Math. Model. Nat. Phenom.
Volume 13, Number 5, 2018
Mathematical Modelling of Physiological Flows
|Number of page(s)||25|
|Published online||03 December 2018|
Simulations of autonomous fluid pulses between active elastic walls using the 1D-IRBFN method
Faculty of Health, Engineering and Sciences, University of Southern Queensland,
QLD 4350, Australia.
2 Department of Mathematics, University of Thi-Qar, Nasiriyah, Iraq.
3 Department of Mathematics, University of Kirkuk, Kirkuk, Iraq.
* Corresponding author: firstname.lastname@example.org
Accepted: 28 September 2018
We present numerical solutions of the semi-empirical model of self-propagating fluid pulses (auto-pulses) through the channel simulating an artificial artery. The key mechanism behind the model is the active motion of the walls in line with the earlier model of Roberts. Our model is autonomous, nonlinear and is based on the partial differential equation describing the displacement of the wall in time and along the channel. A theoretical plane configuration is adopted for the walls at rest. For solving the equation we used the One-dimensional Integrated Radial Basis Function Network (1D-IRBFN) method. We demonstrated that different initial conditions always lead to the settling of pulse trains where an individual pulse has certain speed and amplitude controlled by the governing equation. A variety of pulse solutions is obtained using homogeneous and periodic boundary conditions. The dynamics of one, two, and three pulses per period are explored. The fluid mass flux due to the pulses is calculated.
Mathematics Subject Classification: 74F10 / 76M25 / 76D08
Key words: Fluid / elastic walls / auto-pulses
© EDP Sciences, 2018
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