We develop and analyze a splitting method for fluid-poroelastic structure interaction. The fluid is described using the Stokes equations and the poroelastic structure is described using the Biot equations. The transmission conditions on the interface are mass conservation, balance of stresses, and the Beavers-Joseph-Saffman condition. The splitting method involves single and decoupled Stokes and Biot solves at each time step. The subdomain problems use Robin boundary conditions on the interface, which are obtained from the transmission conditions. The Robin data is represented by an auxiliary interface variable. We prove that the method is unconditionally stable and establish that the time discretization error is $\mathcal{O}(\sqrt{T}\Delta t)$, where $T$ is the final time and $\Delta t$ is the time step. We further study the iterative version of the algorithm, which involves an iteration between the Stokes and Biot sub-problems at each time step. We prove that the iteration converges to a monolithic scheme with a Robin Lagrange multiplier used to impose the continuity of the velocity. Numerical experiments are presented to illustrate the theoretical results.

翻译：我们提出并分析了一种用于流体-多孔弹性结构相互作用的分裂方法。流体采用Stokes方程描述，多孔弹性结构采用Biot方程描述。界面上的传输条件包括质量守恒、应力平衡以及Beavers-Joseph-Saffman条件。该分裂方法在每个时间步仅需进行解耦的Stokes和Biot单次求解。各子域问题在界面上采用Robin边界条件，这些条件由传输条件推导得出。Robin数据通过一个辅助界面变量表示。我们证明了该方法无条件稳定，并建立了时间离散误差为$\mathcal{O}(\sqrt{T}\Delta t)$的结论，其中$T$为最终时间，$\Delta t$为时间步长。我们进一步研究了该算法的迭代版本，该版本在每个时间步需要在Stokes和Biot子问题之间进行迭代。我们证明了该迭代收敛于一个整体格式，其中使用Robin拉格朗日乘子来施加速度连续性。数值实验展示了理论结果。