Mathematical modelling of blood flow through arteries and investigation of some pathological cases in cardiovascular system using grad-div stabilization

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Tezin Türü: Yüksek Lisans

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Fen Bilimleri Enstitüsü, Türkiye

Tezin Onay Tarihi: 2019

Tezin Dili: İngilizce

Öğrenci: İSMAİL TAHİR KÖKTEN

Danışman: Songül Kaya Merdan

Özet:

In this thesis, we investigate the grad-div stabilization method and its feasibility on the cardiovascular system. Governing equations on blood flow is chosen to be Navier-Stokes and numerical solution is obtained by Galerkin finite element approximation. Grad-div stabilization is known as an effective residual based stabilization method and no study exists about its effect on the cardiovascular system. In this thesis, we present a grad-div stabilized fully discrete scheme with backward Euler time discretization, then present its stability and error analysis. To understand its effect on the cardiovascular system, we investigate some numerical cases such as stenosis, aneurysm and branching arteries by considering the changes in velocity, pressure and wall shear stress values. We also numerically investigate the pulsatile nature of blood flow and present some remarks on grad-div stabilization technique. With selection of a O(1) stabilization parameter, the grad-div stabilization method validate the physical expectations in all the experiments, and contribute observable improvement in eccentric stenosis and rate of stenosis problems. We conclude that the grad-div stabilization method is efficient for the cardiovascular system and promising for future studies.