We present recent results from numerical simulations of a magnetized, compressible fluid confined to a spherical segment, spanning the solar convection zone, chromosphere, and corona. In this model, the bottom half of the simulation domain is a convectively unstable, stratified MHD fluid, driven by an imposed heat flux at the bottom. The upper part of the layer corresponds to a simplified chromosphere and corona, which are cooled and heated (respectively) to match a solar-like temperature profile. We are thus able to self-consistently model the dynamics associated with magnetic structures in the solar atmosphere as they evolve in response to sub-photospheric, turbulent convection. We present simulations of arcade-like reconnection in the presence of supergranular-scale flows and discuss possible observational consequences.