Iterative methods for solving the Multiple Network Poroelastic Theory (MPET) model, 2022
Katja Xu Haukebø Phillips
Advisors: Kundan Kumar, Florin A. Radu
Short description of the project:
In this thesis, we study two iterative schemes for solving coupled flow and mechanics in deformable porous media. We consider Biot’s model and its extension to a Multiple Network Poroelastic Theory (MPET) model. Solutions of both models are approximated using the fixed-stress and the undrained splitting methods. These splitting methods divide the equations into two sub-problems: one for the mechanics and one for the flow. In the fixed-stress split, the equation modeling flow is solved first followed by the mechanics equation. The undrained split solves the sub-problems in the opposite order. For the MPET model, we prove that both schemes are contractions which implies the convergence of the approximated solutions. In other words, the splitting methods result in the same solutions as the monolithic scheme. Additionally, the proofs provide estimated convergence rates.