Collaborative Research: High-Fidelity Modeling of Poromechanics with Strong Discontinuities

具有强不连续性的多孔力学具有许多重要的应用，例如模拟自然静态和水力动态断裂中的流体流动，老化骨骼的断裂分析，痴呆和阿尔茨海默病中出现的多网络多孔弹性理论，以及航空航天飞机中陶瓷基复合材料加速降解的评估。这里的数学建模是具有挑战性的，因为它不仅涉及耦合的化学反应，扩散和变形，但也启动，传播和分支的散装基质中的裂纹以及流体流过裂纹。为了应对这些挑战，高保真数值方案和多物理场模型必须耦合，以准确和有效地模拟这些过程及其相互作用。该项目将使公众和决策者受益，包括能源生产商，医疗服务提供者，空气动力学家和水文地质学家。该项目的目标是研究以下连接流动，化学和力学的基本关系：动态不连续Galerkin离散的稳定性、先验和后验误差估计，介质变形和破坏的物理一致材料模型，高效、准确的材料求解技术，以及力学性能的标度特性。 这些知识将用于耦合多孔介质流动，反应性运输和高性能计算平台上有效运行的力学的局部保守有限元方法的设计。 该小组将调查：（1）在化学-力学耦合模型的设置中，发展对具有强不连续性的孔隙力学的基本理解;（2）使用高保真数值算法求解的流动、力学和反应迁移模型的制定和分析;（3）开发迭代耦合求解技术的误差估计;（四）使用目标数据集的公开数据验证和验证流体结构相互作用。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识产权进行评估来支持。优点和更广泛的影响审查标准。

Poromechanics with strong discontinuities has numerous important applications such as simulating fluid flow in natural static and hydraulic dynamic fractures, fracture analysis of aging bones, multiple-network poroelastic theory arising in dementia and Alzheimer's disease, and evaluation of accelerated degradation of ceramic matrix composites in aerospace shuttles. Here mathematical modeling is challenging because it involves not only coupled chemical reactions, diffusion, and deformation but also initiation, propagation, and branching of cracks in the bulk matrix as well as fluid flowing through cracks. To address these challenges, high fidelity numerical schemes and multiphysics models must be coupled in order to simulate these processes and their interactions accurately and efficiently. This project will benefit public and decision makers including energy producers, health providers, aerodynamicists, and hydrogeologists.The objective of this project is to study the following fundamental relationships linking flow, chemistry, and mechanics: stability, a priori, and a posteriori error estimation of dynamic discontinuous Galerkin discretizations, physically consistent material models for the deformation and failure of the media, efficient and accurate material solution techniques, and scaling characteristics of mechanical properties. This knowledge will be used in the design of locally conservative finite element methods coupling porous media flow, reactive transport, and mechanics that run efficiently on high-performance computing platforms. The team will investigate: (1) Development of fundamental understanding of poromechanics with strong discontinuities in the setting of chemo-mechanical coupled models; (2) Formulation and analyses of flow, mechanical, and reactive transport models solved using high-fidelity numerical algorithms; (3) Developing error estimates for iterative coupling solution techniques; (4) Verifying and validating fluid structure interactions using published data from target data sets.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.