  In this paper, we develop the numerical theory of decoupled modified
characteristic finite element method with different subdomain time steps for
the mixed stabilized formulation of nonstationary dual-porosity-Navier-Stokes
model. Based on partitioned time-stepping methods, the system is decoupled,
which means that the Navier-Stokes equations and two different Darcy equations
are solved independently at each time step of subdomain. In particular, the
Navier-Stokes equations are solved by the modified characteristic finite
element method, which overcome the computational difficulties caused by the
nonlinear term. In order to increase the efficiency, different time steps are
used to different subdomains. The stability of this method is proved. In
addition, we verify the optimal $L^2$-norm error convergence order of the
solutions by mathematical induction, whose proof implies the uniform
$L^{\infty}$-boundedness of the fully discrete velocity solution. Finally, some
numerical tests are presented to show efficiency of the proposed method.
