# Simulations of autonomous fluid pulses between active elastic walls using the 1D-IRBFN Method

Article

Ahmed, Fatima Z., Mohammed, Mayada G., 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 (MMNP). 13 (5), pp. 1-25. https://doi.org/10.1051/mmnp/2018058
Article Title Simulations of autonomous fluid pulses between active elastic walls using the 1D-IRBFN Method 32402 Article Ahmed, Fatima Z. (Author), Mohammed, Mayada G. (Author), Strunin, Dmitry V. (Author) and Ngo-Cong, Duc (Author) Mathematical Modelling of Natural Phenomena (MMNP) 13 (5), pp. 1-25 2018058 25 2018 France 0973-5348 1760-6101 https://doi.org/10.1051/mmnp/2018058 https://www.mmnp-journal.org/articles/mmnp/abs/2018/05/mmnp180136/mmnp180136.html 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. fluid, elastic walls, auto-pulses 490303. Numerical solution of differential and integral equations 490109. Theoretical and applied mechanics Faculty of Health, Engineering and Sciences University of Thi-Qar, Iraq School of Agricultural, Computational and Environmental Sciences Computational Engineering and Science Research Centre University of Southern Queensland

https://research.usq.edu.au/item/q4zw0/simulations-of-autonomous-fluid-pulses-between-active-elastic-walls-using-the-1d-irbfn-method

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Zhu, SongPing and Strunin, Dmitry V.. 2002. "A numerical model for the confinement of oil spill with floating booms." Spill Science and Technology Bulletin. 7 (5-6), pp. 249-255. https://doi.org/10.1016/S1353-2561(02)00042-7
##### Nonlinear dynamics on centre manifolds describing turbulent floods: k-\omega model
Georgiev, Dian J., Roberts, A. J. and Strunin, Dmitry V.. 2007. "Nonlinear dynamics on centre manifolds describing turbulent floods: k-\omega model." Discrete and Continuous Dynamical Systems Series A.
##### The dynamics of the vertical structure of turbulence in flood flows
Georgiev, D. J., Roberts, A. J. and Strunin, D. V.. 2007. "The dynamics of the vertical structure of turbulence in flood flows." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 48, pp. C573-C590. https://doi.org/10.0000/anziamj.v48i0.124
##### Models encompassing hydraulic jumps in radial flows over a horizontal plate
Strunin, Dmitry and Roberts, Tony. 2001. "Models encompassing hydraulic jumps in radial flows over a horizontal plate." Kluev, Vitaly and Mastorakis, Nikos (ed.) 2nd WSEAS Multiconference on Applied and Theoretical Mathematics (WSEAS 2001). Cairns, Australia 17 - 23 Dec 2001 Greece.
##### Coupled thermomechanical waves in hyperbolic thermoelasticity
Strunin, D. V., Melnik, R. V. N. and Roberts, A. J.. 2001. "Coupled thermomechanical waves in hyperbolic thermoelasticity." Journal of Thermal Stresses. 24 (2), pp. 121-140. https://doi.org/10.1080/01495730150500433
##### Nonlinear instability in generalized nonlinear phase diffusion equation
Strunin, Dmitry V.. 2003. "Nonlinear instability in generalized nonlinear phase diffusion equation." Progress of Theoretical Physics Supplement.
##### Attractors and centre manifolds in nonlinear diffusion
Strunin, Dmitry V.. 2005. "Attractors and centre manifolds in nonlinear diffusion." 2nd International Conference on Scientific Computing and Partial Differential Equations & The First East Asian SIAM Symposium. Hong Kong, China 12 - 16 Dec 2005 Hong Kong.
##### Nonlinear analysis of rubber-based polymeric materials with thermal relaxation models
Melnik, R. V. N., Strunin, D. V. and Roberts, A. J.. 2005. "Nonlinear analysis of rubber-based polymeric materials with thermal relaxation models." Numerical Heat Transfer Part A: Applications. 47 (6), pp. 549-569. https://doi.org/10.1080/10407780590891236