  In this work, several multilevel decoupled algorithms are proposed for a
mixed Navier-Stokes/Darcy model. These algorithms are based on either
successively or parallelly solving two linear subdomain problems after solving
a coupled nonlinear coarse grid problem. Error estimates are given to
demonstrate the approximation accuracy of the algorithms. Experiments based on
both the first order and the second order discretizations are presented to show
the effectiveness of the decoupled algorithms.
