||The simulation of the behavior of the blood in the arteries help medical personnel or researchers to acquire more information on vascular disease and reduce the risk of surgery. In this paper, we use the Power-law, Bingham, Carreau-Yasuda model to simulate non-Newtonian fluid in a two-dimensional geometry of Backward-facing step, Four-to-One Contraction, Rotational eccentric annulus flow， and three-dimensional geometry of A long Straight ARTERY, an end-to-side Graft, as well as for the individual patient create multiple branching vascular fluid behavior. In the discretization, where a stabilized finite element method is used for the spatial discretization, while an implicit backward Euler finite difference method for the temporal discretization. At each time step, the resulting system solved by the Newton-Krylov-Schwarz algorithm. In order to help us to simulate more complex geometry and speed up the calculation time, Two-level methods.Finally, we also calculated the wall of the shear stress, so that medical applications.|
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