Investigation of models that describe wave propagation in fluid-filled and gas-filled tubes with elastic walls

The paper is devoted to development of models for description of waves in tubes with elastic walls in the case when a tube is filled by liquid or gas. It is also devoted to development of numerical methods for these models. Membrane model and plate model are used for tube. Numerical methods for solving equations for cases of fluid-filled tube and gas-filled tube are given. Riemann problem is solved. Results obtained for fluid-filled tube and gas-filled tube correspond to theory of reversible shocks. Ability of overlapping of waves is analyzed. Method of correction of numerical schemes by the aid of inclusion of additional terms with higher-order derivatives is developed. Hyperbolic simplified equations and Boussinesq-type equations are derived.