University of Calgary
Calgary, Alberta, Canada
In a recent article by Demiray (1996), a rigorous study is undertaken of the propagation of nonlinear waves in a prestressed elastic tube containing an inviscid fluid. Following previous work (e.g., Yomosa , 1987, Erbay et al., 1992), the existence of solitary waves is established therein by means of a reductive perturbation technique, which yields an equation of the Korteweg-deVries type for the first-order approximation. This technique is open to a number of potential causes for concern such as the possibility that the solitary wave obtained might be an artifact of the approximation procedure and that both the obtained shape of the wave and the relation between its amplitude and its speed of propagation are approximate in nature, with no clear estimate of the errors involved. Also, the extension of the perturbation technique beyond the long-wave approximation and/or for more sophisticated modeling of the fluid velocity profile seems unfeasible. The object of this study was to mitigate or remove these concerns given the importance of the results obtained for the purpose of modeling the propagation of pulses in arteries. In this study, therefore, we propose and obtain numerical solutions of the original field equations without recourse to a perturbation procedure, thereby ratifying most of Demiray's results and establishing the range of their validity, permitting the extension of the analysis beyond the long-wave approximation, and opening the door to the incorporation of a more realistic representation of the solid-fluid interaction.