Collaborative Research: Development of Reduced Order Models for Poroelasticity and Related Problems

合作研究：孔隙弹性及相关问题的降阶模型的开发

基本信息

批准号：
2110782
负责人：
Aycil Cesmelioglu
金额：
$ 19.83万
依托单位：
Oakland University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-09-01 至 2024-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2110782&HistoricalAwards=false
关键词：
Collaborative Research Development Reduced Order

项目摘要

Poroelasticity is a framework of continuum mechanics models for problems involving a porous elastic medium and a fluid flow. Poroelasticity problems have real-world applications such as hydrocarbon extraction in petroleum engineering, physiological processes such as the blood flow in the human body, groundwater contamination in environmental engineering, and modeling magma and mantle migration in geophysics. There is a real need to obtain high-resolution numerical solutions for the poroelasticity but these require large computational resources, even with theoretically optimal algorithms. This project will develop methods that can provide high accuracy solutions for large poroelasticity problems with feasible computational costs. Students will be involved and trained in interdisciplinary applications. Poroelasticity problems are parametric partial differential equations (PDEs) which are described by a set of coupled PDEs with various physical parameters. Developing reliable and efficient numerical methods for these problems involving complex forms of physical parameters is crucial to obtain high-resolution solutions in a relatively short time. The project will use the reduced basis method (RBM) approach which can provide fast algorithms for parametric partial differential equations of elliptic and parabolic types and has a solid mathematical framework to derive reduced order models with rigorous, certified error bounds. However, developing an RBM for a system of coupled PDEs is nontrivial because it must be devised to preserve the stability structure of the coupled system. The techniques and analysis developed in this project will advance the understanding of parametric poroelasticity and its related problems. The results of this project can also provide a general guideline in developing RBMs for other coupled parametric PDEs. Once developed, these algorithms can be employed for complex problems that are currently intractable with traditional numerical algorithms. These solutions will lead to advances in fields such as petroleum engineering, environmental engineering, and computational biomechanics with potential beneficial impacts on human life and health.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.

多孔弹性是涉及多孔弹性介质和流体流动问题的连续介质力学模型框架。孔隙弹性问题具有现实世界的应用，例如石油工程中的碳氢化合物提取、人体血液流动等生理过程、环境工程中的地下水污染以及地球物理学中的岩浆和地幔迁移建模。确实需要获得孔隙弹性的高分辨率数值解，但这需要大量的计算资源，即使使用理论上最优的算法也是如此。该项目将开发能够以可行的计算成本为大型孔隙弹性问题提供高精度解决方案的方法。学生将参与跨学科应用并接受培训。孔隙弹性问题是参数偏微分方程 (PDE)，由一组具有各种物理参数的耦合 PDE 来描述。针对这些涉及复杂物理参数形式的问题开发可靠且高效的数值方法对于在相对较短的时间内获得高分辨率解决方案至关重要。该项目将使用降基法（RBM）方法，该方法可以为椭圆和抛物型类型的参数偏微分方程提供快速算法，并具有坚实的数学框架来导出具有严格的、经过认证的误差范围的降阶模型。然而，为耦合偏微分方程系统开发 RBM 并非易事，因为必须设计它来保持耦合系统的稳定性结构。该项目开发的技术和分析将增进对参数孔隙弹性及其相关问题的理解。该项目的结果还可以为其他耦合参数偏微分方程的 RBM 开发提供一般指导。一旦开发出来，这些算法可以用于解决目前传统数值算法难以解决的复杂问题。这些解决方案将推动石油工程、环境工程和计算生物力学等领域的进步，对人类生命和健康产生潜在的有益影响。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。