Open AccessEquations that Describe Waves in Tubes with Elastic Walls and Analysis of Numerical Methods for Reversible and Weakly Dissipative Systems
Author(s) -
И. Б. Бахолдин
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1392/1/012002
Subject(s) - dissipative system , compressibility , numerical analysis , dissipative operator , classical mechanics , mechanics , space (punctuation) , physics , mathematics , mathematical analysis , thermodynamics , computer science , operating system
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.