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:
  • 金额:
    $ 17.49万
  • 依托单位:
  • 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

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。

项目成果

期刊论文数量(14)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Analyzing the Effects of Multi-Layered Porous Intraluminal Thrombus on Oxygen Flow in Abdominal Aortic Aneurysms
多层多孔腔内血栓对腹主动脉瘤血氧流量的影响分析
  • DOI:
    10.3390/oxygen2040034
  • 发表时间:
    2022
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Throop, Alexis;Badr, Durwash;Durka, Michael;Bukač, Martina;Zakerzadeh, Rana
  • 通讯作者:
    Zakerzadeh, Rana
Refactorization of Cauchy’s Method: A Second-Order Partitioned Method for Fluid–Thick Structure Interaction Problems
柯西方法的重构:流体与厚结构相互作用问题的二阶划分方法
  • DOI:
    10.1007/s00021-021-00593-z
  • 发表时间:
    2021
  • 期刊:
  • 影响因子:
    1.3
  • 作者:
    Bukač, Martina;Seboldt, Anyastassia;Trenchea, Catalin
  • 通讯作者:
    Trenchea, Catalin
A Next-Generation Mathematical Model for Drug-Eluting Stents
下一代药物洗脱支架数学模型
  • DOI:
    10.1137/20m1365144
  • 发表时间:
    2021
  • 期刊:
  • 影响因子:
    1.9
  • 作者:
    Čanić, Sunčica;Wang, Yifan;Bukač, Martina
  • 通讯作者:
    Bukač, Martina
Prediction of wall stress and oxygen flow in patient-specific abdominal aortic aneurysms: the role of intraluminal thrombus
患者特异性腹主动脉瘤壁应力和氧流量的预测:腔内血栓的作用
A non‐iterative domain decomposition method for the interaction between a fluid and a thick structure
流体与厚结构相互作用的非迭代域分解方法
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Martina Bukac其他文献

Martina Bukac的其他文献

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{{ truncateString('Martina Bukac', 18)}}的其他基金

Collaborative Research: Time Accurate Fluid-Structure Interactions
合作研究:时间精确的流固耦合
  • 批准号:
    2208219
  • 财政年份:
    2022
  • 资助金额:
    $ 17.49万
  • 项目类别:
    Standard Grant
The Diffuse Interface Method and Applications to Coupled Systems in Fluid Dynamics
扩散界面方法及其在流体动力学耦合系统中的应用
  • 批准号:
    2205695
  • 财政年份:
    2022
  • 资助金额:
    $ 17.49万
  • 项目类别:
    Standard Grant
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
  • 批准号:
    1619993
  • 财政年份:
    2016
  • 资助金额:
    $ 17.49万
  • 项目类别:
    Continuing Grant

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Computational Methods for Analyzing Toponome Data
  • 批准号:
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