Investigation of wave propagation in tubes with elastic walls and analysis of numerical methods

The paper is devoted to development of models for description of waves in tubes with elastic walls. It is also devoted to development and analysis of numerical methods for models with dispersion and analysis of solutions with reversible shock structures. Membrane model and plate model are used for tube. Numerical methods for solving equations are developed. The ability of stabilization of numerical method by the aid of inclusion of additional term with higher-order derivatives is analyzed. Riemann problem is solved. Results obtained for fluid-filled tube correspond to theory of reversible shocks. Simplified equations for description of long waves, equations for waves of nonlinear small amplitude for tube filled by fluid and equations for nonlinear acoustic waves for tube filled by gas are derived. Two-step numerical schemes are analyzed. Main features for calculation of classic and generalized solutions are presented.