Methods of Investigation of Equations that Describe Waves in Tubes with Elastic Walls and Application of the Theory of Reversible and Weak Dissipative Shocks
Keldysh Institute of Applied Mathematics, Miusskaya sq. 4, 125047 Moscow, Russia
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Published online: 14 February 2018
Various models of a tube with elastic walls are investigated: with controlled pressure, filled with incompressible fluid, filled with compressible gas. The non-linear theory of hyperelasticity is applied. The walls of a tube are described with complete membrane model. It is proposed to use linear model of plate in order to take the bending resistance of walls into account. The walls of the tube were treated previously as inviscid and incompressible. Compressibility of material of walls and viscosity of material, either gas or liquid are considered. Equations are solved numerically. Three-layer time and space centered reversible numerical scheme and similar two-layer space reversible numerical scheme with approximation of time derivatives by Runge-Kutta method are used. A method of correction of numerical schemes by inclusion of terms with highorder derivatives is developed. Simplified hyperbolic equations are derived.
© The Authors, published by EDP Sciences, 2018
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