模擬血液在血管裡的行為有助於醫療人員或研究學者對血管疾病掌握更多資訊，並降低手術時的風險。在這篇論文中，我們使用Power-law, Bingham, Carreau-Yasuda 模型來模擬非牛頓流體在二維的幾何圖形Backward-facing step、Four-to-One Contraction、Rotational eccentric annulus flow，與三維的幾何圖形A long straight artery、An end-to-side graft，以及針對個別病患所造出多分支的血管上流體的行為。在離散化方面，對空間上的離散是使用stabilized finite element method，而時間上的離散則是使用implicit backward Euler finite difference method，在每個time step 是用Newton-Krylov-Schwarz algorithm 來解這樣一個非線性系統。而為了幫助我們模擬更複雜的幾何形狀與加快其計算的時間，採用 Two-level methods。最後，我們還計算的壁上的剪應力，以便於醫學上的應用。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.
