Ahmed, Fatima Z. and Mohammed, Mayada G. and Strunin, Dmitry V. and Ngo-Cong, Duc (2018) Simulations of autonomous fluid pulses between active elastic walls using the 1D-IRBFN Method. Mathematical Modelling of Natural Phenomena, 13 (5 - Article 2018058). ISSN 0973-5348
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Abstract
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.
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| Item Type: | Article (Commonwealth Reporting Category C) |
|---|---|
| Refereed: | Yes |
| Item Status: | Live Archive |
| Additional Information: | Published online: 3 December 2018. Published version deposited in accordance with the copyright policy of the publisher. |
| Faculty / Department / School: | Current - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences |
| Date Deposited: | 09 Jan 2019 05:37 |
| Last Modified: | 14 Jan 2019 22:54 |
| Uncontrolled Keywords: | fluid, elastic walls, auto-pulses |
| Fields of Research : | 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations 01 Mathematical Sciences > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics |
| Socio-Economic Objective: | E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences |
| Identification Number or DOI: | 10.1051/mmnp/2018058 |
| URI: | http://eprints.usq.edu.au/id/eprint/35323 |
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