This Project Grant from the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049) provides $210,272 to Penn State University for collaborative research on adaptive mixed-dimensional modeling and simulation of porous media from August 1, 2022 to July 31, 2025. The research aims to develop stable numerical methods for simulating flow in fractured porous media based on mixed-dimensional modeling approaches. Key products include advanced discretization schemes coupling stabilized linear elasticity and Darcy flow methods; adaptive approximations in the mixed-dimensional framework with solid theoretical foundations; and robust linear solvers for the discrete systems incorporating preconditioners and multigrid methods justified theoretically and numerically. Main applications are linear poromechanics in fractured porous media, with potential generalization to nonlinear formulations. Results will be implemented in an open-source software package to benefit the scientific community.
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