Equations that Describe Waves in Tubes with Elastic Walls and Analysis of Numerical Methods for Reversible and Weakly Dissipative Systems

Abstract

Abstract Models of tube with elastic walls are presented: 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. Equations are solved numerically. General approach for calculation of non-dissipative and weakly dissipative systems is given. Three-layer time and space centered reversible numerical scheme and similar two-layer space reversible numerical schemes with approximation of time derivatives by high-order Runge-Kutta methods are analysed. A method of correction of numerical schemes by inclusion of terms with high-order derivatives is developed. Additional terms with high-order derivatives my be included also in order to calculate non-dissipative and dissipative shocks at the same time.