Application Of The Navier-stokes Equations In The Localisation Of Atherosclerosis

Abstract

Localization of atherosclerosis plaque has been a great problem for many centuries. Many researchers have done a lot of studies in blood flow with the motivations of understanding the localization of atherosclerosis in arteries. This project presents a mathematical modeling of the arterial blood flow which is derived from the Navier-Stokes equation and some assumptions. A system of non-linear partial differential equations for blood flow is obtained. Finite element method (FEM) is then adopted to solve the equations numerically. Apart from FEM, we will use the Galerkin stabilization method to solve the problem of oscillations of solutions at high Reynolds numbers. We will also use the method of artificial incompressibility and the Newton-Raphson method, to deal with the problems of incompressibility and the problem of non-linear terms respectively. The results obtained will help in explaining the localization of the atherosclerosis disease.