Axisymmetric Cylindrical Converging Shock-Interface Interaction

A %$(r,t)$% wave diagram is built from 1D highly refined cylindrical radially symetric simulations (axisymetry is modeled using geometrical source terms on the RHS of the Euler equations). The absolute value of the density gradient (Schlieren) is displayed along radius and time, in a log scale:

A series of re-shocks, of decreasing strength, is observed. The formation of these shocks between the apex and the interface is particular to the converging geometry. The equivalent planar case gives the following wave diagram:

As shown in the following close-up of the first and second reshocks, super-imposing the Schlieren picture with the %$u-a$% set of characteristics enables us to understand the phenomenon of re-shock in the cylindrical converging geometry:

-- ManuelLombardini - Aug 2006