Shock-compressible-vortex interactions: Computing approximate post-shock fields

An approximate, semi-analytical method to compute the net effect of the passage of a planar shock through a steady compressible vortex is developed. To compute the approximate post-shock fields, the steady pre-shock vortex is decomposed into a sum of frozen sinusoidal modes, the shock wave is treated as an instantaneous event (an ansatz most suited to weak shocks), and the interaction of each frozen mode with the shock wave analytically computed. The post-shock fields are then obtained by numerically resuming the shocked Fourier modes. This theory is applied to the interaction of a shock with the compressible Stuart vortex array, Meiron et al.1. The evolution of these approximate post-shock fields are compared with numerical solutions to actual initial-value problem, where the passage of the shock is computed numerically. These simulations are done using AMROC, Deiterding2–4, in conjunction with Hill & Pullin’s5 tuned-centered-difference-WENO method.