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Development and analysis of high-order partitioned schemes for fluid-structure interaction problems

流固耦合问题高阶划分方案的开发和分析

基本信息

批准号：
1619993
负责人：
Martina Bukac
金额：
$ 18.79万
依托单位：
University of Notre Dame
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2016
资助国家：
美国
起止时间：
2016-06-15 至 2020-05-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1619993&HistoricalAwards=false
关键词：
Development analysis order partitioned schemes

项目摘要

Fluid-structure interaction (FSI) problems arise in many applications, such as aerodynamics, geomechanics and biomedical engineering. In hemodynamics, FSI models have been used to describe the interaction between blood and arterial walls. More precisely, numerical algorithms for fluid-structure interaction problems can provide predictions in many cardiovascular diseases, such as aneurysms or atherosclerosis. Since combining state-of-the-art algorithms with non-invasive clinical measurement tools provides an innovative approach to medical diagnosis and surgical decision making, there is an increasing demand for fast and efficient numerical schemes to solve FSI problems. The PI will develop and analyze a class of stable and robust high-order partitioned numerical methods for FSI problems. The development of stable and efficient algorithms for fluid-structure problems is crucial for performing patient specific diagnostic tests, and this work will make a major contribution in biomedical research.The goal of this research is a development and analysis of a class of higher-order partitioned numerical methods for interactions between an incompressible, viscous fluid and a thin, elastic structure. The discretization in space will be performed using the finite element method, and different partitioned methods will be proposed based on the time discretization. In particular, algorithms will be developed based on the kinematically coupled scheme (Project 1), the Strang operator splitting approach (Project 2) and the Crank-Nicolson and Leapfrog method (Project 3). Energy estimates and convergence rates will be derived for each proposed algorithm. A comparison of all the proposed methods based on their performance, stability and convergence properties will be made, allowing other researchers to identify optimal algorithms for specific choices of parameter values. The proposed algorithms, numerical analysis and simulation results will be published and made available to the community. In that way, they will serve as a set of reference data that can be used for model validation by other researchers.

流固耦合问题在空气动力学、地质力学和生物医学工程等领域有着广泛的应用。在血液动力学中，流固耦合模型已被用来描述血液和动脉壁之间的相互作用。更确切地说，流体-结构相互作用问题的数值算法可以提供许多心血管疾病的预测，如动脉瘤或动脉粥样硬化。由于将最先进的算法与非侵入性临床测量工具相结合，为医疗诊断和手术决策提供了一种创新方法，因此对快速有效的数值方案来解决FSI问题的需求越来越大。PI将开发和分析一类稳定和鲁棒的高阶分区数值方法用于FSI问题。流体结构问题的稳定和有效的算法的发展是至关重要的，为执行病人的具体诊断测试，这项工作将作出重大贡献，在生物医学research.The本研究的目标是一类高阶分区数值方法的发展和分析之间的相互作用不可压缩，粘性流体和薄，弹性结构。空间离散采用有限元法，时间离散采用不同的分区方法。特别是，将开发基于运动学耦合方案（项目1），斯特朗算子分裂方法（项目2）和Crank-Nicolson和蛙跳方法（项目3）的算法。能量估计和收敛速度将得出每个拟议的算法。所有提出的方法的性能，稳定性和收敛性能的基础上进行比较，允许其他研究人员确定最佳算法的参数值的具体选择。提出的算法，数值分析和模拟结果将公布，并提供给社会。通过这种方式，它们将作为一组参考数据，可用于其他研究人员的模型验证。