The development of precipitating warm clouds is affected by several effects of small-scale air turbulence including enhancement of droplet-droplet collision rate by turbulence, entrainment and mixing at the cloud edges, and coupling of mechanical and thermal energies at various scales. Large-scale computation is a viable research tool for quantifying these multiscale processes. Specifically, top-down large-eddy simulations (LES) of shallow convective clouds typically resolve scales of turbulent energy-containing eddies while the effects of turbulent cascade toward viscous dissipation are parameterized. Bottom-up hybrid direct numerical simulations (HDNS) of cloud microphysical processes resolve fully the dissipation-range flow scales but only partially the inertial subrange scales. it is desirable to systematically decrease the grid length in LES and increase the domain size in HDNS so that they can be better integrated to address the full range of scales and their coupling. In this paper, we discuss computational issues and physical modeling questions in expanding the ranges of scales realizable in LES and HDNS, and in bridging LES and HDNS. We review our on-going efforts in transforming our simulation codes towards PetaScale computing, in improving physical representations in LES and HDNS, and in developing better methods to analyze and interpret the simulation results.