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：本文提出了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性的流体网络共同作用下弹性多孔介质内流体流动与变形的同步建模。我们采用基于总压力的公式体系，将固体位移、总压力及网络压力设为主要未知量。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形式，在避免弹性闭锁效应、简化离散过程等方面具有显著优势。值得注意的是，该算法具有无条件收敛性，能够收敛至基于总压力的耦合算法解。通过数值实验验证了方法的准确性与高效性，并系统研究了算法对物理参数及离散参数的鲁棒性。