A Global-in-time Domain Decomposition Method for the Coupled Nonlinear Stokes and Darcy Flows

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 flow region and porous medium. The coupled system is formulated as space-time interface problem condition mass conservation. then solved by nested iteration approach involves, at each Newton iteration, solution of linearized and, Krylov parallel Stokes Darcy problems. Consequently, local discretizations (and space) to efficiently handle multiphysics systems equations evolving temporal scales. Numerical results with nonconforming grids are presented illustrate performance proposed method.