Cumulative behavior of convergent shocks with dissipation effects

The constraints placed upon the cumulation of converging shock waves in a self-similar solution (including the state of reflection of the shock wave) by the effects of energy dissipation are investigated. The set of one-dimensional gas dynamic equations describing gas behavior near the center or axis of symmetry of a spherical or cylindrical configuration, respectively, is analyzed, including effects of gas viscosity and thermal conductivity. It is shown that dissipation constrains all the hydrodynamic and thermodynamic flow parameters, and a general expression is derived for the maximal cumulation parameters (normalized velocity, pressure and temperature), which is determined by the characteristics of both the self-similar solution and dissipative effects. The case of a fully ionized ideal plasma is considered in detail, and it is pointed out that deviations from one-dimensional (symmetric) flow are insignificant to the results under sufficiently symmetric initial and boundary conditions.