We study a decoupling iterative algorithm based on domain decomposition for the time-dependent nonlinear Stokes-Darcy model, in which different time steps can be used in the flow region and in the porous medium. The coupled system is formulated as a space-time interface problem based on the interface condition for mass conservation. The nonlinear interface problem is then solved by a nested iteration approach which involves, at each Newton iteration, the solution of a linearized interface problem and, at each Krylov iteration, parallel solution of time-dependent linearized Stokes and Darcy problems. Consequently, local discretizations in time (and in space) can be used to efficiently handle multiphysics systems of coupled equations evolving at different temporal scales. Numerical results with nonconforming time grids are presented to illustrate the performance of the proposed method.

中文翻译：

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耦合非线性 Stokes 和 Darcy 流的全局时域分解方法

我们研究了一种基于域分解的解耦迭代算法，用于瞬态非线性 Stokes-Darcy 模型，其中可以在流动区域和多孔介质中使用不同的时间步长。基于质量守恒的界面条件，耦合系统被表述为时空界面问题。然后通过嵌套迭代方法解决非线性界面问题，该方法涉及在每次牛顿迭代时求解线性化界面问题，以及在每次 Krylov 迭代时求解与时间相关的线性化斯托克斯和达西问题。因此，时间（和空间）局部离散化可用于有效处理在不同时间尺度上演化的耦合方程的多物理场系统。