Moist atmospheric convection couples turbulent transport, phase change, and buoyancy in ways that remain a leading source of uncertainty in weather and climate prediction. This thesis develops a consistent framework for shallow moist convection that bridges classical Rayleigh–Bénard convection and atmospheric dynamics with phase change. The model is built on a simplified Baer–Nunziato four-equation diffuse-interface formulation and implemented in the parallel solver FluTAS. Rather than resolving a sharp liquid–gas interface, a mixture description is adopted, in which the two phases share a single velocity, pressure, and temperature field, and the condensate is represented through a transported volume fraction, while chemical non-equilibrium is retained to capture condensation and evaporation.