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Numerical Methods for Fluid-Structure Interaction Problems with Large Displacements

大位移流固耦合问题的数值方法

基本信息

批准号：
1912908
负责人：
Martina Bukac
金额：
$ 17.49万
依托单位：
University of Notre Dame
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：
2019-07-01 至 2023-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1912908&HistoricalAwards=false
关键词：
Numerical Methods Fluid Structure Interaction

项目摘要

Fluid-structure interaction (FSI) problems arise in many applications, such as geomechanics, aerodynamics, and blood flow dynamics (hemodynamics). In hemodynamic applications, mathematical models must capture the non-linear coupling between blood and the elastic structural dynamics of vessel walls, soft tissue, or cardiac muscles. These structural dynamics create 'moving domain' FSI problems that are challenging to numerically solve and analyze. Fast and efficient FSI solvers are valuable for bioengineering applications since the combination of numerical algorithms with experimental and clinical measurements provides an innovative approach to understanding the basic function of many components of the cardiovascular system and their mutual interaction. The PI will develop a class of numerical methods and underlying theory for non-linear FSI problems with large displacements. The research aims at making fundamental contributions to development of algorithms and numerical analysis of such problems. The proposed research will push the boundaries of our ability to model FSI problems in hemodynamics, including fracture propagation in soft tissue. The goal of this project is the development of a class of numerical methods and underlying theory for solving non-linear FSI problems with large displacements. Proposed methods will be specially designed for problems arising from hemodynamics. We will consider elastic and poroelastic structures where solid mechanics are described by hyperelastic constitutive models. Both partitioned and monolithic methods will be developed. Special attention will be given to numerical analysis of the proposed methods. The research goals will be achieved through the following specific aims: Aim 1: Development of noniterative, domain decomposition methods for FSI problems with porohyperelastic structures using secondorder Backward Differentiation Formula time discretization and the Crank-Nicolson Leapfrog time discretization; Aim 2: Development of non-iterative, domain decomposition methods for FSI problems with thick, hyperelastic structures; and Aim 3: Development and analysis of a monolithic, phase-field approach for FSI problems with hyperelastic structures.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.

流固耦合(FSI)问题广泛存在于地质力学、空气动力学、血液动力学等诸多领域。在血液动力学应用中，数学模型必须捕捉血液和血管壁、软组织或心肌的弹性结构动力学之间的非线性耦合。这些结构动力学产生了“移动域”的FSI问题，这些问题很难用数值方法解决和分析。快速和高效的FSI解算器对于生物工程应用是有价值的，因为数值算法与实验和临床测量的结合提供了一种创新的方法来了解心血管系统许多组件的基本功能及其相互作用。PI将为具有大位移的非线性FSI问题发展一类数值方法和基本理论。本研究旨在为算法的发展和此类问题的数值分析做出基础性贡献。这项拟议的研究将推动我们在血液动力学中模拟FSI问题的能力的界限，包括软组织中的骨折扩展。这个项目的目标是发展一类数值方法和基本理论来解决具有大位移的非线性FSI问题。建议的方法将专门针对血液动力学问题而设计。我们将考虑弹性和孔弹性结构，其中固体力学由超弹性本构模型描述。将开发分区方法和整体方法。我们将特别注意对所提出的方法进行数值分析。研究目标将通过以下具体目标来实现：目标1：利用二阶向后微分公式时间离散化和Crank-Nicolson LeapFrog时间离散化，为多孔超弹性结构的FSI问题发展非迭代的区域分解方法；目标2：为厚的、超弹性结构的FSI问题发展非迭代的区域分解方法；以及目标3：为具有超弹性结构的FSI问题发展和分析整体的相场方法。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。