An Iteratively Decoupled Algorithm for Multiple-Network Poroelastic Model with Applications in Brain Edema Simulations

In this work, we present an iteratively decoupled algorithm for solving the quasi-static multiple-network poroelastic model. Our approach employs a total-pressure-based formulation with solid displacement, total pressure, and network pressures as primary unknowns. This reformulation decomposes the original problem into a generalized Stokes problem and a parabolic problem, offering key advantages such as reduced elastic locking effects and simplified discretization. The algorithm guarantees unconditional convergence to the solution of the fully coupled system. Numerical experiments demonstrate the accuracy, efficiency, and robustness of the method with respect to physical parameters and discretization. We further apply the algorithm to simulate the brain edema process, showcasing its practical utility in biomechanical modeling.