  In this paper, we construct and analyze new first- and second-order
implicit-explicit (IMEX) schemes for the unsteady Navier-Stokes-Darcy model to
describe the coupled free flow-porous media system, which is based on the
scalar auxiliary variable (SAV) approach in time and finite element method in
space. The constructed schemes are linear, only require solving a sequence of
linear differential equations with constant coefficients at each time step, and
can decouple the Navier-Stokes and Darcy systems. The unconditional stability
of both the first- and second-order IMEX schemes can be derived for the coupled
system equipped with the Lions interface condition, where the key point is that
we should construct a new trilinear form to balance the fully explicit
discretizations of the nonlinear terms in the complex system. We can also
establish rigorous error estimates for the velocity and hydraulic head of the
first-order scheme without any time step restriction. Numerical examples are
presented to validate the proposed schemes.
