  Numeric convergence studies demonstrate that the evolution of an adiabatic
clump is well-captured by roughly 100 cells per clump radius. The presence of
radiative cooling, however, imposes limits on the problem due to the removal of
thermal energy. Numerical studies which include radiative cooling typically
adopt the 100--200 cells per clump radius resolution. In this paper we present
the results of a convergence study for radiatively cooling clumps undertaken
over a broad range of resolutions, from 12 to 1,536 cells per clump radius,
employing adaptive mesh refinement (AMR) in a 2D axisymmetric geometry
("2.5D"). We also provide a fully 3D simulation, at 192 cells per clump radius,
which supports our 2.5D results. We find no appreciable self-convergence at
~100 cells per clump radius as small-scale differences owing to increasingly
resolving the "cooling length" have global effects. We therefore conclude that
self-convergence is an insufficient criterion to apply on its own when
addressing the question of sufficient resolution for radiatively cooled shocked
clump simulations. We suggest the adoption of alternate criteria to support a
statement of sufficient resolution, such as the demonstration of adequate
resolution of the cooling layers behind shocks. We discuss an associated
refinement criteria for AMR codes.
