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

• 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

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.

孔隙弹性问题是由广泛的现实世界问题引起的，其中流体流过由于流体压力而变形的多孔培养基。 例如，对流增强的药物输送到肿瘤部位，膝盖弯曲的功能和二氧化碳隔离都涉及固体（位移）和液体（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，以增强我们在理解，预测和控制这些复杂的物理过程方面的能力。 该研究项目旨在开发一个针对毛弹性问题的新型准确，高效和鲁棒的数值方法。 该项目的重点是针对毛弹性问题的新型有限元方法的设计，分析，实施和应用。 基于位移压力的两体配方，将开发弱绿膜有限元方法，以近似于固体位移和流体压力。 将研究这些子问题解决器稳定耦合的条件。 新方法将应用于膝盖弯面条上的工程问题。这些新方法还将作为MATLAB和C ++代码模块（在Deal.ii平台上）实现，科学计算社区可以公开访问。该项目中开发的高效且可靠的计算工具可以应用于许多现实世界中的问题，这些问题涉及毛弹性，例如药物输送到肿瘤部位，食品加工，储层工程和组织工程。 这些将对更好地利用自然资源或疾病的治疗方法产生进一步的经济影响。 该项目中开发的方法可以应用于处理多个物理过程的大量科学计算任务。 该项目还将为研究生和本科生提供动手培训机会。该奖项反映了NSF的法定任务，并使用基金会的知识分子优点和更广泛的影响审查标准，被视为值得通过评估来提供支持。

项目成果

Poroelasticity Modules in DarcyLite

• DOI: 10.1007/978-3-030-77980-1_15
• 发表时间: 2021
• 作者: Jiangguo Liu;Zhuoran Wang

deal.II implementation of a weak Galerkin finite element solver for Darcy flow

deal.II 达西流弱伽辽金有限元求解器的实现

• DOI: 10.1007/978-3-030-22747-0_37
• 发表时间: 2019
• 期刊: International Conference on Computational Science
• 作者: Wang, Zhuoran;Harper, Graham;O'Leary, Patrick;Liu, Jiangguo;Tavener, Simon
• 通讯作者: Tavener, Simon

Analysis of a 2-field finite element solver for poroelasticity on quadrilateral meshes

• DOI: 10.1016/j.cam.2021.113539
• 发表时间: 2021-03
• 期刊: J. Comput. Appl. Math.
• 作者: Zhuoran Wang;S. Tavener;Jiangguo Liu

A lowest-order weak Galerkin finite element method for Stokes flow on polygonal meshes

• DOI: 10.1016/j.cam.2019.112479
• 发表时间: 2020-04
• 期刊: J. Comput. Appl. Math.
• 作者: Jiangguo Liu;Graham Harper;Nolisa S. Malluwawadu;S. Tavener

Penalty-Free Any-Order Weak Galerkin FEMs for Elliptic Problems on Quadrilateral Meshes

• DOI: 10.1007/s10915-020-01239-4
• 发表时间: 2020-06
• 期刊: Journal of Scientific Computing
• 影响因子: 2.5
• 作者: Jiangguo Liu;S. Tavener;Zhuoran Wang