NUMERICAL ANALYSIS OF BLOOD VESSEL CONSTRICTION DUE TO ATHEROSCLEROSIS DISEASE USING FINITE VOLUME METHOD

Abstract

Atherosclerosis is a leading cause of coronary heart disease. This study analyses how elliptically shaped stenoses alter blood-flow velocity in coronary arteries. The governing equations are discretised with the finite-volume method, coupling pressure and velocity through the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm and accelerating convergence with the Successive Over-Relaxation (SOR) technique. A weighted Gauss–Seidel iteration whose over-relaxation factor ( in this work) damps low-frequency error modes, cutting the number of iterations needed for residuals to fall below 10⁻⁴ by roughly 40 % compared with the standard Gauss–Seidel scheme. Simulations of 30 %, 50 %, and 70 % constrictions were carried out in MATLAB R2013a and ANSYS Fluent. Quantitative and qualitative cross-validation of the two software packages confirmed consistent velocity and pressure fields, though minor discrepancies arose from differing numerical schemes and model assumptions, underscoring the need for experimental verification. The highest centre-line velocity occurred at 70 % stenosis—0.72075 m/s in MATLAB versus 0.90 m/s in Fluent—while the lowest was recorded at 30 %. Velocity–pressure profiles showed that increasing inlet velocity or degree of narrowing elevates velocity but decreases pressure, with the largest drop (11492.4 Pa in MATLAB; 11747.32 Pa in Fluent) again at 70% stenosis. Study limitations include modelling blood as a Newtonian fluid and idealising arterial geometry; future work should incorporate non-Newtonian rheology and patient-specific shapes to enhance physiological accuracy.