In this work, we introduce an iterative decoupled algorithm designed for addressing the quasi-static multiple-network poroelasticity problem. This problem pertains to the simultaneous modeling of fluid flow and deformations within an elastic porous medium permeated by multiple fluid networks, each with distinct characteristics. Our approach focuses on the total-pressure-based formulation, which treats the solid displacement, total pressure, and network pressures as primary unknowns. This formulation transforms the original problem into a combination of the generalized Stokes problem and the parabolic problem, offering certain advantages such as mitigating elastic locking effects and streamlining the discretization process. Notably, the algorithm ensures unconditional convergence to the solution of the total-pressure-based coupled algorithm. To validate the accuracy and efficiency of our method, we present numerical experiments. The robustness of the algorithm with respect to the physical parameters and the discretization parameters is carefully investigated.

翻译：本研究提出一种针对准静态多网络孔隙弹性问题的迭代解耦算法。该问题涉及多个具有不同特征的流体网络在弹性多孔介质中同时进行流体流动与变形的建模。我们的方法基于总压力公式，将固体位移、总压力和网络压力作为主要未知量。该公式将原问题转化为广义斯托克斯问题与抛物型问题的组合，具有缓解弹性锁定效应、简化离散化过程等优势。值得注意的是，该算法能确保无条件收敛至基于总压力的耦合算法解。为验证方法的准确性与效率，我们开展了数值实验，并系统研究了算法对物理参数和离散化参数的鲁棒性。