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

Kökten, İsmail Tahir
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.


An integrated, dynamic model for cardiovascular and pulmonary systems
Yılmaz, Neval A; Eyüboğlu, Behçet Murat; Department of Electrical and Electronics Engineering (2006)
In this thesis an integrated, dynamic model for cardiovascular and respiratory systems has been developed. Models of cardiopulmonary system, airway mechanics and gas exchange that preexisted in literature have been reviewed, modified and combined. Combined model composes the systemic and pulmonary circulations, left/right ventricles, tissue/lung compartments, airway/lung mechanics and gas transportation. Airway resistance is partitioned into three parts (upper, middle, small airways). A collapsible airways ...
Gurbuz, Merve; Tezer, Münevver (2019-01-01)
In this study, the radial basis function (RBF) approximation is applied for solving the unsteady fluid flow and magnetohydrodynamic (MHD) convection flow problems with the use of explicit Euler time discretization and relaxation parameters to accelerate the convergence. The stability analysis is also carried out in terms of the spectral radius of related RBF discretized coefficient matrices. The optimal choices of the time increment, relaxation parameters and physical problem parameters are found for achiev...
Direct experimental visualization of the global Hamiltonian progression of two-dimensional Lagrangian flow topologies from integrable to chaotic state
Başkan Perçin, Özge; Metcalfe, G.; Clercx, H. J. H. (2015-10-01)
Countless theoretical/numerical studies on transport and mixing in two-dimensional (2D) unsteady flows lean on the assumption that Hamiltonian mechanisms govern the Lagrangian dynamics of passive tracers. However, experimental studies specifically investigating said mechanisms are rare. Moreover, they typically concern local behavior in specific states (usually far away from the integrable state) and generally expose this indirectly by dye visualization. Laboratory experiments explicitly addressing the glob...
Aydin, Umit; Serinağaoğlu Doğrusöz, Yeşim (2009-07-01)
Kalman filter approach provides a natural way to include the spatio-temporal prior information in cardiac electrical imaging. This study focuses on the performance of Kalman filter approach with geometric errors present in inverse Electrocardiography (ECG) problem. The geometric errors considered here are the wrong determination of the heart's size and location. In addition to Kalman filtering, we also compare the performances of Tikhonov regularization and Bayesian MAP estimation when geometric errors are ...
Numerical investigation of coupled heat and mass transfer inside the adsorbent bed of an adsorption cooling unit
Solmus, Ismail; Rees, D. Andrew S.; Yamali, Cemil; Baker, Derek Keıth; KAFTANOĞLU, BİLGİN (2012-05-01)
In this study, the influence of several design parameters on the transient distributions of temperature, pressure and amount adsorbed in the radial direction of a cylindrical adsorbent bed of an adsorption cooling unit using silica gel/water have been investigated numerically. For this purpose, a transient one-dimensional local thermal non-equilibrium model that accounts for both internal and external mass transfer resistances has been developed using the local volume averaging method. For the conditions in...
Citation Formats
İ. T. Kökten, “Mathematical modelling of blood flow through arteries and investigation of some pathological cases in cardiovascular system using Grad-div stabilization,” Thesis (M.S.) -- Graduate School of Applied Mathematics. Mathematics., Middle East Technical University, 2019.