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UBC Theses and Dissertations

Incompressible viscous flow in tubes with occlusions Huang, Huaxiong


Viscous, incompressible flow in tubes with partial occlusion is investigated using numerical and experimental procedures. The study is related to the problem of atherosclerosis, one of the most common diseases of the circulatory system. One of the computational difficulties in solving the incompressible Navier-Stokes equations is the lack of pressure or vorticity boundary conditions. A finite difference approach, referred to as the interior constraint (IC) method, is proposed to resolve this difficulty. As a general numerical method, it is formulated for both the stream function-vorticity and primitive (physical) variable formulations. The procedure is explained using onedimensional model with extensive numerical tests presented for two-dimensional cases including flow in a driven cavity, and flow over a backward facing step. Results are obtained with second-order accuracy. Next, the IC method is applied to flow in a tube with an occlusion, which is used as the model for blood flow in stenosed arteries in the study of the pathology of atherosclerosis. Numerical results are obtained for both steady and pulsatile flows. Results are compared with those of S I M P L E , one of the commercially available numerical algorithms. The pulsatile flow study revealed several interesting new features. It suggests that the high shear stress is not likely to initiate atherosclerosis lesions. The recirculation region, which is a prominent feature of the unsteady flow, is more likely to cause the initiation and development of the disease. Experimental measurements for steady flow complement the numerical study and show qualitative agreement.

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