A multilevel decoupling method for the Navier–Stokes/Darcy model

摘要

This paper considers a multilevel decoupling method for the coupled Navier–Stokes/Darcy model describing a free flowing fluid over a porous medium. The method utilizes a sequence of meshes on which a low dimensional fully coupled nonlinear problem is solved only on a very coarse initial mesh. On subsequent finer meshes, the approximate solution in each flow region is obtained by solving a linear decoupled problem and performing a correction step. The correction step in each domain is achieved by solving a linear system that differs from the original decoupled system only in the right hand side. We prove optimal error estimates and demonstrate that for a sequence of meshes with spacing hj=hj−12, the decoupling method is computationally efficient and achieves the same order of approximation as the fully coupled method.