Numerical study of shock propagation and attenuation in narrow tubes including friction and heat losses

Numerical simulations of shock propagation and attenuation in narrow tubes are carried out using a one-dimensional approach. The discretization of the convective terms is based on the fifth-order weighted essentially non-oscillatory interpolation. The influence of the dissipative processes such as momentum and heat losses is investigated. Viscosity as well as heat losses are found to play a key role in the attenuation of the shock speed as well as the shock intensity in the long-time evolution, demonstrating the transition from a hyperbolic behavior towards a diffusive regime. Specifically, when only strong heat exchanges are considered, numerical tests, corroborated by a simple asymptotic analysis, showed a transition from a hyperbolic adiabatic regime to an isothermal regime. Furthermore, the influence of the scaling parameter ReD/4Ls, through the variation of the tube diameter, D, the viscous length scale, Ls, and the Reynolds number on the shock propagation behavior is examined.