Numerical simulations of the convective granular motions in the solar photosphere are presented. Realistic background physics allows a detailed comparison with observed characteristics of the solar granulation. The numerical methods are based on a bivariate Fourier representation in the horizontal plane, combined with a cubic spline representation in the vertical direction. Using a numerical grid with 16×16×16 grid points, which cover a unit cell of dimension ⋍ 3600×3600×1500 km, granular motions have been followed over several turnover times. The simulated motion shows the characteristics of granular motion. The evolution of large granules into bright rings (“Exploding granules”) is a consequence of the accumulating excess pressure at the granule center, necessary to support the horizontal velocities required by the continuity equation. The increasing pressure evenutally inhibits further upward motion at the granule center, which cools radiatively and shows up as a dark center in the expanding granule.