A Stabilized Finite Element Formulation of Non-Newtonian Fluid Model of Blood Flow in A Bifurcated Channel with Overlapping Stenosis

Abstract

A stabilized form of finite element formulation known as the Galerkin least-squares (GLS) method is implemented here for solving the two-dimensional incompressible non-Newtonian fluid model of blood flow in a diseased artery. The modelling for this type of flow is based on the conservation of mass and momentum equations, coupled with the generalised Newtonian liquid (GNL) constitutive equation characterized by the generalised power law (GPL) model. The flow of blood in this present study are assumed as steady, laminar and fully developed. The finite element algorithms considered herein are first solved for the Newtonian fluid in a straight artery with a bell shaped stenosis for validation purposes. As the efficiency and validity of the proposed algorithms are obtained through comparison with the findings from existing literature and COMSOL Multiphysics 5.2 software. Then, the algorithms are being implemented to the generalised power law fluid model of blood flow in a bifurcated artery with overlapping stenosis located at the parent's arterial lumen. The numerical results illustrate the arising of distinct sizes of vortex shedding downstream of the stenotic region for each generalised power law index.

Study of Bio-Fluid Dynamics in Carotid Artery System Using Numerical Methods

“…The low-intensity helicity begins at the flow divider region of bifurcation zone and later develops fully into the sinus region in the ICA. The observations are similar for all the carotid cases qualitatively, however, there exists few flow reversal changes during later part of cardiac cycle [7,19,26]. Regions having lesser helical intensity seemingly start from the sinus and intensified in the lower ICA.…”

“…Haemodynamics study pertaining to large artery will be widely beneficial in the diagnosing and treating vascular diseases. Clinically analysing the haemodynamics will not benefit the exhaustive study with radiology imaging tools such as Digital angiography, Computer Tomography, Magnetic Resonance and Ultrasound duplex scanning [7]. The required haemodynamics data through numerical simulations results in better flow visualization.…”

Variation of Shear Stresses and Flow Dynamics in Stented Patient Specific Carotid Bifurcation Model using Numerical Investigation

“…Computational studies of patient-specific carotid artery bifurcations necessitate the presence of geometric data that may be used to create the fluid and solid computational domains. This is normally obtained by reconstructing the data obtained by Computed Tomography, Magnetic Resonance Imaging or Magnetic Resonance Angiography techniques [1,9,17,[20][21][22][23] and in some cases Doppler Ultrasound too [32,40,41]. The prevalent used of the former group of techniques is due to their superior resolution which then allows for fairly accurate three-dimensional (3D) geometry reconstruction of the required vessel wall (subject to adequate contrast) and the lumen.…”

Applications of Linear Programming on Diet Problem for Subways’ Sets Menu in Malaysia

“…The finite element method is widely used in mathematical modelling to approximate and solve complex physical phenomena by dividing them into smaller, manageable elements. This method had been used by researchers like Mohamad et al, [3], Mohd et al, [4], and Law Ruen et al, [5] in numerous studies to look into a variety of topics, including structural analysis, fluid dynamics, heat transfer, and electromagnetic simulations. On the other hand, the Lagrange method is usually employed in mathematical modelling to optimize systems by formulating and solving constrained optimization problems.…”