  We consider the solutions of the Guderley problem, consisting of a converging
and diverging hydrodynamic shock wave in an ideal gas with a power law initial
density profile. The self-similar solutions, and specifically the reflected
shock coefficient, which determines the path of the reflected shock, are
studied in detail, for cylindrical and spherical symmetries and for a wide
range of values of the adiabatic index and the spatial density exponent.
Finally, we perform a comprehensive comparison between the analytic solutions
and Lagrangian hydrodynamic simulations, by setting proper initial and boundary
conditions. A very good agreement between the analytical solutions and the
numerical simulations is obtained. This demonstrates the usefulness of the
analytic solutions as a code verification test problem.
