Two-dimensional numerical simulations of laminar and turbulent natural convection in a fluid with internal heat generation in a square cavity are presented. The simulations were carried out at Rayleigh numbers 10(6)-10(11) and Prandtl numbers 0.25 and 0.6. The turbulent fluid motion was captured with a large-eddy simulation (LES) model. The Rayleigh-Taylor instabilities at the upper boundary and the Kelvin-Helmholtz instabilities at the side boundaries cause first local and then global transition from laminar to turbulent motion. Lower Prandtl numbers enhance heat transfer through the bottom region, whereas higher Prandtl numbers enhance heat transfer through the upper region of the simulation domain. The simulations also reveal that the Rayleigh-Nusselt number relation is not uniformly linear in a log(10)-log(10) diagram.