Excellence in Research: Numerical Algorithms for Fluid Poroelastic Structure Interaction Models

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The research project aims at developing advanced numerical methods for the complex fluid poroelastic structure interaction (FPSI) models, which play a critical role in various applications. For example, they are widely used in biomechanic modeling of tissues, teeth, and bones. Other application areas include environmental sciences and reservoir engineering. The research team will propose, analyze, and implement effective and efficient numerical algorithms for some FPSI models. The project will involve postdoc researchers and some undergraduate students at a HBCU and therefore broaden the participation of underrepresented groups in research. The research and educational efforts are expected to help the participants to gain experience from such a challenging computational science topic.Numerical simulations of fluid poroelastic structure interaction problems are challenging because they are multi-domain, multi-scale, and multi-physics models, the subdomain models are of different types, discretization schemes that mimic physical laws are difficult to design, and the stability and accuracy are hard to preserve in partitioned numerical algorithms which decouple the computations of the coupled models. The objective of this project aims at developing efficient and effective numerical algorithms that can address the these difficulties. In particular, the investigator and the team members will consider decoupled preconditioning techniques based on a monolithic formulation, two-grid methods combined with the Robin-Neumann iteration, multi-rate time-stepping schemes which use different time step sizes in different subdomain models, domain decomposition methods, and multigrid methods that can accelerate the convergence of the numerical algorithms. The project has the potential of stimulating more novel decoupled algorithms for various coupled multi-domain and multi-physics models in different applications. It is expected that the algorithms and the corresponding analysis in this project will have a broad impact on several branches of applied mathematics such as numerical analysis and computational physics. The developed numerical algorithms will also provide powerful tools in biomechanic computation and reservoir engineering simulation.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.