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.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Leland Jameson
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University of Texas at San Antonio
San Antonio
United States
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