Numerical simulation of Oldroyd-B fluid with application to hemodynamics

Oldroyd-B viscoelastic fluid is numerically simulated using the stabilized Galerkin least squares finite element method. The instabilities due to the connective nature of the Oldroyd-B model is treated using the discrete viscous elastic split stress method. The model is used to study the behavior of the flow of blood through an abdominal aortic segment. The results show that the viscoelastic nature of the blood should be considered specially at low shear rates.

[1]  R. Budwig,et al.  Steady flow in abdominal aortic aneurysm models. , 1993, Journal of biomechanical engineering.

[2]  E Shirani,et al.  Numerical simulation of blood pulsatile flow in a stenosed carotid artery using different rheological models. , 2011, Journal of biomechanics.

[3]  M. F. Tomé,et al.  A finite difference technique for simulating unsteady viscoelastic free surface flows , 2002 .

[4]  Richard J. Lozowy,et al.  Low wall shear stress predominates at sites of abdominal aortic aneurysm rupture. , 2015, Journal of vascular surgery.

[5]  K. Kent,et al.  Clinical practice. Abdominal aortic aneurysms. , 2014, The New England journal of medicine.

[6]  Alvaro Valencia,et al.  Numerical simulation of fluid–structure interaction in stenotic arteries considering two layer nonlinear anisotropic structural model ☆ , 2009 .

[7]  C. M. Scotti,et al.  Wall stress and flow dynamics in abdominal aortic aneurysms: finite element analysis vs. fluid–structure interaction , 2008, Computer methods in biomechanics and biomedical engineering.

[8]  Yiannis Ventikos,et al.  CFD and PTV steady flow investigation in an anatomically accurate abdominal aortic aneurysm. , 2009, Journal of biomechanical engineering.

[9]  Xikui Li,et al.  Numerical modeling of viscoelastic flows using equal low-order finite elements , 2010 .

[10]  L Niu,et al.  Steady flow in an aneurysm model: correlation between fluid dynamics and blood platelet deposition. , 1996, Journal of biomechanical engineering.

[11]  F. Baaijens.  Mixed finite element methods for viscoelastic flow analysis : a review , 1998 .

[12]  S. Berger,et al.  Flows in Stenotic Vessels , 2000 .

[13]  A. Leuprecht,et al.  Computer Simulation of Non-Newtonian Effects on Blood Flow in Large Arteries , 2001, Computer methods in biomechanics and biomedical engineering.

[14]  Marcelo Epstein,et al.  Boundary conditions for hyperbolic systems of partial differentials equations , 2012, Journal of advanced research.

[15]  P. Scherer,et al.  Flow in axisymmetrical glass model aneurysms. , 1973, Journal of biomechanics.

[16]  Amr Guaily,et al.  Pressure stabilized finite elements simulation for steady and unsteady Newtonian fluids , 2017 .

[17]  W. Stehbens,et al.  Flow disturbances in glass models of aneurysms at low Reynolds numbers. , 1974, Quarterly journal of experimental physiology and cognate medical sciences.

[18]  Bülent Karasözen,et al.  Finite volume simulation of viscoelastic laminar flow in a lid-driven cavity , 2009 .

[19]  Luoding Zhu,et al.  Simulation of a pulsatile non-Newtonian flow past a stenosed 2D artery with atherosclerosis , 2013, Comput. Biol. Medicine.

[20]  Max Gunzburger,et al.  Incompressible Computational Fluid Dynamics: Trends and Advances , 2009 .

[21]  Simon C. M. Yu,et al.  Steady and pulsatile flow studies in Abdominal Aortic Aneurysm models using Particle Image Velocimetry , 2000 .

[22]  T. Bodnár,et al.  Numerical Simulations of Blood Flow in a Stenosed Vessel under Different Flow Rates using a Generalized Oldroyd‐B Model , 2009 .

[23]  F N van de Vosse,et al.  The influence of the non-Newtonian properties of blood on the flow in large arteries: unsteady flow in a 90 degrees curved tube. , 1999, Journal of biomechanics.

[24]  T W Taylor,et al.  Three-dimensional simulation of blood flow in an abdominal aortic aneurysm--steady and unsteady flow cases. , 1994, Journal of biomechanical engineering.

[25]  Ender A Finol,et al.  Flow-induced Wall Shear Stress in Abdominal Aortic Aneurysms: Part I - Steady Flow Hemodynamics , 2002, Computer methods in biomechanics and biomedical engineering.

[26]  Mahmud Ashrafizaadeh,et al.  A comparison of non-Newtonian models for lattice Boltzmann blood flow simulations , 2009, Comput. Math. Appl..

[27]  van de Fn Frans Vosse,et al.  The influence of the non-Newtonian properties of blood on the flow in large arteries: unsteady flow in a 90° curved tube , 1999 .

[28]  Tayfan E. Tezduyar,et al.  Stabilized Finite Element Formulations for Incompressible Flow Computations , 1991 .