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In this paper, we propose and analyze the parallel Robin-Robin domain decomposition method based on the modified characteristic finite element method for the time-dependent dual-porosity-Navier-Stokes model with the Beavers-Joseph interface condition. For the coupling terms, we treat them in an explicit manner which takes advantage of information obtained in previous time steps to construct a non-iteration domain decomposition method. By this means, two single dual-porosity equations and a single Navier-Stokes equation are needed to solve at each time. In particular, we solve the Navier-Stokes equation by the modified characteristic finite element method, which avoids the computational inefficiency caused by the nonlinear convection term. Furthermore, we prove the error convergence of solutions by mathematical induction, whose proof implies the uniform L ∞ -boundedness of the fully discrete velocity solution in conduit flow. Finally, some numerical examples are presented to show the effectiveness and efficiency of the proposed method. KeywordsTime-dependent dual-porosity-Navier-Stokes model • Beavers-Joseph interface condition • Domain decomposition methods • Modified characteristic finite element methods • Parallel algorithms

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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 ∞ -boundedness of the fully discrete velocity solution. Finally, some numerical tests are presented to show efficiency of the proposed method.