Density as a function of radius for the standard and well-balanced schemes with N = 256 (left panel) and N = 512 (right panel). In both panels the (black) solid, (blue) dashed and the (red) dash-dotted line represent the reference solution (the well-balanced with N = 8192 in both panels), the solutions computed with standard and the well-balanced scheme, respectively. For both resolution, the well-balanced solutions are indistinguishable from the reference.