Self-Convergence of Radiatively Cooling Clumps

TL;DR

This study investigates the resolution requirements for accurately simulating radiatively cooling clumps, revealing that traditional convergence criteria are insufficient and proposing alternative methods for ensuring adequate resolution.

Contribution

The paper provides a comprehensive convergence analysis for radiatively cooling clumps using AMR, highlighting the limitations of standard convergence criteria and suggesting new resolution assessment methods.

Findings

No self-convergence at ~100 cells per clump radius due to cooling length effects.

Higher resolutions reveal small-scale differences affecting global evolution.

Proposes alternative criteria based on resolving cooling layers behind shocks.

Abstract

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.