Developing Efficient and Robust Computational Tools for Subdiffusive Transport in Poroelastic Media

多孔介质中的转运在现实世界中广泛存在，例如CO2的固存和将治疗剂输送到肿瘤部位。本项目旨在为此类多尺度多物理过程开发鲁棒高效的数值模拟工具箱。这将增强我们对这些复杂现象的理解，从而对更好地利用自然资源和治疗疾病产生进一步的影响。该项目还将为学生提供实践培训机会。本项目的重点是设计、分析、实现和应用一系列新的数值方法来研究孔隙弹性介质中的亚扩散输运。将开发新的有限元方法来近似固体位移、流体压力和被输送物质的浓度。研究子问题解的稳定耦合条件。这些方法将应用于药物输送、组织工程、储层工程和其他类似的多物理过程的模拟。这些新颖的求解器将以c++和Matlab代码模块的形式实现，对科学计算社区开放。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Transport in porous media occurs in a broad range of real world problems, e.g., CO2 sequestration and delivery of therapy agents to tumor sites. This project aims at development of robust and efficient numerical simulation toolboxes for such multi-scale multi-physics processes. This will enhance our understanding of these complicated phenomena and accordingly have further impact on better use of natural resources and cures for diseases. The project will also provide hands-on training opportunities for students.The focus of this project is on design, analysis, implementation, and applications of a family of novel numerical methods for subdiffusive transport in poroelastic media. Novel finite element methods will be developed for approximating solid displacement, fluid pressure, and concentration of substance being transported. Conditions for stable coupling of sub-problem solvers will be investigated. These methods will be applied to simulations of drug delivery, tissue engineering, and reservoir engineering, and other similar multi-physics processes. These novel solvers will be implemented as C++ and Matlab code modules that are openly accessible to the scientific computing community.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.