Regardless of the steady increase of computing power during the last decades, numerical models in a 3D spherical shell are only used in specific setups to investigate the thermochemical convection in planetary interiors, while 2D geometries are typically 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 results in comparison to each other and in which setup has not yet been extensively investigated. Here we performed a thorough and systematic study in order to assess which 2D geometry reproduces best the 3D spherical shell. 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, namely Mercury, the Moon, and Mars, which have different interior structures, were used to compare the 2D and 3D geometries. Our investigations show that the 2D spherical annulus geometry provides results closer to models in a 3D spherical shell compared to the 2D cylindrical geometry. Our study indicates where acceptable differences can be expected when using a 2D instead of a 3D geometry and where to be cautious when interpreting the results.

N2 - Plain Language Summary: In geodynamic modeling, numerical models are used in order to investigate how the interior of a terrestrial planet evolves from the earliest stage, after the planetary formation, up to present day. Often, the mathematical equations that are used to model the physical processes in the interior of rocky planets are discretized and solved using geometric meshes. The most commonly applied geometries are the 3D spherical shell, the 2D cylinder, and the 2D spherical annulus. While being the most accurate and realistic, the 3D geometry is expensive in terms of computing power and time of execution. On the other hand, 2D geometries provide a reduced accuracy but are computationally faster. Here we perform an extensive comparison between 2D and 3D geometries in scenarios of increasing complexity. The 2D spherical annulus geometry shows much closer results to the 3D spherical shell when compared to the 2D cylinder and should be given preference in 2D modeling studies. N2 - Key Points:Interior dynamics models using the 2D spherical annulus geometry match the results of a 3D spherical shell better than the 2D cylinder

The difference between 2D and 3D geometries decreases when models are heated from below by the core and from within by radioactive elements

The 2D spherical annulus shows negligible differences to 3D for the thermal evolution of Mercury and the Moon, and acceptable values for Mars