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

多孔介质中的输运发生在广泛的真实的世界问题中，例如，CO2封存并将治疗剂输送到肿瘤部位。该项目旨在为这种多尺度多物理过程开发强大而有效的数值模拟工具箱。这将加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。该项目的重点是设计，分析，实施和应用一系列新的数值方法在多孔弹性介质中的亚扩散输运。新的有限元方法将被开发用于近似固体位移，流体压力和被输送物质的浓度。将研究子问题求解器稳定耦合的条件。这些方法将被应用于药物输送、组织工程和储库工程以及其他类似的多物理过程的模拟。这些新颖的求解器将被实现为C++和Matlab代码模块，这些代码模块可供科学计算社区公开访问。该奖项反映了NSF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.