Collaborative Research: Physics-Preserving Adaptive Finite Element Methods for Thermo-Poroelasticity

合作研究：热多孔弹性的物理保持自适应有限元方法

• 批准号: 2208402
• 负责人: Sanghyun Lee
• 金额: $ 24.02万
• 依托单位: Florida State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-07-01 至 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2208402&HistoricalAwards=false
• 关键词: Collaborative; Research; Physics; Preserving; Adaptive

Geothermal energy is one of the most promising renewable energy sources and has proven to be reliable, clean, and safe. When designing enhanced geothermal systems (EGS), it is necessary to understand the multiscale, multiphysics, thermal-hydraulic-mechanical (THM) processes that impact the EGS dynamics and productivity. This project aims to gain a fundamental understanding of key mechanisms controlling the dynamics in EGS (solid displacement, fluid flow, and heat transfer) and sustainability of EGS reservoirs through numerical simulations. A novel numerical simulation framework to be built through this project will allow for designing, managing, and optimizing energy production from EGS. The THM processes in EGS can be described by Biot’s thermo-poroelasticity model, a coupled system of nonlinear partial differential equations. Any desirable numerical methods for THM systems should preserve the underlying physical laws, such as mass and energy conservation, and present no numerical instabilities for a wide range of physical and simulation parameters. This project seeks to develop a unified numerical modeling framework based on adaptive enriched Galerkin (EG) methods to provide robust and physics-preserving numerical methods whose numerical analysis is feasible. The proposed EG schemes are mass conservative and free of numerical instabilities commonly present in poroelasticity and coupled flow-transport problems. The mass conservation property, stability, and convergence behaviors of the proposed methods will be studied mathematically and confirmed numerically. Moreover, residual-based a posteriori error estimators will be derived and utilized for designing dynamic mesh adaptivity techniques. The developed EG algorithms will be implemented within finite element software packages to verify the theoretical results and validate the new numerical model's capabilities to capture the EGS dynamics. The performance of the new EG methods will be compared with that of state-of-the-art numerical methods.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.

地热能是最有前途的可再生能源之一，并已被证明是可靠、清洁和安全的。在设计增强型地热系统 (EGS) 时，有必要了解多尺度、多物理、热力-水力-机械 (THM)。该项目旨在通过数值模拟对控制 EGS 动力学（固体置换、流体流动和传热）和 EGS 储层可持续性的关键机制有基本的了解。通过该项目构建的模拟框架将允许设计、管理和优化 EGS 中的 THM 过程，可以通过 Biot 的热孔隙弹性模型（非线性偏微分方程的耦合系统）来描述任何所需的数值方法。 THM 系统应保留基本的物理定律，例如质量和能量守恒，并且对于各种物理和模拟参数不存在数值不稳定性。该项目旨在开发一个基于自适应丰富伽辽金的统一数值建模框架。 (EG) 方法提供稳健且物理保持的数值方法，其数值分析是可行的，并且没有孔隙弹性和耦合流动传输问题中常见的数值不稳定性。此外，将导出基于残差的后验误差估计器，并将其用于设计动态网格自适应技术，并将在有限元软件包中实现。验证理论结果并验证新的数值模型捕获 EGS 动力学的能力。新的 EG 方法的性能将与最先进的数值方法进行比较。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优点和更广泛的影响审查标准进行评估来支持。

项目成果

Locking-Free and Locally-Conservative Enriched Galerkin Method for Poroelasticity

用于孔隙弹性的无锁定且局部保守的丰富伽辽金方法

• DOI: 10.1007/s10915-022-02079-0
• 发表时间: 2023
• 期刊: Journal of Scientific Computing
• 影响因子: 2.5
• 作者: Lee, Sanghyun;Yi, Son-Young
• 通讯作者: Yi, Son-Young