Abstract

Diseases such as atherosclerosis, which appear due to area reduction or
recirculation of the flow into an artery, have a process which is not uniform.
Lesions appear meanly at sinus of the internal carotid artery, a region where
velocity tends to reduce and fat deposition can occur, and can originate some
kind of cerebrum problems, infart and can kill mostly adults.
Many hypothesis relate hemodynamic loads with the location of atherosclerosis
lesions. They are usually based on the influence of tension in the walls of an
artery, and its relation to the flow intensity and characteristics. In this
way, a local velocity distribution takes a very important role to analyze the
surgement and dangers of this disease.
There are non-invasive techniques based on ultrasound that help us to detect
atherosclerosis lesions in their initial stage. However, they are not perfect
and a numerical study of this complex flow can be used to better understand
this phenomenon and to find or construct better equipment for its detection.
Many characteristics, including rheological properties, distensibility,
geometry and frequency of heart pulsation are important to model the blood
flow through the arteries.
It is a not so easy task to model an artery because its geometry varies
between individuals and its walls are anisotropic and viscoelastic. However,
it is a good approximation to consider the flow to be fully developed few
diameters before the carotid bifurcation and that its geometry remains almost
the same.
This work shows some numerical simulations of the transient flow over a square
step and through the carotid artery bifurcation. The model considers the flow
for low levels of deformation rates, incompressible, bidimensional and for
rigid walls. The numerical method is based on the finite differences explicit
Runge-Kutta three-stage scheme with central spatial discretization and is
second order time-accurate. Obviously, the most executed sections of the code
are those related to computing the velocities and pressure. Care has been
exercised to ensure that the code runs as fast as possible; we have also
minimized the number of arrays used and organized the
computation to reduce data traffic to and from the memory.
Numerical tests are carried out for the flow over a square step in the duct
and the carotid region, for Reynolds numbers ranging from 100 and 500 and the
results are found to compare well with numerical/experimental data available
in the literature.