It is well-recognized that triggering of convective cells through cold pools is key to the organization of convection. Yet, numerous studies have found that both the characterization and parameterization of these effects in numerical models is cumbersome - in part due to the lack of numerical convergence, $\Delta x\rightarrow 0$, achieved in typical cloud-resolving simulators.
Through a comprehensive numerical convergence study we systematically approach the $\Delta x \rightarrow 0$ limit in a set of idealized large-eddy simulations capturing key cold pool processes: free propagation, frontal collision and incident merging of gust fronts.
We characterize at which $\Delta x$ convergence is achieved for physically relevant quantities, namely accumulated upwards water mass fluxes, leading front vortical rates, tropospheric moistening and group velocity.
The understanding gained from this analysis lays the groundwork to develop robust subgrid models for CP dynamics able to sustain their growth and combat artificial numerical dissipation and dispersion.