Development of a numerical model for blood rheology subjected to pulsating Poiseuille flow in a cylindrical vessel
Date
2019
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
University of Delaware
Abstract
The overall goal of this project is to develop a robust and accurate numerical
method for studying the flow of blood in arterial, pulsatile flow. The most important
contribution of this work is the development of an efficient code, that is able
to solve complex blood flow constitutive models. This can be a great aid in defining
new rheological models more suited for pulsating Poiseuille flow in the future,
coming one step closer to modelling the flow conditions in the human body. The
model is meant to use in combination with a microfluidic device that acts under
the same flow conditions. It can help to understand the underlying physics and to
make realistic predictions for other flow parameters. Experiments with microfluidic
device are needed to come up with better conditioned models and better adapted
parameters for pulsating Poiseuille flow. This opens the path to a new method of researching
blood rheology in a way that more closely resembles the flow conditions
in the human body. ☐ The code is designed to take advantage of the mathematical form of the flow
conditions and the cylindrical geometry. The result is a collocation method, where
orthogonal Fourier and Chebyshev polynomials are fitted to the solutions. This
makes the solution semi-analytic and introduces only an interpolation error on top
of the machine error. The model was successfully validated for the calculation of
Newtonian fluids, elastic solid, Maxwellian fluids and power law fluids, whilst also
showing the capability to solve more complicated models including a structural parameter.
The algorithm is able to reach much higher accuracies than finite difference
methods whilst solving for much less unknowns, making it also faster.