The flow pattern and the temperature field in empty and partitioned, two-dimensional (2D) rectangular enclosures were studied numerically at Rayleigh numbers 10(10)-10(12), using an algebraic model for turbulent heat transport <(theta u(i))over bar>. The geometries considered, with partial, downward-extending and full adiabatic and conductive vertical partitions, imitate neighbouring rooms in real buildings with a doorway in between. Two closure levels were applied in parallel : three- and four-equation models, k-epsilon-<(theta(2))over bar> and k-epsilon-<(theta(2))over bar>-epsilon(o), both incorporating the low-Re-number modifications, which allow integration up to the wall and prediction of turbulence transition. The computations confirmed earlier experimental findings that in this range of Ra numbers the flow becomes turbulent, but the turbulence remains confined to only some regions of the enclosure. Noticeable improvements in capturing details of turbulence field, particularly at transitional Rayleigh numbers, are achieved with the algebraic model for turbulent heat transport <(theta u(i))over bar> with both the three- and four-equation models, as compared with eddy diffusivity hypotheses. The paper presents some results for the mean how and turbulence field, as well as for Nusselt number, in several cases of undivided and partitioned enclosures at transitional and higher Ra numbers and for several combinations of boundary conditions, including heating from sides and from below.