Asymptotic nonlinear and dispersive pulsatile flow in elastic vessels with cylindrical symmetry

Dimitrios Mitsotakis, Denys Dutykh, Qian Li

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

The asymptotic derivation of a new family of one-dimensional, 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 non-dispersive 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.

Original languageBritish English
Pages (from-to)4022-4047
Number of pages26
JournalComputers and Mathematics with Applications
Volume75
Issue number11
DOIs
StatePublished - 1 Jun 2018

Keywords

  • Blood flow
  • Boussinesq systems
  • Elastic vessel

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