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Development of Numerical Tools for Hemodynamics and Fluid Structure Interactions

Ma, Jieyan

[Thesis]. Manchester, UK: The University of Manchester; 2014.

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Abstract

The aim of this study is to create CFD tools and models capable of simulating pulsatile blood flow in abdominal aortic aneurysm (AAA) and stent graft. It helps to increase the current physiological understanding of rupture risk of AAA and stent graft fixation or migration. Firstly, in order to build a general solver for the AAA modeling with reasonable accuracy, a third/fourth order modified OCI scheme is originally developed for general numerical simulation. The modified OCI scheme has a wider cell Reynolds number limitation. This high order scheme performs well with general rectangular mesh for incompressible fluid. Second, a velocity based finite volume method is originally developed to calculate the stress field for solid in order to capture the transient changes of the blood vessel since the artery is a rubber like material. All one, two and three dimensional classical cases for solid are tested and good results are obtained. The velocity based finite volume method show good potential to calculate the stress field for solid and easy to blend with the finite volume fluid solver. It has been recognized that fluid structure interaction (FSI) is very crucial in biomechanics. In this regard, the velocity based finite volume method is then further developed for FSI application. A well known one dimensional piston problem is studied to understand the feasibility of the fluid structure coupling. The numerical prediction matches the analytical solution very well. The velocity based method introduces less numerical damping compared with a stagger method and a monolithic method. Finally, the work focuses on practical pulsatile boundary conditions, non-Newtonian blood viscous properties and bifurcating geometry, and provides an overview of the hemodynamic within the AAA model. A modified Womersley inlet and imbalance pressure outlet boundary conditions are originally used in this study. The Womersley inlet boundary represents better approximation for pulsatile flow compared with the parabolic inlet condition. Numerical results are presented providing comparison between different boundary conditions using different viscous models in both 2D and 3D aneurysms. Good agreement between the numerical predictions and the experimental data is achieved for 2D case. 3D stent models with different bifurcation angles are also tested. The Womersley inlet boundary condition improves the existing inlet conditions significantly and it can reduce the Aneurysm neck computation domain. The influence of the non-Newtonian model to the wall shear stress (WSS) and strain-rate is also studied. The non-Newtonian model tends to produce higher WSS at both proximal and distal end of the aneurysm as compared with the Newtonian model (both 2D and 3D cases). The computed strain-rate distribution at the centre of the aneurysm is different between these two models. The influence of imbalance outlet pressure at the iliac arteries to the blood flow is originally investigated. The imbalance outlet pressure boundary conditions affect the computed wall shear stress significantly near the bifurcation point. All the pulsatile Womersley inlet, non-Newtonian viscosity properties and the imbalance pressure outlet need to be considered in blood flow simulation of AAA.