A decoupled modified characteristic finite element method is proposed for the time dependent Navier-Stokes/Biot problem.  In the numerical scheme, the implicit backward Euler scheme is used for the time discretization, whereas the coupling terms are treated explicitly.  At each time step, we only need to solve two decoupled problems, one is the Navier-Stokes equations solved by the modified characteristic finite element method, and the other is Biot equations. The stability and the error estimates are established for the proposed fully-discrete scheme. Numerical experiments are provided to illustrate the theory.

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