Nonlinear waves in a viscous fluid contained in a viscoelastic tube
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CitationDemiray, H. (2001). Nonlinear waves in a viscous fluid contained in a viscoelastic tube. Zeitschrift Für Angewandte Mathematik Und Physik, 52(6), 899-912. doi:10.1007/PL00001586
In the present work the propagation of weakly nonlinear waves in a prestressed viscoelastic thin tube filled with a viscous fluid is studied. Using the reductive perturbation technique in analyzing the nonlinear equations of a viscoelastic tube and the approximate equations of a viscous fluid, the propagation of weakly nonlinear waves in the longwave approximation is studied. Depending on the order of viscous effects, various evolution equations like, Burgers', Korteweg-de Vries, Korteweg-de Vries-Burgers' equations and their perturbed forms are obtained. Ravelling wave type of solutions to some of these evolution equations are sought. Finally, utilizing the finite difference scheme, a numerical solution is presentede for the perturbed KdVB equation and the result is discussed.