Approximating 3D Models of Planetary Evolution in 2D: A Comparison of Different Geometries

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.