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 brain flow dynamics, showcasing its practical utility in biomechanical modeling.

翻译：本文提出了一种用于求解准静态多网络多孔弹性模型的迭代解耦算法。该方法采用基于总压力的公式，以固体位移、总压力和网络压力为主要未知量。此重构将原始问题分解为一个广义Stokes问题和一个抛物型问题，具有减少弹性锁定效应和简化离散化等关键优势。该算法保证无条件收敛到全耦合系统的解。数值实验证明了该方法在物理参数和离散化方面的准确性、效率和鲁棒性。我们进一步应用该算法模拟脑血流动力学，展示了其在生物力学建模中的实际效用。