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.
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