Asymptotic nonlinear and dispersive pulsatile flow in elastic vessels with cylindrical symmetry
Abstract
The asymptotic derivation of a new family of onedimensional, weakly nonlinear and weakly dispersive equations that model the flow of an ideal fluid in an elastic vessel is presented. Dissipative effects due to the viscous nature of the fluid are also taken into account. The new models validate by asymptotic reasoning other nondispersive systems of equations that are commonly used, and improve other nonlinear and dispersive mathematical models derived to describe the blood flow in elastic vessels. The new systems are studied analytically in terms of their basic characteristic properties such as the linear dispersion characteristics, symmetries, conservation laws and solitary waves. Unidirectional model equations are also derived and analysed in the case of vessels of constant radius. The capacity of the models to be used in practical problems is being demonstrated by employing a particular system with favourable properties to study the blood flow in a large artery. Two different cases are considered: A vessel with constant radius and a tapered vessel. Significant changes in the flow can be observed in the case of the tapered vessel.
 Publication:

arXiv eprints
 Pub Date:
 April 2018
 arXiv:
 arXiv:1804.01300
 Bibcode:
 2018arXiv180401300M
 Keywords:

 Physics  Fluid Dynamics;
 Physics  Biological Physics;
 Physics  Classical Physics;
 Physics  Computational Physics;
 Physics  Medical Physics
 EPrint:
 46 pages, 13 figures, 2 tables, 64 references. Other author's papers can be downloaded at http://www.denysdutykh.com/