In this paper we consider a fluid-fluid system coupled with a friction-type interface condition which is described by a jump of the velocities along the tangential interface. Based on domain decomposition, we propose a Schwarz type iterative method to decouple the different physical process in each subdomain occupied by a single fluid, which allows solving in each subdomain only the physical process described by a Stokes problem. Using energy estimate, we prove that the algorithm converges for any traction coefficient. A more detailed analysis based on Fourier analysis shows that the convergence rate depends on both the fluids' properties, the traction coefficient and the time stepsize, but is independent of the spatial mesh. We finally use numerical examples to illustrate the theoretical results.

在本文中，我们考虑与摩擦类型的界面条件耦合的流体系统，该条件通过沿切线界面的速度跳跃来描述。基于域分解，我们提出了一种Schwarz型迭代方法，以解耦由一种流体占据的每个子域中的不同物理过程，从而允许仅在每个子域中解决斯托克斯问题描述的物理过程。使用能量估计，我们证明了该算法在任何牵引系数下都收敛。基于傅立叶分析的更详细的分析表明，收敛速度取决于流体的性质，牵引系数和时间步长，但与空间网格无关。最后，我们使用数值示例来说明理论结果。