Regardless of the steady increase of computing power during the last
decades, 3D numerical models continue to be used in specific setups to
investigate the thermochemical convection of planetary interiors, while
the use of 2D geometries is still favored in most exploratory studies
involving a broad range of parameters. The 2D cylindrical and the more
recent 2D spherical annulus geometries are predominantly used in this
context, but the extent to how well they reproduce the 3D spherical
shell in comparison to each other, and in which setup, has not yet been
extensively studied. Here we performed a thorough and systematic study
in order to assess which 2D geometry reproduces best the 3D one. In a
first set of models, we investigated the effects of the geometry on
thermal convection in steady-state setups while varying a broad range of
parameters. Additional thermal evolution models of three terrestrial
bodies, respectively Mercury, the Moon, and Mars, which have different
interior structures, were used to compare the 2D and 3D geometries. Our
study shows that the spherical annulus geometry improves results
compared to cylindrical geometry when reproducing 3D models. Our results
can be used to determine for which setup acceptable differences are
expected when using a 2D instead of a 3D geometry.