Efficient Two-Scale Modeling of Porous Media Using NumericalModel Reduction with Fully Computable Error Bounds

Book chapter, 2022

The microscale problem arizing from computational homogenization of porous media problems is solved by adopting the concept of Numerical Model Reduction. Thereby, the displacement and pore pressure are the unknown fields. A suitable reduced basis is constructed for the pore pressure approximation using Proper Orthogonal Decomposition (POD), whereby it is possible to compute the appropriate basis for the displacement field in the spirit of Nonlinear Transformation Field Analysis (NTFA). Inexpensive fully computable error bounds are obtainable, and the performance of the error estimates is illustrated in this paper.