与 MPM 的耦合代表了一个有前途的组合。事实上，FEM 对于小变形可以达到最佳精度，而 MPM 混合欧拉-拉格朗日公式在发生大变形时会变得有利。事实上，只有极少数作者（包括 PI）研究了 FEM-MPM 耦合，并且 FSI 框架与 MPM 方法的耦合还有待探索。 使用质点方法可以避免困扰许多现有 FSI 方法的网格缠结问题。为了设计所需的耦合方法，需要进行前期工作。首先，将使用 FSI 文献中的基准问题来解决浸入 FEM 流体中的 MPM 实体之间的耦合。同时，将研究采用混合 FSI-MPM 方法离散化的实体的力学性能，并使用圆柱体撞击刚性壁的泰勒杆试验来研究该方法的准确性。然后，从准备工作中获得的知识将用于实现生物瓣膜的 FSI-MPM 耦合方法，其中瓣膜小叶采用 MPM 建模，并在 FEM-FSI 框架中描述血管和血流。还将选择和研究适当的求解器和预处理器，因为离散非线性和线性系统可能很大且高度耦合。最后，FSI-MPM 耦合方法也将应用于支架动脉的模拟，并使用 MPM 描述支架。这样，可以避免支架复杂的网格划分过程，同时捕获其动态行为。 拟议研究中开发的计算技术将适用并被证明是广泛应用的宝贵工具，例如人体瓣膜流体和结构动力学、航空航天和土木工程问题、大坝破坏和翼型设计等。我们所有的发现都将在 FEMuS 中实现，FEMuS 是一个用 C++ 语言编写的开源库，可在线免费下载。我们的努力有望有助于目前仅在研究软件中可用的新颖计算技术的标准化。尽管如此，来自世界各地的研究人员都有可能获得我们的研究结果并加入我们的努力，从而大大加快标准化进程。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值进行评估，被认为值得支持以及更广泛的影响审查标准。