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Developing Efficient and Accessible Computational Tools for Poroelasticity Problems

开发有效且易于使用的计算工具来解决孔隙弹性问题

基本信息

批准号：
1819252
负责人：
Jiangguo Liu
金额：
$ 14.99万
依托单位：
Colorado State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-08-01 至 2022-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1819252&HistoricalAwards=false
关键词：
Developing Efficient Accessible Computational Tools

项目摘要

Poroelasticity problems arise from a broad range of real world problems, in which fluid flows through a porous medium that can deform due to the fluid pressure. For example, convection-enhanced drug delivery to tumor sites, functioning of knee meniscus, and CO2 sequestration all involve this type of interaction between solid (displacement) and fluid (pressure). Mathematical modeling and computer simulations will provide valuable tools to enhance our ability in understanding, predicting, and controlling these complicated physical processes. This research project aims at developing a family of novel accurate, efficient, and robust numerical methods for poroelasticity problems. The focus of this project is on design, analysis, implementation, and applications of a family of novel finite element methods for poroelasticity problems. Based on the displacement-pressure two-field formulation, weak Galerkin finite element methods will be developed for approximating both solid displacement and fluid pressure. Conditions for stable coupling of these sub-problem solvers will be investigated. The new methods will be applied to an engineering problem on knee meniscus. These new methods will also be implemented as Matlab and C++ code modules (on deal.II platform) that are openly accessible to the scientific computing community. The efficient and robust computational tools developed in this project can be applied to many real world problems that involve poroelasticity such as drug delivery to tumor sites, food processing, reservoir engineering, and tissue engineering. These will have further economic impact on better use of natural resources or cures for diseases. The methodology developed in this project can be applied to a large class of scientific computing tasks that deal with multiple physical processes. This project will also provide hands-on training opportunities for both graduate and undergraduate students.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.

多孔弹性问题源于广泛的真实的世界问题，其中流体流过多孔介质，该多孔介质可以由于流体压力而变形。例如，对流增强的药物输送到肿瘤部位，膝关节半月板的功能和CO2隔离都涉及固体（位移）和流体（压力）之间的这种相互作用。数学建模和计算机模拟将提供有价值的工具，以提高我们理解，预测和控制这些复杂的物理过程的能力。本研究计划旨在发展一系列精确、有效且稳健的数值方法来求解孔隙弹性问题。这个项目的重点是设计，分析，实施和应用的一个家庭的新的有限元方法的孔隙弹性问题。基于位移-压力双场公式，弱伽辽金有限元方法将被开发用于同时近似固体位移和流体压力。这些子问题求解器的稳定耦合的条件将被调查。新方法将应用于膝关节半月板的工程问题。这些新方法也将被实现为Matlab和C++代码模块（在deal.II平台上），科学计算社区可以公开访问。在这个项目中开发的高效和强大的计算工具可以应用于许多真实的世界的问题，涉及多孔弹性，如药物输送到肿瘤部位，食品加工，水库工程和组织工程。这些将对更好地利用自然资源或治疗疾病产生进一步的经济影响。在这个项目中开发的方法可以应用于一个大类的科学计算任务，处理多个物理过程。该奖项反映了NSF的法定使命，并被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。