发表机构
Beijing Normal-Hong Kong Baptist University; Leibniz University Hannover; East China Normal University; Wuhan University（北京师范大学-香港浸会大学联合国际学院; 汉诺威莱布尼茨大学; 华东师范大学; 武汉大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出一种无条件稳定的二阶Robin分区方法，用于求解流体-多孔弹性结构相互作用问题，通过引入辅助界面变量实现子问题独立求解，并验证了收敛性与适用性。
AI 中文摘要
我们研究了一个非定常流体-多孔弹性结构相互作用（FPSI）问题，其中自由流体区域由不可压缩Stokes方程控制，多孔弹性区域由完全动态Biot系统控制。原始的物理耦合条件被等价地重新表述为Robin型界面条件，并引入一个辅助界面变量作为两个子系统共享的公共Robin数据。这种重新表述将耦合的FPSI问题分解为分别定义在各自子域上的流体和多孔弹性子问题。该问题在空间上采用有限元方法（FEM）离散，而在时间离散上采用向后Euler格式和结合二阶界面外推的BDF2格式。通过利用所得的离散动态关系，我们推导出辅助界面变量的更新公式，并获得完全离散的一阶和二阶Robin分区格式，其中两个子问题在每个时间步独立求解。两种格式的无条件稳定性被严格建立。数值实验验证了所提出格式的时间收敛阶，并研究了Robin参数的影响。一个经典的压力波基准验证了所提出方法的准确性，而补充的非线性移动域模拟则展示了它们在更复杂的FPSI配置中的适用性。
英文摘要
We study an unsteady fluid-poroelastic structure interaction (FPSI) problem, in which the free fluid region is governed by the incompressible Stokes equations and the poroelastic region by the fully dynamic Biot system. The original physical coupling conditions are equivalently reformulated as Robin-type interface conditions and an auxiliary interface variable is introduced as common Robin data shared by the two subsystems. This reformulation decomposes the coupled FPSI problem into fluid and poroelastic subproblems posed on their respective subdomains. The problem is discretized in space by the finite element method (FEM), while the backward Euler scheme and the BDF2 scheme combined with the second-order interface extrapolation are employed for the temporal discretization. By exploiting the resulting discrete dynamic relations, we derive an update formula for the auxiliary interface variable and obtain fully discrete first- and second-order Robin partitioned schemes in which the two subproblems are solved independently at each time step. The unconditional stability of both schemes is rigorously established. Numerical experiments verify the temporal convergence orders of the proposed schemes and investigate the influence of the Robin parameter. A classical pressure-wave benchmark verifies the accuracy of the proposed methods, while supplementary nonlinear moving-domain simulations illustrate their applicability to more complex FPSI configurations.
