Natural convection in a two-dimensional cell filled with a porous medium was investigated using two direct numerical simulation (DNS) methods. The cell was heated at the lower wall and cooled at the upper wall. The buoyancy force was modeled by the Boussinesq approximation. The Rayleigh numbers ranged from 50 to 20, 000. The DNS results from both DNS methods indicate the linear relationship between Nu and Ra. However, the numerical methods have some effects on the small flow structures. The fish bone structures are clearly identified by the space-time plots of the temperature in a slice close to the boundary layer. Four motion patterns showing mega-plumes and proto-plumes can be observed in the fish bone structures. The characteristic length, velocity, and temperature scales in the boundary layer were studied based on the DNS results.