Stability of an imploding spherical shock wave in avan der Waals gas.

摘要

A nonlinear stability analysis is carried out for an imploding strong spherical shock wave in an imperfect gas, modeled by a van der Waals equation of state. The shock wave is initiated by a perturbed spherical 'piston' and its evolution is examined by solving the conservation laws of gas dynamics in a radially contracting frame of reference. The equations are solved numerically by the Essentially Non-Oscillatory (ENO) method of Shu and Osher. Two types of behavior are found, depending on the parameter b˜ = brho0, where b is the van der Waals excluded volume and rho0 is the initial uncompressed density. For small b˜, initially smooth shock surfaces develop polygonal-shaped cross sections for a 'big' initial perturbation of any type. This is consistent with experimental results for cylindrical shocks as well as with other investigations of cylindrical and spherical shocks in an ideal gas (b = 0). For larger values of b˜ , the shock front evolves smoothly, with no evidence of instability of any type.