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.