A radially symmetric Gaussian profile about r=0 spreads out radially.
For comparison, the 1d equations with radial source terms are solved in subdirectory 1drad on a fine grid.
Left column: Pseudocolor plots of pressure in x-y-z.
Right column: Comparison of q(x,y=0,z=0) (blue line) and 1d solution (red line)
Several frames are shown around time t=1.3 when the ingoing shock bounces at the origin. This is not well resolved in this 3d computation.
Note that extrapolation boundary conditions work quite well as the disturbance leaves the 3d computational domain.
See also: A comparison of results using split and unsplit methods