| In this work, the two-dimensional Navier-Stokes equations in the bifurcation region with dissipative boundary conditions are considered. A fully discrete implicit finite element approximation based on the material derivative is proposed.Reduced-basis techniques are employed to solve one-generation human tracheal bifurcation flow field simulation, in addition, electrical resistance in the law to solve the many generations of human tracheo-bronchial tree of the flow field simulation is used. From one to three generations, a specific simulation is made, the effectiveness of the proposed method in this paper is demonstrated by the numerical results.
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